Pre-training techniques based on functional connectivity (FC) have demonstrated great potential in brain disease diagnosis. However, previous studies may disrupt the functional information of training data when designing pre-training tasks, and may be limited by biases stemming from single-task learning or insufficient coordination among multiple task components, thereby hindering the acquisition of robust and generalizable feature representations. To address these limitations, we proposed a novel pre-training framework, named Multi-view Contrastive and Masked ROI Learning (CoMa), to learn general representations from healthy datasets through improved learning tasks, with flexible domain-adaptive fine-tuning for downstream tasks. Results showed that the proposed CoMa achieved superior performance across a broad spectrum of diagnostic tasks, significantly outperforming the alternative methods, emphasizing its generalization and effectiveness. Furthermore, the model can further enhance the diagnostic accuracy through task-specific fine-tuning within particular disease domains, indicating its potential for adaptive disease diagnosis. Additionally, we also identified interpretable diagnostic biomarkers for childhood developmental disorders, psychiatric disorders, and neurodegenerative disorders. Overall, the proposed CoMa is instrumental toward the application of fundamental model for disease diagnosis and improves our understanding of underlying mechanisms of common brain disorders.

Multimodal fusion provides cross-modality information to understand the human brain from different perspectives that may be missed in single modality analysis. Supervised fusion focuses on extracting multimodal patterns related to specific clinical measures by further incorporating a prior interested reference. However, existing supervised fusion methods cannot extract component that have weak correlations with the reference, which may be lost during the optimization process. Here, we propose a reference-guided parallel independent component analysis (RG-PICA) aiming at identifying multimodal covarying features related to interested reference through global optimization. The intra-modality independence, the inter-modality correlation, and the correlation between modalities and the reference are maximized globally. Simulations show that RG-PICA can accurately extract multimodal features correlated with the weak related reference while keeping cross-modality linkage comparing with seven fusion methods. In real data application, RG-PICA reveals co-varying patterns in schizophrenia (SZ) that links with cognition and correlates between modalities. These results demonstrate RG-PICA can jointly optimize for target components that correlate with the reference while keeping cross-modality linkage. This approach can improve the meaningful detection of reliable reference-linked multimodal brain patterns for brain disorders.

As a highly interconnected complex network system, the brain exhibits changes in interactions due to common brain disorders. Studying changes in brain network interactions can help us quantitatively analyze functional network patterns and changes in these patterns that are linked to brain disorders. However, relationships between brain regions estimated by most current approaches use a single connectivity that does not fully reflect multiple interactions. Here, we propose a novel functional connectivity (FC) construction method, which can estimate both cooperative and competitive (C-C) relationships between the same regions of interest (ROIs) through improved Ising model. We redefine the Ising dynamic equation to represent pairwise interactions from single to C-C relationships. Results show that the estimated C-C connectivities are normally distributed, with intra-subjects’ (n=970) similarity being consistently and significantly higher than inter-subjects’ similarity across datasets. C-C FCs between occipital, parietal, temporal cortex and the limbic system of schizophrenia (SZ, n=178) are more competitive, while healthy control (HC, n=219) tends to be more cooperative. Group differences in C-C patterns between SZ and HC show significant differences in frontal, parietal and occipital regions. The proposed C-C approach provide new insights into the brain dysfunction in SZ, which can also be applied to investigate other brain disorders.

Multimodal fusion provides multiple benefits over single modality analysis by leveraging both shared and complementary information from different modalities. Notably, supervised fusion enjoys extensive interest for capturing multimodal co-varying patterns associated with clinical measures. A key challenge of brain data analysis is how to handle confounds, which, if unaddressed, can lead to an unrealistic description of the relationship between the brain and clinical measures. Current approaches often rely on linear regression to remove covariate effects prior to fusion, which may lead to information loss, rather than pursue the more global strategy of optimizing both fusion and covariates removal simultaneously. Thus, we propose "CR-mCCAR" to jointly optimize for confounds within a guided fusion model, capturing co-varying multimodal patterns associated with a specific clinical domain while also discounting covariate effects. Simulations show that CR-mCCAR separate the reference and covariate factors accurately. Functional and structural neuroimaging data fusion reveals co-varying patterns in attention deficit/hyperactivity disorder (ADHD, striato-thalamo-cortical and salience areas) and in autism spectrum disorder (ASD, salience and fronto-temporal areas) that link with core symptoms but uncorrelate with age and motion. These results replicate in an independent cohort. Downstream classification accuracy between ADHD/ASD and controls is markedly higher for CR-mCCAR compared to fusion and regression separately. CR-mCCAR can be extended to include multiple targets and multiple covariates. Overall, results demonstrate CR-mCCAR can jointly optimize for target components that correlate with the reference(s) while removing nuisance covariates. This approach can improve the meaningful detection of reliable phenotype-linked multimodal biomarkers for brain disorders.

Functional magnetic resonance imaging (fMRI), as a non-invasive method to reveal brain function alterations, frequently yields time series with unequal lengths in real-world scenarios, which may arise from factors such as motion artifacts, participant state, and differing scan protocols. This variability conflicts with the traditional methods relying on isometric inputs, which poses a significant challenge for the downstream applications such as brain age prediction. To address this challenge, we introduced Gaussian Process Regression (GPR) to normalize the length of time series and proposed split-channel residual convolution (SC) and self-attention mechanisms (SA) to perform brain age estimation, called GPR-SCSANet. Results showed that the proposed framework, GPR-SCSANet, is able to fully utilize the inherent information and learn richer feature representations from unequal-length fMRI time courses, which significantly improved the prediction accuracy across 3 brain atlases and 5 prediction models. The results demonstrated the effectiveness and robustness of the proposed GPR-SCSANet, showcasing the potential for broader applications in brain age prediction task.

To capture different aspects of a complex system, the modeling approach should be able to take these effectively into consideration. Two aspects of the human brain we are quite interested in are its interconnected nature and its dynamism. One modeling approach that can capture these two aspects is based on networks that change with time and go beyond pairwise interactions. Partly because of the size of these temporal high-order networks, analyzing and visualizing them is quite a challenge. In this work, we propose a pipeline based on canonical polyadic (CP) decomposition to analyze high-order networks that are resolved in both time and frequency estimated from resting-state functional magnetic resonance imaging (fMRI) data. We show that we can combine different subjects' information into a common frame of reference for comparison. We also show that different factors provide different patterns that are easy to visualize and interpret. To the best of our knowledge, this is the first work that has proposed a pipeline for analyzing different subjects' brain networks while also incorporating temporal and spectral information about high-order interactions.

Joint blind source separation (JBSS) is a powerful framework for extracting latent sources from multiple datasets while keeping their coherence across multiple linked datasets. Algorithms for JBSS, while offering the capability of improved estimation performance, often incur high computational complexity and hence are not scalable to studies with hundreds or thousands of datasets. In this paper, we propose a simple yet efficient method for source separation that exploits both the correlation among sources within each dataset and across the datasets. The proposed method, named reference-guided component analysis (RGCA), uses source templates as references to (i) guide the separation of sources on each dataset and (ii) establish source dependence and automatically align them across the datasets. In addition, we promote independence among latent sources within each dataset by adding orthogonal constraints on the demixing vectors. The resulting optimization admits an analytic solution that enables extremely fast implementation of RGCA. Our numerical results demonstrate that RGCA obtains competitive performance while having a runtime far superior to other JBSS methods. The proposed method provides a robust and scalable solution to multi-subject functional magnetic resonance imaging (fMRI) studies, enabling joint analysis of thousands of subjects within a few minutes.

Subgroup identification is a fundamental step in precision medicine. Recent research applying data-driven methods such as independent component/vector analysis to multi-subject functional magnetic resonance imaging (fMRI) data has effectively revealed meaningful subgroups. These methods typically focus on single-dimensional information, such as individual functional networks or assuming uniform subgroup structures across networks. Given the complex nature of psychiatric disorders, considering the relationships among subjects across different functional networks can offer valuable insights into diagnostic heterogeneity. We introduce a novel subgroup identification method that leverages multiplex community detection to identify subgroups from multi-subject resting-state fMRI data. The proposed method models subject correlations across functional networks as a multiplex network and identifies common communities across multiple networks and unique communities specific to each functional network. Results from applying the proposed method to 464 psychotic patients show that the identified subgroups exhibit significant group differences on multiple meaningful functional networks as well as the clinical scores, which demonstrate the effectiveness of our method on identifying meaningful subgroups.

Discovering components that are shared in multiple datasets, next to dataset-specific features, has great potential for studying the relationships between different subjects or tasks in functional Magnetic Resonance Imaging (fMRI) data. Coupled matrix and tensor factorization approaches have been useful for flexible data fusion, or decomposition to extract features that can be used in multiple ways. However, existing methods do not directly recover shared and dataset-specific components, which requires post-processing steps involving additional hyperparameter selection. In this paper, we propose a tensor-based framework for multi-task fMRI data fusion, using a partially constrained canonical polyadic (CP) decomposition model. Differently from previous approaches, the proposed method directly recovers shared and dataset-specific components, leading to results that are directly interpretable. A strategy to select a highly reproducible solution to the decomposition is also proposed. We evaluate the proposed methodology on real fMRI data of three tasks, and show that the proposed method finds meaningful components that clearly identify group differences between patients with schizophrenia and healthy controls.

This paper deals with dynamic Blind Source Extraction (BSE) from where the mixing parameters characterizing the position of a source of interest (SOI) are allowed to vary over time. We present a new source extraction model called CvxCSV which is a parameter-reduced modification of the recent Constant Separation Vector (CSV) mixing model. In CvxCSV, the mixing vector evolves as a convex combination of its initial and final values. We derive a lower bound on the achievable mean interference-to-signal ratio (ISR) based on the Cramér-Rao theory. The bound reveals advantageous properties of CvxCSV compared with CSV and compared with a sequential BSE based on independent component extraction (ICE). In particular, the achievable ISR by CvxCSV is lower than that by the previous approaches. Moreover, the model requires significantly weaker conditions for identifiability, even when the SOI is Gaussian.

Independent vector analysis (IVA) generalizes independent component analysis (ICA) to multiple datasets, and when used with a multivariate Gaussian model (IVA-G), provides a powerful tool for joint analysis of multiple datasets in an array of applications. While IVA-G enjoys uniqueness guarantees, the current solution to the problem exhibits significant variability across runs necessitating the use of a scheme for selecting the most consistent one, which is costly. In this paper, we present a penalized maximum-likelihood framework for the problem, which enables us to derive a non-convex cost function that depends on the precision matrices of the source component vectors, the main mechanism by which IVA-G leverages correlation across the datasets. By adding a quadratic regularization, a block-coordinate proximal algorithm is shown to offer a suitable solution to this minimization problem. The proposed method also provides convergence guarantees that are lacking in other state-of-the-art approaches to the problem. This also allows us to obtain overall slightly better performance, and in particular, we show that our method yields better estimation in average than the current IVA-G algorithm for various source numbers, datasets, and degrees of correlation across the data.

Joint blind source separation (JBSS) is a powerful tool for analyzing multiple linked datasets, distinguished by the key ability to exploit cross-dataset dependencies. Despite this ability generally improving overall estimation performance, joint decompositions also incur considerable computational costs, which can lead to intractable problems with hundreds or thousands of datasets. In this paper, we introduce an efficient method for large-scale JBSS by multilinear regression. We consider a model where out of all datasets, only a selected subset are first decomposed to provide regressors that sufficiently estimate sources across all datasets. These regressors define a per-source cost function that naturally extends independent vector analysis (IVA) with a multivariate Gaussian source prior (IVA-G), a powerful formulation for exploiting cross-dataset dependencies. Using simulated and real fMRI data, we demonstrate significant advantages of this method compared with other JBSS methods.

Independent component analysis (ICA) of multi-subject functional magnetic resonance imaging (fMRI) data has proven useful in providing a fully multivariate summary that can be used for multiple purposes. ICA can identify patterns that can discriminate between healthy controls (HC) and patients with various mental disorders such as schizophrenia (Sz). Temporal functional network connectivity (tFNC) obtained from ICA can effectively explain the interactions between brain networks. On the other hand, dictionary learning (DL) enables the discovery of hidden information in data using learnable basis signals through the use of sparsity. In this paper, we present a new method that leverages ICA and DL for the identification of directly interpretable patterns to discriminate between the HC and Sz groups. We use multi-subject resting-state fMRI data from 358 subjects and form subject-specific tFNC feature vectors from ICA results. Then, we learn sparse representations of the tFNCs and introduce a new set of sparse features as well as new interpretable patterns from the learned atoms. Our experimental results show that the new representation not only leads to effective classification between HC and Sz groups using sparse features, but can also identify new interpretable patterns from the learned atoms that can help understand the complexities of mental diseases such as schizophrenia.

In this paper, we develop an expectation-maximization (EM)-like scheme, called ${\mathcal{K}}$-BM, for iterative numerical computation of the minimum ${\mathcal{K}}$-divergence estimator (M${\mathcal{K}}$DE). This estimator utilizes Parzen’s non-parameteric ${\mathcal{K}}$ernel density estimate to down weight low density areas attributed to outliers. Similarly to the standard EM algorithm, the ${\mathcal{K}}$-BM involves successive Maximizations of lower Bounds on the objective function of the M${\mathcal{K}}$DE. Differently from EM, these bounds do not rely on conditional expectations only. The proposed ${\mathcal{K}}$-BM algorithm is applied to robust parameter estimation of a finite-order multivariate Gaussian mixture model (GMM). Simulation studies illustrate the performance advantage of the ${\mathcal{K}}$-BM as compared to other state-of-the-art robust GMM estimators.

Identification of subgroups of subjects homogeneous functional networks is a key step for precision medicine. Independent vector analysis (IVA) is shown to be effective for this task, however, it has a substantial computing cost. We propose a constrained independent component analysis algorithm based on minimizing the entropy bound (c-EBM) to overcome the computational complexity limitation of IVA. A set of spatial maps used as constraints provides a connection across the datasets, provides alignment across subject-wise ICA analyses and serves as a foundation for subgroup identification. The approach makes use of the available prior knowledge while allowing flexible density modeling without an orthogonality requirement for the demixing matrix. Synthetic data and large scale multi-subject resting state fMRI data have both been used to evaluate the performance of the new algorithm, c-EBM. The findings demonstrate that c-EBM is adaptable in terms of various settings for the constraint parameter on the synthetic data. With multi-subject resting state fMRI data, c-EBM can effectively identify subgroups and discover meaningful brain networks that show significant group differences between subgroups.

Data fusion—the joint analysis of multiple datasets—through coupled factorizations has the promise to enable enhanced knowledge discovery, and hence is an active area. Various formulations of coupled matrix factorizations have been proposed, each with its own modeling assumptions. In this paper, we study two such methods, namely Independent Vector Analysis (IVA), i.e., extension of Independent Component Analysis (ICA) to multiple datasets, and PARAFAC2, a tensor factorization approach. We demonstrate the modeling assumptions of IVA and PARAFAC2 using simulations, revealing that both methods can accurately capture the latent components, albeit with certain differences in capturing the corresponding subject scores. By making use of a rich multi-task functional Magnetic Resonance Imaging (fMRI) dataset, we show how the two methods can be used for achieving two important goals at once, namely capturing group differences between patients with schizophrenia and healthy controls with interpretable components, as well as understanding the relationship across multiple tasks. This is achieved through the definition of source component vectors across datasets.

Identification of homogeneous subgroups of subjects plays a key role in the study of precision medicine. While there are a number of approaches based on the clustering of low-level features such as behavioral variables, work that makes use of fully multivariate nature of medical imaging data is very limited. Given that the individual variability in brain functional networks obtained from functional magnetic resonance imaging (fMRI) data is noted as being both significant and consistent like fingerprints, its use provides a particularly appealing approach to this challenging problem. We present a completely data-driven approach, subgroup identification using independent vector analysis (SI-IVA), which leverages the desirable properties of IVA to uncover the relationship across subjects along with the discovery of subgroup structures revealed by Gershgorin disc theorem. We show that SI-IVA outperforms an eigenanalysis-based approach by simulations. We then apply the method to real fMRI data obtained from patients of during resting state to identify group differences in multiple relevant brain regions including primary somatosensory and motor cortex, which demonstrates that SI-IVA provides interpretable and meaningful results.

Due to the wide use of multi-sensor technology, analysis of multiple sets of data is at the heart of many challenging engineering problems. Independent vector analysis (IVA), a recent generalization of independent component analysis (ICA), enables the joint analysis of datasets and extraction of latent sources through the use of a simple yet effective generative model. However, the success of IVA is tied to proper estimation of the probability density function (PDF) of the multivariate latent sources; information that is generally unknown. In this work, we propose a new flexible and efficient multivariate PDF estimation technique based on the maximum entropy principle and apply this technique to the development of an effective IVA algorithm that successfully matches multivariate latent sources from a wide range of distributions. We verify the effectiveness of the new estimation technique and further demonstrate the superior performance of the new IVA algorithm numerically using simulated data.

Given the prevalence of independent component analysis (ICA) for signal processing, many methods for improving the convergence properties of ICA have been introduced. The most utilized methods operate by iterative rotations over pre-whitened data, whereby limiting the space of estimated demixing matrices to those that are orthogonal. However, a proof of the identifiability conditions for orthogonal ICA methods has not yet been presented in the literature. In this paper, we derive the identifiability conditions, starting from the orthogonal ICA maximum likelihood cost function. We then review efficient optimization approaches for orthogonal ICA defined on the Lie group of orthogonal matrices. Afterwards, we derive a new efficient algorithm for orthogonal ICA, by defining a mapping onto a space of constrained matrices which we define as hyper skew-symmetric. Finally, we experimentally demonstrate the advantages of the new algorithm over the pre-existing Lie group methods.

Unsupervised latent variable models-blind source separation (BSS) especially-enjoy a strong reputation for their interpretability. But they seldom combine the rich diversity of information available in multiple datasets, even though multidatasets yield insightful joint solutions otherwise unavailable in isolation. We present a direct, principled approach to multidataset combination that takes advantage of multidimensional subspace structures. In turn, we extend BSS models to capture the underlying modes of shared and unique variability across and within datasets. Our approach leverages joint information from heterogeneous datasets in a flexible and synergistic fashion. We call this method multidataset independent subspace analysis (MISA). Methodological innovations exploiting the Kotz distribution for subspace modeling, in conjunction with a novel combinatorial optimization for evasion of local minima, enable MISA to produce a robust generalization of independent component analysis (ICA), independent vector analysis (IVA), and independent subspace analysis (ISA) in a single unified model. We highlight the utility of MISA for multimodal information fusion, including sample-poor regimes ( N = 600 ) and low signal-to-noise ratio, promoting novel applications in both unimodal and multimodal brain imaging data.

Characterizing time-evolving networks is a challenging task, but it is crucial for understanding the dynamic behavior of complex systems such as the brain. For instance, how spatial networks of functional connectivity in the brain evolve during a task is not well-understood. A traditional approach in neuroimaging data analysis is to make simplifications through the assumption of static spatial networks. In this paper, without assuming static networks in time and/or space, we arrange the temporal data as a higher-order tensor and use a tensor fac-torization model called PARAFAC2 to capture underlying patterns (spatial networks) in time-evolving data and their evolution. Numerical experiments on simulated data demonstrate that PARAFAC2 can successfully reveal the underlying networks and their dynamics. We also show the promising performance of the model in terms of tracing the evolution of task-related functional connectivity in the brain through the analysis of functional magnetic resonance imaging data.

Dynamic functional connectivity analysis is an effective way to capture the networks that are functionally associated and continuously changing over the scanning period. However, these methods mostly analyze the dynamic associations across the activation patterns of the spatial networks while assuming that the spatial networks are stationary. Hence, a model that allows for the variability in both domains and reduces the assumptions imposed on the data provides an effective way for extracting spatiotemporal networks. Independent vector analysis (IVA) is a joint blind source separation technique that allows for estimation of spatial and temporal features while successfully preserving variability. However, its performance is affected for higher number of datasets. Hence, we develop an effective two-stage method to extract time-varying spatial and temporal features using IVA, mitigating the problems with higher number of datasets while preserving the variability across subjects and time. The first stage is used to extract reference signals using group-independent component analysis (GICA) that are used in a parameter-tuned constrained IVA framework to estimate time-varying representations of these signals by preserving the variability through tuning the constraint parameter. This approach effectively captures variability across time from a large-scale resting-state fMRI data acquired from healthy controls and patients with schizophrenia and identifies more functionally relevant connections that are significantly different among healthy controls and patients with schizophrenia, compared with the widely used GICA method alone.

Methods based on independent component analysis (ICA) and canonical correlation analysis (CCA) as well as their various extensions have become popular for the fusion of multimodal data as they minimize assumptions about the relationships among multiple datasets. Two important extensions that are widely used, joint ICA (jICA) and parallel ICA (pICA), make a number of simplifying assumptions that might limit their usefulness such as identical mixing matrices for jICA, and the requirement for the same number of components for jICA and pICA. In this paper, we propose a new, flexible hybrid method for fusion based on ICA and CCA, called consecutive independence and correlation transform (C-ICT), which relaxes the main limitations of jICA and pICA. We demonstrate performance advantages of C-ICT both through simulations and application to real medical data collected from schizophrenia patients and healthy controls performing an auditory oddball task (AOD).

Recently, much attention has been devoted to examining time-varying changes in functional connectivity to understand the network structure in the human brain. Most studies, however, analyze the time-varying functional connectivity but ignore the time-varying spatial information. In this paper, we propose a method based on independent vector analysis (IVA) to study dynamic functional network connectivity (dFNC) as well as dynamic spatial functional network connectivity (dsFNC) in fMRI data. Though IVA allows one to effectively capture both, its performance degrades with the increase in the number of datasets. Hence, we propose an effective scheme to bypass this limitation followed by graph theoretical analysis to study both inter-network dynamics and intra-network stationarity. We observe higher dFNC fluctuations for patients with schizophrenia in the default-mode (DM)-salience network and cerebellum with associated connections. dsFNC analysis indicates higher inter-network fluctuation in patients while DM, anterior DM and frontal networks demonstrate significant intra-network fluctuation in controls.

Independent component analysis (ICA) has found wide application in a variety of areas, and analysis of functional magnetic resonance imaging (fMRI) data has been a particularly fruitful one. Maximum likelihood provides a natural formuiation for ICA and allows one to take into account multiple statistical properties of the data-forms of diversity. While use of multiple types of diversity allows for additional flexibility, it comes at a cost, leading to high variability in the solution space. In this paper, using simulated as well as fMRI-like data, we provide insight into the trade-offs between estimation accuracy and algorithmic consistency with or without deviations from the assumed model and assumptions such as the statistical independence. Additionally, we propose a new metric, cross inter-symbol interference, to quantify the consistency of an algorithm across different runs, and demonstrate its desirable performance for selecting consistent run compared to other metrics used for the task.

Dynamic functional connectivity has become a prominent approach for tracking the changes of macroscale statistical dependencies between regions in the brain. Effective parametrization of these statistical dependencies, referred to as brain states, is however still an open problem. We investigate different emission models in the hidden Markov model framework, each representing certain assumptions about dynamic changes in the brain. We evaluate each model by how well they can discriminate between schizophrenic patients and healthy controls based on a group independent component analysis of resting-state functional magnetic resonance imaging data. We find that simple emission models without full covariance matrices can achieve similar classification results as the models with more parameters. This raises questions about the predictability of dynamic functional connectivity in comparison to simpler dynamic features when used as biomarkers. However, we must stress that there is a distinction between characterization and classification, which has to be investigated further.

Graph-theoretical methods are being increasingly used in areas of interest within the IEEE and beyond. Graphs are mathematical abstractions that can be used to represent networks of various types: physical (e.g., the internet or electrical networks), biological (e.g., brain networks), or social (e.g., online social networks). Furthermore, graphs can provide tools for flexible representation of data sets in which data points have irregular positions with respect to each other. Common examples of this include data sets acquired by a sensor network, where uniform sensor placement may not be possible, or machine learning data sets, where training samples are not uniformly distributed in feature space. In some instances, a graph representation arises as a natural way to describe the problem, while in other areas, e.g., image processing, they are being used to develop powerful, content-dependent alternatives to conventional processing tools.

Trends, they are not only for the fashion industry after all. Within the engineering and computer science research communities as well, we periodically observe the phenomenon, see how certain methods suddenly start receiving particular attention, and sometimes, even though they emerge as an attractive solution for a given set of problems, they tend to become a hammer looking for new nails. At fi rst, using a new method on old problems is the natural and reasonable way to proceed. There have been remarkable successes achieved through the adoption of a tool from another fi eld or a new way of looking at old problems that brings new insights and solutions. There have been a number of such trends throughout the years in every field. In signal processing, a few notable ones include maximum entropy, wavelets, kernel methods, and the multiple up and down cycles of neural nets. A current tool that is on the rise is sparsity, more specifically solutions that promote sparsity, including coding, compressive sensing, sparse learning/estimation, sparse factorizations, and of course deep nets, which, without careful use of sparsity, would be useless. We will use sparsity as the major example in this Point of View article because it is current and illustrates the points we are making very well. While we agree that sparsity is very useful and has led to some excellent results in the past decade or so, it also allows us to address the dangers and pitfalls of blindly following trends in research. These problems are reflected in our publications and help define the overall research climate. In the following, we provide an overview on use of sparsity and then discuss a couple of specific problems.

Human brain connectivity is complex. Graph theory based analysis has become a powerful and popular approach for analyzing brain imaging data, largely because of its potential to quantitatively illuminate the networks, the static architecture in structure and function, the organization of dynamic behavior over time, and disease related brain changes. The first step in creating brain graphs is to define the nodes and edges connecting them. We review a number of approaches for defining brain nodes including fixed versus data-driven nodes. Expanding the narrow view of most studies which focus on static and/or single modality brain connectivity, we also survey advanced approaches and their performances in building dynamic and multi-modal brain graphs. We show results from both simulated and real data from healthy controls and patients with mental illnesse. We outline the advantages and challenges of these various techniques. By summarizing and inspecting recent studies which analyzed brain imaging data based on graph theory, this article provides a guide for developing new powerful tools to explore complex brain networks.

Due to the potential for object occlusion in crowded areas, the use of multiple cameras for video surveillance has prevailed over the use of a single camera. This has motivated the development of a number of techniques to analyze such multi-camera video sequences. However, most of these techniques require a camera calibration step, which is cumbersome and must be done for every new configuration. Additionally, these techniques fail to exploit the complementary information across these multiple datasets. We propose a data-driven solution to the problem by making use of the inherent similarity of temporal signatures of objects across video sequences. We introduce an effective solution for the detection of abandoned objects using this inherent diversity based on the transposed independent vector analysis (tIVA) model. By taking advantage of the similarity across multiple cameras, the new technique does not require any calibration and thus can be readily applied to any camera configuration. We demonstrate the superior performance of our technique over the single camera-based method using the PETS 2006 dataset.

The existence of complementary information across multiple sensors has driven the proliferation of multivariate datasets. Exploitation of this common information, while minimizing the assumptions imposed on the data has led to the popularity of data-driven methods. Independent vector analysis (IVA), in particular, provides a flexible and effective approach for the fusion of multivariate data. In many practical applications, important prior information about the data exists and incorporating this information into the IVA model is expected to yield improved separation performance. In this paper, we propose a general formulation for non-orthogonal constrained IVA (C-IVA) framework that can incorporate prior information about either the sources or the mixing coefficients into the IVA cost function. A powerful decoupling method is the major enabling factor in this task. We demonstrate the improved performance of C-IVA over the unconstrained IVA model using both simulated as well as real medical imaging data.

Independent component analysis (ICA) is a powerful method for blind source separation based on the assumption that sources are statistically independent. Though ICA has proven useful and has been employed in many applications, complete statistical independence can be too restrictive an assumption in practice. Additionally, important prior information about the data, such as sparsity, is usually available. Sparsity is a natural property of the data, a form of diversity, which, if incorporated into the ICA model, can relax the independence assumption, resulting in an improvement in the overall separation performance. In this work, we propose a new variant of ICA by entropy bound minimization (ICA-EBM)-a flexible, yet parameter-free algorithm-through the direct exploitation of sparsity. Using this new SparseICA-EBM algorithm, we study the synergy of independence and sparsity through simulations on synthetic as well as functional magnetic resonance imaging (fMRI)-like data.

Functional magnetic resonance imaging (fMRI) has provided a window into the brain with wide adoption in research and even clinical settings. Data-driven methods such as those based on latent variable models and matrix/tensor factorizations are being increasingly used for fMRI data analysis. There is increasing availability of large-scale multi-subject repositories involving 1,000+ individuals. Studies with large numbers of data sets promise effective comparisons across different conditions, groups, and time points, further increasing the utility of fMRI in human brain research. In this context, there is a pressing need for innovative ideas to develop flexible analysis methods that can scale to handle large-volume fMRI data, process the data in a distributed and policy-compliant manner, and capture diverse global and local patterns leveraging the big pool of fMRI data. This paper is a survey of some of the recent research in this direction.

Exploitation of complementary information is the principal reason for collecting data from multiple neurological sensors. Since little is known about the latent processes underlying neural function, it is important to minimize the assumptions placed on the data when performing a joint analysis. This motivates the use of data-driven fusion methods, such as independent vector analysis (IVA), for the analysis of neurological data. For neural datasets, the complementary information exploited by fusion methods may be in the form of similar spatial activation across datasets, the spatial IVA (sIVA) model, or similar subject relations across datasets, the transposed IVA (tIVA) model. Despite the potential power of these two models, no study has investigated how the differences in the modeling assumptions of sIVA and tIVA inform the fusion of real neuro-imaging data. In this paper, we utilize a unique set of multitask functional magnetic resonance imaging data from 271 subjects to directly compare the sIVA and tIVA models and visualize their differences using a novel technique, global difference maps. Through this application, we note important similarities between the results from the two methods that increase our confidence in their overall performance, though differences in modeling assumptions result in certain differences in the decompositions.

The use of in vivo calcium imaging has granted researchers the unprecedented ability to study large populations of neurons in real time, enabling direct observation of how the brain processes information. Such data offers great potential, however for current analysis techniques, successful extraction of the true neuronal signals is intimately tied to the proper selection of multiple user-defined parameters, which must be tuned for each video sequence. To overcome such issues, we propose a novel parameter-free independent component analysis (ICA)-based method, ICA with signal reconstruction and ordering (ICA+SRO), to automatically extract neuronal signals from calcium imaging sequences. The power of ICA+SRO is demonstrated on a real calcium imaging sequence. We compare the results of ICA+SRO with those from the popular principal component analysis-ICA based technique and show significant improvement. The results demonstrate the simplicity of a parameter-free method and its power in extracting neuronal signals from calcium imaging sequences.

Neuroimaging modalities such as functional magnetic resonance imaging (fMRI) and electroencephalography (EEG) provide information about neurological functions in complementary spatiotemporal resolutions; therefore, fusion of these modalities is expected to provide better understanding of brain activity. In this paper, we jointly analyze fMRI and EEG data collected during an auditory oddball task with the goal of capturing brain activity patterns that differ between patients with schizophrenia and healthy controls. Rather than selecting a single electrode or matricizing the third-order tensor that can be naturally used to represent multi-channel EEG signals, we preserve the multi-way structure of EEG data and use a coupled matrix and tensor factorization (CMTF) model to jointly analyze fMRI and EEG signals. Our analysis reveals that (i) joint analysis of EEG and fMRI using a CMTF model can capture meaningful temporal and spatial signatures of patterns that behave differently in patients and controls, and (ii) these differences and the interpretability of the associated components increase by including multiple electrodes from frontal, motor and parietal areas, but not necessarily by including all electrodes in the analysis.

The extraction of information from multiple sets of data is a problem inherent to many disciplines. This is possible by either analyzing the data sets jointly as in data fusion or separately and then combining as in data integration. However, selecting the optimal method to combine and analyze multiset data is an ever-present challenge. The primary reason for this is the difficulty in determining the optimal contribution of each data set to an analysis as well as the amount of potentially exploitable complementary information among data sets. In this paper, we propose a novel classification rate-based technique to unambiguously quantify the contribution of each data set to a fusion result as well as facilitate direct comparisons of fusion methods on real data and apply a new method, independent vector analysis (IVA), to multiset fusion. This classification rate-based technique is used on functional magnetic resonance imaging data collected from 121 patients with schizophrenia and 150 healthy controls during the performance of three tasks. Through this application, we find that though optimal performance is achieved by exploiting all tasks, each task does not contribute equally to the result and this framework enables effective quantification of the value added by each task. Our results also demonstrate that data fusion methods are more powerful than data integration methods, with the former achieving a classification rate of 73.5 % and the latter achieving one of 70.9 %, a difference which we show is significant when all three tasks are analyzed together. Finally, we show that IVA, due to its flexibility, has equivalent or superior performance compared with the popular data fusion method, joint independent component analysis.

Automated detection of abandoned object (AO) is an important application in video surveillance for security purposes. Because of its importance, a number of techniques have been proposed to automatically detect abandoned objects in the past years. However, these techniques require prior knowledge on the properties of the object such as its shape and color, in order to classify foreground objects as abandoned object. In contrast, independent component analysis (ICA) does not require such prior knowledge. However, it can only model one dataset at a time, thus limiting its usage to monochrome frames. In this paper, we propose to use independent vector analysis (IVA), a recent extension of ICA to multivariate data that takes the dependence across multiple datasets into account while retaining the independence within each dataset. We present a new framework for AO detection using IVA and show that it provides successful performance in complicated scenarios, such as for videos with crowd, illumination change, and occlusion.

Conventional feature extraction methods cannot fully exploit both the spectral and spatial information of hyperspectral imagery. In this paper, we propose an ensemble method of subspace independent component analysis (ICA) and edge-preserving filtering (EPF) for the classification of hyper-spectral data to achieve this task. First, several subsets are randomly selected from the original feature space. Second, ICA is used to extract spectral independent components followed by a recent and effective EPF method, rolling guidance filter (RGF), to produce spatial features. The spatial features are treated as the input of a random forest (RF) classifier. Finally, the classification results from each subset are integrated together to produce the final map. Experimental results on real hyperspectral data demonstrate the effectiveness of the proposed method. A sensitivity analysis of this new classifier is also performed.

Spectral analysis of brain activation in different regions, either in the form of network time-courses or regions of interest (ROI) time-series, has been a topic of interest in recent studies. Such studies hypothesize that observed brain fluctuations are due to different underlying sources of neurophysiological activation. Among these studies, brain fluctuations during the resting-state, as an unconstrained condition, have been a subject of interest. Some clinical studies have employed spectral analysis to locate differences between diagnostic groups such as schizophrenia and bipolar disorder. Other studies have argued that resting-state brain fluctuations are in fact dynamic, and that activation and connectivity of brain regions develops and evolves spontaneously. In this study, we combine both approaches and focus on capturing dynamics of the spectral properties of network time-courses estimated from independent components analysis (ICA) and categorizing spontaneous frequency profiles of network time-courses into three major profiles, which we call "frequency modes". We show that brain networks have distinct time-varying frequency domain characteristics, differing from one another in their occupancy rates of the frequency modes. Additionally, we identify some networks in which the occurrence rates of the different modes are significantly different based on the gender of the subjects.

With the increasing availability of various sensor technologies, we now have access to large amounts of multiblock (also called multiset, multirelational, or multiview) data that need to be jointly analyzed to explore their latent connections. Various component analysis methods have played an increasingly important role for the analysis of such coupled data. In this article, we first provide a brief review of existing matrix-based (two-way) component analysis methods for the joint analysis of such data with a focus on biomedical applications. Then, we discuss their important extensions and generalization to multiblock multiway (tensor) data. We show how constrained multiblock tensor decomposition methods are able to extract similar or statistically dependent common features that are shared by all blocks, by incorporating the multiway nature of data. Special emphasis is given to the flexible common and individual feature analysis of multiblock data with the aim to simultaneously extract common and individual latent components with desired properties and types of diversity. Illustrative examples are given to demonstrate their effectiveness for biomedical data analysis.

To obtain accurate classification results of hyperspectral images, both spectral and spatial information should be fully exploited in the classification process. In this paper, we propose a novel method using independent component analysis (ICA) and edge-preserving filtering (EPF) via an ensemble strategy for the classification of hyperspectral data. First, several subsets are randomly selected from the original feature space. Second, ICA is used to extract spectrally independent components followed by an effective EPF method, to produce spatial features. Two strategies (i.e., parallel and concatenated) are presented to include the spatial features in the analysis. The spectral-spatial features are then classified with a random forest or a rotation forest classifier. Experimental results on two real hyperspectral data sets demonstrate the effectiveness of the proposed methods. A sensitivity analysis of the new classifiers is also performed.

The estimation of a probability density function is one of the most fundamental problems in statistics. The goal is achieving a desirable balance between flexibility while maintaining as simple a form as possible to allow for generalization, and efficient implementation. In this paper, we use the maximum entropy principle to achieve this goal and present a density estimator that is based on two types of approximation. We employ both global and local measuring functions, where Gaussian kernels are used as local measuring functions. The number of the Gaussian kernels is estimated by the minimum description length criterion, and the parameters are estimated by expectation maximization and a new probability difference measure. Experimental results show the flexibility and desirable performance of this new method.

The articles in this special issue focus on multimodal data fusion. These papers provide a review of current approaches and results on multimodal data fusion from different disciplines, and by including the required background in each domain, aims to provide a common forum for the exchange of ideas in this very active field of research.

The joint independent component analysis (jICA) and the transposed independent vector analysis (tIVA) models are two effective solutions based on blind source separation (BSS) that enable fusion of data from multiple modalities in a symmetric and fully multivariate manner. The previous paper in this special issue discusses the properties and the main issues in the implementation of these two models. In this accompanying paper, we consider the application of these two models to fusion of multimodal medical imaging data-functional magnetic resonance imaging (fMRI), structural MRI (sMRI), and electroencephalography (EEG) data collected from a group of healthy controls and patients with schizophrenia performing an auditory oddball task. We show how both models can be used to identify a set of components that report on differences between the two groups, jointly, for all the modalities used in the study. We discuss the importance of algorithm and order selection as well as tradeoffs involved in the selection of one model over another. We note that for the selected data set, especially given the limited number of subjects available for the study, jICA provides a more desirable solution, however the use of an ICA algorithm that uses flexible density matching provides advantages over the most widely used algorithm, Infomax, for the problem.

Fusion of information from multiple sets of data in order to extract a set of features that are most useful and relevant for the given task is inherent to many problems we deal with today. Since, usually, very little is known about the actual interaction among the datasets, it is highly desirable to minimize the underlying assumptions. This has been the main reason for the growing importance of data-driven methods, and in particular of independent component analysis (ICA) as it provides useful decompositions with a simple generative model and using only the assumption of statistical independence. A recent extension of ICA, independent vector analysis (IVA) generalizes ICA to multiple datasets by exploiting the statistical dependence across the datasets, and hence, as we discuss in this paper, provides an attractive solution to fusion of data from multiple datasets along with ICA. In this paper, we focus on two multivariate solutions for multi-modal data fusion that let multiple modalities fully interact for the estimation of underlying features that jointly report on all modalities. One solution is the Joint ICA model that has found wide application in medical imaging, and the second one is the the Transposed IVA model introduced here as a generalization of an approach based on multi-set canonical correlation analysis. In the discussion, we emphasize the role of diversity in the decompositions achieved by these two models, present their properties and implementation details to enable the user make informed decisions on the selection of a model along with its associated parameters. Discussions are supported by simulation results to help highlight the main issues in the implementation of these methods.

In various disciplines, information about the same phenomenon can be acquired from different types of detectors, at different conditions, in multiple experiments or subjects, among others. We use the term “modality” for each such acquisition framework. Due to the rich characteristics of natural phenomena, it is rare that a single modality provides complete knowledge of the phenomenon of interest. The increasing availability of several modalities reporting on the same system introduces new degrees of freedom, which raise questions beyond those related to exploiting each modality separately. As we argue, many of these questions, or “challenges,” are common to multiple domains. This paper deals with two key issues: “why we need data fusion” and “how we perform it.” The first issue is motivated by numerous examples in science and technology, followed by a mathematical framework that showcases some of the benefits that data fusion provides. In order to address the second issue, “diversity” is introduced as a key concept, and a number of data-driven solutions based on matrix and tensor decompositions are discussed, emphasizing how they account for diversity across the data sets. The aim of this paper is to provide the reader, regardless of his or her community of origin, with a taste of the vastness of the field, the prospects, and the opportunities that it holds.

Multivariate generalized Gaussian distribution (MGGD) has been an attractive solution to many signal processing problems due to its simple yet flexible parametric form, which requires the estimation of only a few parameters, i.e., the scatter matrix and the shape parameter. Existing fixed-point (FP) algorithms provide an easy to implement method for estimating the scatter matrix, but are known to fail, giving highly inaccurate results, when the value of the shape parameter increases. Since many applications require flexible estimation of the shape parameter, we propose a new FP algorithm, Riemannian averaged FP (RA-FP), which can effectively estimate the scatter matrix for any value of the shape parameter. We provide the mathematical justification of the convergence of the RA-FP algorithm based on the Riemannian geometry of the space of symmetric positive definite matrices. We also show using numerical simulations that the RA-FP algorithm is invariant to the initialization of the scatter matrix and provides significantly improved performance over existing FP and method-of-moments (MoM) algorithms for the estimation of the scatter matrix.

We consider the problem of removing gradient artifact from electroencephalogram (EEG) signal, registered during a functional magnetic resonance imaging (fMRI) acquisition, by calculating and utilizing the statistical properties of the artifacts. We propose a new approach to EEG data organization for extracting artifactual components using independent vector analysis. This new approach estimates the gradient artifact signal as a single component thus alleviating the need of using advanced order selection algorithm before back reconstruction of EEG data. Experimental results are compared with average artifact subtraction method on real EEG data collected concurrently with fMRI data.

Independent component analysis (ICA) has proven quite useful for the analysis of functional magnetic resonance imaging (fMRI) data. However, stability of ICA decompositions is an issue in ICA of fMRI analysis primarily due to the noisy nature of fMRI data and the iterative nature of algorithms. In this work, we present an approach that utilizes an objective criterion and that is particularly suitable for image analysis to select the best of multiple ICA runs to use for further analysis and inference. In addition, a growing number of studies are focusing on the decomposition of single subject data and/or using high ICA model order, which both require an effective way to align components obtained from different ICA runs. In this paper, while presenting a method that provides superior performance in selecting the best run and interpreting the statistical reliability of ICA estimates, we also address the component sorting issue. Both simulated and real fMRI results show that our method selects more useful ICA runs than those selected by the widely used ICASSO software and that it is a more objective and better motivated approach to evaluate results and hence a promising tool for ICA analysis of fMRI data.

Estimating likelihood or entropy rate is one of the key issues in many signal processing problems. Mutual information rate, which leads to the minimization of entropy rate, provides a natural cost for achieving blind source separation (BSS). In many complex-valued BSS applications, the latent sources are non-Gaussian, noncircular, and possess sample dependence. Consequently, an effective estimator of entropy rate that jointly considers all three properities of the sources is required. In this paper, we propose such an entropy rate estimator that assumes the sources are generated by invertible filters. With this new entropy rate estimator, we propose a complex entropy rate bound minimization algorithm. Simulation results show that the new method exploits all three properties effectively.

Independent component analysis (ICA) has been effectively used for the analysis of functional magnetic resonance imaging (fMRI) data, and recently for the analysis of fMRI data in its native complex-valued form. When performing complex ICA of fMRI analysis, it is desirable to take all three types of diversity - statistical property - that are present in the complex fMRI data into account: non-Gaussianity, sample dependence and noncircularity. In this paper, we study the performance of complex ICA by entropy rate bound minimization (CERBM) algorithm for fMRI analysis that takes all these three types of diversity into account. We perform a thorough comparison of its performance with that of complex Infomax (CInfomax) and complex ICA by entropy bound minimization (CEBM), two other important choices. While evaluating the performance of ICA algorithms for fMRI analysis, there are a number of challenges, including the lack of ground truth of fMRI data and inconsistent estimates due to the iterative nature of ICA algorithms. In this work, we also propose a statistical framework that utilizes an objective criterion to evaluate consistency of ICA algorithms. Using this framework, we show that CERBM leads to significant improvement in the estimations of components of interest in terms of providing lower mutual information rate, higher active scores and more numbers of activated voxels than those of CInfomax and CEBM, and the corresponding time courses present best task-relatedness with the paradigm.

When characterizing the density of a vector process, it is desirable to consider the most general case, hence, account for higher-order statistics, sample dependence, and dependence across entries of the vector process. Entropy rate provides a powerful framework for exploiting all three properties. However, its estimation is a difficult problem in general since it is defined based on the joint distribution of the whole vector process. In this paper, we discuss the vector autoregressive (AR) signal model, and propose an entropy rate estimator based on this model. We use a suite of maximum entropy distributions to form a flexible model with a reasonable model complexity. The new entropy rate estimator is shown to exploit all three statistical properties effectively, and to provide desirable performance in analysis of functional magnetic resonance imaging (fMRI) data.

Despite its multivariate nature, independent component analysis (ICA) is generally limited to univariate latents in the sense that each latent component is a scalar process. Independent subspace analysis (ISA), or multidimensional ICA (MICA), is a generalization of ICA which identifies latent independent vector components instead. While ISA/MICA considers multidimensional latent components within a single dataset, our work specifically considers the case of multiple datasets. Independent vector analysis (IVA) is a related technique that also considers multiple datasets explicitly but with a fixed and constrained model. Here, we first show that 1) ISA/MICA naturally extends to the case of multiple datasets (which we call MISA), and that 2) IVA is a special case of this extension. Then we develop an algorithm for MISA and demonstrate its performance on both IVA- and MISA-type problems. The benefit of these extensions is that the vector sources (or subspaces) capture higher order statistical dependence across datasets while retaining independence between subspaces. This is a promising model that can explore complex latent relations across multiple datasets and help identify novel biological traits for intricate mental illnesses such as schizophrenia.

The recent extensions of independent component analysis (ICA) to exploit source dependence across multiple datasets, termed independent vector analysis (IVA), have thus far only considered two multivariate source distribution models: the Gaussian and a second-order uncorrelated Laplacian distribution. In this paper, we introduce the use of the Kotz distribution family as a more flexible source distribution model which exploits both second and higher-order statistics. The Cramér-Rao lower bound (CRLB) for IVA performance prediction is shown to be analogous to the bound for blind source separation (BSS). Lastly, we provide an analytic expression for the CRLB when the sources follow the multivariate power exponential (MPE) subclass of distributions within the Kotz family.

Co-training is a practical and powerful semi-supervised learning method. It yields high classification accuracy with a training data set containing only a small set of labeled data. Successful performance in co-training requires two important conditions on the features: diversity and sufficiency. In this paper, we propose a novel mutual information (MI) based approach inspired by the idea of dependent component analysis (DCA) to achieve feature splits that are maximally independent between-subsets (diversity) or within-subsets (sufficiency). We evaluate the relationship between the classification performance and the relative importance of the two conditions. Experimental results on actual tire data indicate that compared to diversity, sufficiency has a more significant impact on their classification accuracy. Further results show that co-training with feature splits obtained by the MI-based approach yields higher accuracy than supervised classification and significantly higher when using a small set of labeled training data.

Since in many blind source separation applications, latent sources are both non-Gaussian and have sample dependence, it is desirable to exploit both non-Gaussianity and sample dependency. In this paper, we use the Markov model to construct a general framework for the analysis and derivation of algorithms that take both properties into account. We also present two algorithms using two effective source priors. The first one is a multivariate generalized Gaussian distribution and the second is an autoregressive model driven by a generalized Gaussian distributed process. We derive the Cramér-Rao lower bound and demonstrate that the performance of the algorithms approach the lower bound especially when the underlying model matches the parametric model. We also demonstrate that a flexible semi-parametric approach exhibits very desirable performance.

When applied to functional magnetic resonance imaging (fMRI) data, independent vector analysis (IVA) provides superior performance in capturing subject variability within one group, as compared to the widely used group independent component analysis (ICA) approach. However, the effectiveness of IVA algorithms in preserving variability between different groups of subjects has not been studied yet, although it is of great interest in most fMRI studies, especially for identifying biomarkers for diagnosis of mental disorders. In this paper, we introduce a methodology that uses graph-theoretical analysis and statistical analysis for assessing the ability of IVA algorithms to capture group variability. We generate multi-subject fMRI-like datasets with increasing spatial variability for a selected component between two groups and compare a robust IVA algorithm to group ICA approach. Our experimental results show that IVA can successfully preserve group variability, indicating its potential in extracting biomarkers across groups of subjects in fMRI analysis.

We present a new supervised tensor regression method based on multi-way array decompositions and kernel machines. The main issue in the development of a kernel-based framework for tensorial data is that the kernel functions have to be defined on tensor-valued input, which here is defined based on multi-mode product kernels and probabilistic generative models. This strategy enables taking into account the underlying multilinear structure during the learning process. Based on the defined kernels for tensorial data, we develop a kernel-based tensor partial least squares approach for regression. The effectiveness of our method is demonstrated by a real-world application, i.e., the reconstruction of 3D movement trajectories from electrocorticography signals recorded from a monkey brain.

The nine papers in this special section represent the state-of-art in the area of multimodal biomedical imaging algorithms and applications.

Matrix optimization of cost functions is a common problem. Construction of methods that enable each row or column to be individually optimized, i.e., decoupled, are desirable for a number of reasons. With proper decoupling, the convergence characteristics such as local stability can be improved. Decoupling can enable density matching in applications such as independent component analysis (ICA). Lastly, efficient Newton algorithms become tractable after decoupling. The most common method for decoupling rows is to reduce the optimization space to orthogonal matrices. Such restrictions can degrade performance. We present a decoupling procedure that uses standard vector optimization procedures while still admitting nonorthogonal solutions. We utilize the decoupling procedure to develop a new decoupled ICA algorithm that uses Newton optimization enabling superior performance when the sample size is limited.

Detecting the number of signals in a given number of observations, or order detection, is one of the key issues in many signal processing problems. Information theoretic criteria are widely used to estimate the order. In many applications, data does not follow the independently and identically distributed (i.i.d.) sampling assumption. Previous approaches address dependent samples by downsampling the dataset so that existing order detection methods can be used. By downsampling the data, the sample size is decreased so that the accuracy of the order estimation is degraded. In this paper, we introduce two linear mixture models with dependent samples. The likelihood for each model is developed based on the entire data set and used in an information theoretic framework to improve the order estimation performance for dependent samples. Experimental results show performance improvement using this new method.

This paper considers the problem of joint blind source separation (J-BSS), which appears in many practical problems such as blind deconvolution or functional magnetic resonance imaging (fMRI). In particular, we establish the necessary and sufficient conditions for the solution of the J-BSS problem by exclusively exploiting the second-order statistics (SOS) of the observations. The identifiability analysis is based on the idea of equivalently distributed sets of latent variables, that is, latent variables with covariance matrices related by means of a diagonal matrix. Interestingly, the identifiability analysis also allows us to introduce a measure of the identifiability degree based on Kullback-Leibler projections. This measure is clearly correlated with the performance of practical SOS-based J-BSS algorithms, which is illustrated by means of numerical examples.

We propose a data fusion method for the fusion of simultaneously acquired functional magnetic resonance imaging (fMRI) and single trial electroencephalography (EEG) data from multiple subjects using multi-set canonical correlation analysis (M-CCA). Our proposed technique utilizes the common time series information in the multimodal datasets to find trial-to-trial covariations across modalities, and based on these covariations, the data is decomposed into spatial maps for the fMRI data and a corresponding temporal evolution for the EEG data. Additionally, the analysis is performed simultaneously on data from a group of subjects, thus providing an efficient tool to make group inferences about cross-modality covariation. The proposed method is multivariate and hence facilitates the study of brain connectivity along with localization of brain function. We demonstrate the promise of the method in finding covarying trial-to-trial amplitude modulations in an auditory task involving implicit pattern learning.

It has been shown that using minimum error entropy as the cost function leads to important performance gains in adaptive filtering, especially when the Gaussianity assumptions on the error distribution do not hold. In this paper, we show that by using the entropy bound rather than the entropy, we can derive an efficient algorithm for supervised training. We demonstrate its effectiveness by a system identification problem using a generalized Gaussian noise model.

We propose a new entropy rate estimator for a second and/or higher-order correlated source by modeling it as the output of a linear filter, which can be mixed-phase, driven by Gaussian or non-Gaussian noise. Based on this estimator, we develop a new spatiotemporal blind source separation (BSS) algorithm, full BSS (FBSS), by minimizing the entropy rate of separated sources. FBSS provides more flexibilities in exploiting the temporal structures of sources than the state-of-the-art spatiotemporal BSS algorithms, which use AR models, and thus imply minimum-phase property of sources.

Data-driven analysis methods, in particular independent component analysis (ICA) has proven quite useful for the analysis of functional magnetic imaging (fMRI) data. In addition, by enabling one to work in its native, complex form, complex-valued ICA algorithms provide better estimation performance compared to the traditional approach that uses only the magnitude data. In the complex domain, circularity has been a common assumption even though most data acquisition methods collect fMRI data that end up being noncircular when saved in complex form. In this paper, we show that a complex ICA approach that does not assume circularity and also adapts to the source density is the more desirable one for performing ICA of complex fMRI data. We show that by adaptively matching the underlying fMRI density model, the analysis performance can be improved in terms of both the estimation of the task-related time courses and in the spatial activation.

Independent component analysis (ICA) has been successfully applied for the analysis of functional magnetic resonance imaging (fMRI) data. However, independence might be too strong a constraint for certain sources. In this paper, we present an independent subspace analysis (ISA) framework that forms independent subspaces among the estimated sources having dependencies by a hierarchial clustering approach and subsequently separates the dependent sources in the task-related subspace using prior information. We study the incorporation of two types of prior information to transform the sources within the task-related subspace: sparsity and task-related time courses. We demonstrate the effectiveness of our proposed method for source separation of multi-subject fMRI data from a visuomotor task. Our results show that physiologically meaningful dependencies among sources can be identified using our subspace approach and the dependent estimated components can be further separated effectively using a subsequent transformation.

Analysis of functional magnetic resonance imaging (fMRI) data in its native, complex form has been shown to increase the sensitivity of the analysis both for data driven techniques such as independent component analysis (ICA) and for model-driven techniques; however, the noisy nature of the phase poses a challenge for successful study of fMRI data. In addition, for complex ICA, the inherent scaling ambiguity, which has a phase term, introduces additional difficulty for group analysis and visualization of the results. In this paper, we address these issues, which have been among the main reasons phase information has been traditionally discarded and introduce a phase correction scheme that can be either applied subsequent to ICA of fMRI data or can be incorporated into the ICA algorithm in the form of prior information to eliminate the need for further processing for phase correction. In addition, we introduce methods for visualization of the analysis results as well as preprocessing the complex fMRI data to mitigate the effects of noise in the phase which are not limited to ICA algorithms. We demonstrate the successful application of the methods using actual fMRI data.

Typically data acquired through imaging techniques such as functional magnetic resonance imaging (fMRI), structural MRI (sMRI), and electroencephalography(EEG) are analyzed separately. Each modality records brain structure and function at different scales, and fusing information from such complementary modalities promises to provide additional insight into connectivity across brain networks and changes due to disease. Recently, a number of methods have been proposed for data integration and fusion of two brain imaging modalities. We propose a new data fusion scheme based on canonical correlation analysis that enables the detection of associations across multiple modalities. Our multimodal canonical correlation analysis (mCCA) scheme works at the feature level using multi-set CCA to determine inter-subject covariations across modalities. We apply mCCA to fMRI, sMRI, and EEG data collected from patients diagnosed with schizophrenia and healthy controls. Through data collected from an auditory oddball task, we show that the fusion of multiple modalities detects more specific associations as compared to fusion of two modalities.

Target detection in sea clutter is a challenging problem in radar detection, specifically, when the Doppler return of the target and clutter are collocated. Polarization diverse radars provide additional information that enhances target detection. In this paper, we use an effective independent component analysis (ICA) approach, adaptive complex maximization of non-Gaussianity (A-CMN), to efficiently combine polarimetric radar data prior to detection. We show that A-CMN estimates the polarimetric scatter coefficients for the single target in clutter case, thereby providing matched-filter performance without the need for clutter or target models. The detection performance using ICA is evaluated with sea clutter collected with the McMaster IPIX radar off the coast of Canada. We also demonstrates the ability of this approach to adapt to the changing sea clutter conditions using simulation results.

We provide a review of independent component analysis (ICA) for complex-valued improper and noncircular random sources. An improper random signal is correlated with its complex conjugate, and a noncircular random signal has a rotationally variant probability distribution. We present methods for ICA using second-order statistics, and higher-order statistics. For ICA based on second-order statistics, we emphasize the key role played by the circularity coefficients, which are the canonical correlations between the source and the complex conjugate. For ICA based on higher-order statistics, we show how to extend algorithms for real-valued ICA to the complex domain using Wirtinger calculus.

Knowing the statistical properties of a complex-valued signal is important in many signal processing applications by providing the necessary information for choosing the appropriate algorithm. In this paper, we provide generalized likelihood ratio tests (GLRT), based on the complex generalized Gaussian distribution (CGGD), for detecting two important signal properties: 1) the circularity of a complex random variable, not constrained to the Gaussian case and 2) whether a complex random variable is complex Gaussian. These tests can be combined to statistically determine if a complex random variable is, the often assumed, circular Gaussian. Simulations are used to quantify the performance of the detectors followed by application to communication signals and actual radar data.

The acquisition of multiple brain imaging types for a given study is a very common practice. There have been a number of approaches proposed for combining or fusing multitask or multimodal information. These can be roughly divided into those that attempt to study convergence of multimodal imaging, for example, how function and structure are related in the same region of the brain, and those that attempt to study the complementary nature of modalities, for example, utilizing temporal EEG information and spatial functional magnetic resonance imaging information. Within each of these categories, one can attempt data integration (the use of one imaging modality to improve the results of another) or true data fusion (in which multiple modalities are utilized to inform one another). We review both approaches and present a recent computational approach that first preprocesses the data to compute features of interest. The features are then analyzed in a multivariate manner using independent component analysis. We describe the approach in detail and provide examples of how it has been used for different fusion tasks. We also propose a method for selecting which combination of modalities provides the greatest value in discriminating groups. Finally, we summarize and describe future research topics.

The desirable asymptotic optimality properties of the maximum likelihood (ML) estimator make it an attractive solution for performing independent component analysis (ICA) as well. Wirtinger calculus is shown to provide an attractive framework for the derivation and analysis of complex-valued algorithms using nonlinear functions, and hence of ICA algorithms as well. Local stability analysis of complex ICA based on ML presents a unique challenge, since in addition to the need for computation of derivatives, the Hessian of a matrix quantity needs to be evaluated, and for the complex case, it assumes a significantly more complicated form than the real-valued case. In this paper, we demonstrate how Wirtinger calculus allows the use of an elegant approach proposed by Amari et al. (1997) in the analysis, thus enabling the derivation of the conditions for local stability of complex ML ICA. We further study the implications of the conditions for a generalized Gaussian density model.

In this work, we propose a scheme for joint blind source separation (BSS) of multiple datasets using canonical correlation analysis (CCA). The proposed scheme jointly extracts sources from each dataset in the order of between-set source correlations. We show that, when sources are uncorrelated within each dataset and correlated across different datasets only on corresponding indices, (i) CCA on two datasets achieves BSS when the sources from the two datasets have distinct between-set correlation coefficients, and (ii) CCA on multiple datasets (M-CCA) achieves BSS with a more relaxed condition on the between-set source correlation coefficients compared to CCA on two datasets. We present simulation results to demonstrate the properties of CCA and M-CCA on joint BSS. We apply M-CCA to group functional magnetic resonance imaging (fMRI) data acquired from several subjects performing a visuomotor task and obtain interesting brain activations as well as their correlation profiles across different subjects in the group.

The complex fast independent component analysis (c-FastICA) algorithm is one of the most popular methods for solving the ICA problem with complex-valued data. In this study, we extend the work of Bingham and Hyvarinen [1] by deriving conditions for local stability for the more general case of noncircular sources. We use the results of the analysis to quantify the effects of noncircularity on the performance of the algorithm using various nonlinearities and source distributions. Simulations are presented to demonstrate the results of our analysis.

Independent component analysis (ICA) is a statistical and computational technique for revealing hidden factors that underlie sets of signals. We propose an improved ICA framework for group data analysis by adding an adaptive constraint to the mixing coefficients, namely, constrained coefficients ICA (CCICA). The method is dedicated to identification and increasing the accuracy of components that show significant group differences reflected in the mixing coefficients. Performance of CCICA is assessed by simulations under different signal to noise ratios. An application to multitask functional magnetic resonance imaging analysis is conducted to illustrate the advantages of CCICA. It is shown that CCICA provides stable results and can estimate both the components and the mixing coefficients with a relatively high accuracy compared to Infomax, hence is a promising tool for the identification of biomarkers from brain imaging data.

We present a data-driven approach for target detection and identification based on a linear mixture model. Our aim is to determine the existence of certain targets in a mixture without specific information on the targets or the background, and to identify the targets from a given library. We use the maximum canonical correlation between the target set and the observations as the detection score, and use coefficients of the canonical vector to identify the indices of the present components from the given target library. The performance of the detector is enhanced using subspace partitioning on the target library. Both simulation and experimental results are presented to demonstrate the effectiveness of the proposed method in Raman spectroscopy for detection of surface-deposited chemical agents.

Functional magnetic resonance imaging (fMRI) data are originally acquired as complex-valued images, while virtually all fMRI studies only use the magnitude of the data in the analysis. Since little is known for devising models for the phase, independent component analysis (ICA) emerges as a promising technique for data-driven analysis of fMRI data in its native complex form. In this paper, we compare the performance of ICA on real-valued and complex-valued fMRI data and show the advantages of the complex approach. We also develop complex-valued order selection scheme to improve the estimation of the number of independent components in complex-valued fMRI data using information-theoretic criteria. Comparisons on order selection using real-valued and complex-valued fMRI data demonstrate the more informative nature of complex data.

We present a novel multivariate approach called source based morphometry (SBM) to study the novel structural MRI phase images and get sources of relative gray matter and white matter differences between patients and healthy controls. SBM considers the information cross brain voxels and provides spatially maximal independent sources about localization of changes. The structural MRI phase images efficiently summarize the relationship that exists between the gray and white matter without having to increase the dimensionality of the problem. SBM was then applied to the phase images. Results identified patient versus control differences in gray matter and white matter for visual-motor cortex as well as other areas. These interesting findings show that SBM is a useful multivariate approach for studying the brain. Moreover, the use of structural MRI phase images to joint gray and white matter together provides a significant advantage.

In this paper, we introduce a novel way of performing real-valued optimization in the complex domain. This framework enables a direct complex optimization technique when the cost function satisfies the Brandwood's independent analyticity condition. In particular, this technique has been used to derive three algorithms, namely, kurtosis maximization using gradient update (KM-G), kurtosis maximization using fixed-point update (KM-F), and kurtosis maximization using Newton update (KM-N), to perform the complex independent component analysis (ICA) based on the maximization of the complex kurtosis cost function. The derivation and related analysis of the three algorithms are performed in the complex domain without using any complex-real mapping for differentiation and optimization. A general complex Newton rule is also derived for developing the KM-N algorithm. The real conjugate gradient algorithm is extended to the complex domain similar to the derivation of complex Newton rule. The simulation results indicate that the fixed-point version (KM-F) and gradient version (KM-G) are superior to other similar algorithms when the sources include both circular and noncircular distributions and the dimension is relatively high.

In this paper, we use complex analytic functions to achieve independent component analysis (ICA) by maximization of non-Gaussianity and introduce the complex maximization of non-Gaussianity (CMN) algorithm. We derive both a gradient-descent and a quasi-Newton algorithm that use the full second-order statistics providing superior performance with circular and noncircular sources as compared to existing methods. We show the connection among ICA methods through maximization of non-Gaussianity, mutual information, and maximum likelihood (ML) for the complex case, and emphasize the importance of density matching for all three cases. Local stability conditions are derived for the CMN cost function that explicitly show the effects of noncircularity on convergence and demonstrated through simulation examples.

We introduce a framework for complex-valued signal processing such that all computations can be directly carried out in the complex domain. The framework, based on an elegant result due to Brandwood, allows for easy derivation of many complex-valued algorithms and their efficient analyses. We demonstrate its application to derivation of relative gradient updates for independent component analysis using maximum likelihood and discuss the selection of score functions within this framework.

We introduce a fixed-point algorithm, the complex QAM (C-QAM) algorithm, for separation of quadrature amplitude modulated (QAM) sources through independent component analysis. The algorithm matches the input QAM distribution through a mixture of Gaussian kernels and uses fixed-point updates that fully take advantage of complex domain processing. We demonstrate the performance of the C-QAM algorithm through simulations and note that it provides improved performance over a wide range of operating conditions such as low signal-to-noise ratio, small sample sizes, and large number of sources.

Functional magnetic resonance imaging (fMRI) data provides spatially localized subcentimeter information about blood flow and oxygenation secondary to neuronal activation, but with temporal resolution on the order of seconds. Event-related potential (ERP) studies provide millimeter resolution measurements of the electric changes induced by neuronal activity, but spatial information is not well localized and suffers from an ill-posed inverse problem since there are much fewer sensors than solutions. Combining or fusing these two techniques thus has the potential to provide simultaneous higher temporal and high spatial resolution. Localization of the brain's response to infrequent, task-relevant target 'oddball' stimuli in humans has remained challenging due to the lack of a single imaging technique with good spatial and temporal resolution. In this paper, we use independent component analysis to fuse ERP and fMRI modalities to identify, for the first time in humans, the dynamics of the auditory oddball response with high spatiotemporal resolution across the entire brain. The results illuminate a new era of brain research utilizing the precise temporal information in ERPs and the high spatial resolution of fMRI

We derive the form of the best non-linear functions for performing independent component analysis (ICA) by maximum likelihood estimation. We show that both the form of nonlinearity and the relative gradient update equations for likelihood maximization naturally generalize to the complex case, and that they coincide with the real case. We discuss several special cases for the score function as well as adaptive scores.

Complex maximization of nongaussianity (CMN) has been shown to provide reliable separation of both circular and noncircular sources. It is also shown that the algorithm converges to the principal component of the source distribution when studied in the estimation direction. In this paper, we study the local stability of the CMN algorithm and determine the conditions under which local stability is achieved by extending our previous work to all dimensions of the weight vector. We use these conditions of stability to quantify convergence performance for a number of complex nonlinear functions, and present simulation results to demonstrate the effectiveness of these functions.

We propose an integrated maximum a posteriori equalization and turbo product coding (IMAP-TPC) scheme for optical fiber communications systems (OFCS). The scheme uses accurate probabilistic characterization of electrical current in the presence of polarization mode dispersion (PMD)-induced intersymbol interference (ISI) and amplified spontaneous emission (ASE) noise. In the new IMAP-TPC scheme, TPC decoding is integrated with a symbol-by-symbol maximum a posteriori (MAP) detector. The MAP detector calculates the log-likelihood ratio (LLR) of a received symbol using the estimated conditional pdfs, and hence, obtains a much more accurate reliability measure for use in the TPC decoder. Similar to the case in the recent hardware implementation of TPC decoder for optical systems, we generate TPC by serial concatenation of two Bose, Chaudhuri, and Hocquenghem codes with low overhead. Simulation results with all-order PMD and ASE noise demonstrate both the practicality and the effectiveness of the IMAP-TPC scheme for OFCS.

We study the performance of five blind source separation (BSS) algorithms when applied to analysis of functional magnetic resonance imaging (fMRI) data. We introduce a Matlab-based toolbox, the group ICA of fMRI toolbox (GIFT), which enables analysis of groups of subjects using BSS algorithms, in particular those based on independent component analysis (ICA). We use the visualization and computational tools included in GIFT to quantitatively analyze the performance of different BSS algorithms for fMRI analysis and discuss the results.

We present a projection-based framework for a feature-selective independent component analysis (FS-ICA) scheme and study its convergence property for two ICA algorithms, FastICA and Infomax. As examples, we implement bandpass filter as the feature-selective filter to improve the estimation of a bandpass signal from the mixtures and a periodic task-related time course embedded in the functional magnetic resonance imaging (fMRI) data. Hence, we demonstrate that the proposed method can incorporate a priori information into ICA to effectively improve estimation of the underlying components of practical interest, such as periodic time courses and smooth brain activation areas in fMRI data.

We develop a practical method to accurately estimate the distribution of electrical current in optical communications systems in the presence of polarization mode dispersion (PMD)-induced intersymbol interference (ISI) and amplified spontaneous emission (ASE) noise. We then introduce an integrated coding and equalization scheme that use these estimated probabilities of the received current given a transmitted sequence. Simulation results with all-order PMD and ASE noise show the effectiveness of the scheme.

We present approximations for eigenvalues of autocorrelation matrices in the presence of noncentral and signal-dependent noise as a function of eigenvalues of noiseless input. We derive error bounds for the approximations and discuss their properties. The results of the eigenanalysis are applied to the study of first-order polarization mode dispersion for optical systems. The simulation results demonstrate a good match between the approximated and true eigenvalues.

Surface reconstruction is a critical step in three-dimensional image processing and understanding. In this letter, a discontinuity-embedded deformable model has been developed to model surfaces with discontinuities. Governed by the Lagrange motion equation, a finite-element representation of the model can dynamically fit the data in both continuous and discontinuous components, reaching its equilibrium in response to induced forces. Experimental results on synthetic and range images demonstrate a significant improvement in preserving depth discontinuities over conventional approaches.

A number of complex nonlinear functions are proposed for the independent component analysis (ICA) of complex-valued data. We discuss the properties of these nonlinearities and show their efficiency in generating the higher order statistics needed for ICA.

A maximum a posteriori equalizer is presented for optical communication systems. Assuming that the span of the intersymbol interference (ISI) does not extend beyond the neighboring bits - as is typically the case for the distortion introduced by polarization mode dispersion (PMD) - we derive the conditional probability distribution function in the electrical domain in the presence of PMD and amplifier spontaneous emission dominated noise. Simulation results with an accurate receiver model and all-order PMD show the success of the MAP equalizer in reducing the ISI due to PMD, and that the analytical conditional PDF we derive provides a good match to the actual distribution.

Electronic equalizers, which have been used widely in wireless and wireline communications, have recently been recognized as effective solutions for mitigating the impairments in the optical communications channel as well. Now with the increasing availability of voltage-tunable integrated circuits for high speed operation, equalizers, in particular those based on the minimum mean-square error (MMSE) criterion have emerged as practical and cost-effective solutions. Certain properties of the optical domain, however, are different than other communications systems where these equalizers have been used. We study the effects of these properties on the performance of the MMSE equalizers through eigenanalysis of the input autocorrelation matrix.

Independent component analysis (ICA) for separating complex-valued sources is needed for convolutive source-separation in the frequency domain, or for performing source separation on complex-valued data, such as functional magnetic resonance imaging data. Functional magnetic resonance imaging (fMRI) is a technique that produces complex-valued data; however the vast majority of fMRI analyses utilize only magnitude images. We compare the performance of the complex infomax. algorithm that uses an analytic (and hence unbounded) nonlinearity with the traditional complex infomax approaches that employ bounded (and hence non-analytic) nonlinearities as well as with a cumulant-based approach. We compare the performances of these algorithms for processing both simulated and real fMRI data and show that the complex infomax. using analytic nonlinearity has the ability to separate both sub- and super-Gaussian sources with a hyperbolic tangent nonlinearity. The complex infomax algorithm that uses analytic nonlinearity thus provides a potentially powerful method for exploratory analysis of fMRI data.

We investigate the approximation ability of a multilayer perceptron (MLP) network when it is extended to the complex domain. The main challenge for processing complex data with neural networks has been the lack of bounded and analytic complex nonlinear activation functions in the complex domain, as stated by Liouville's theorem. To avoid the conflict between the boundedness and the analyticity of a nonlinear complex function in the complex domain, a number of ad hoc MLPs that include using two real-valued MLPs, one processing the real part and the other processing the imaginary part, have been traditionally employed. However, since nonanalytic functions do not meet the Cauchy-Riemann conditions, they render themselves into degenerative backpropagation algorithms that compromise the efficiency of nonlinear approximation and learning in the complex vector field. A number of elementary transcendental functions (ETFs) derivable from the entire exponential function e(z) that are analytic are defined as fully complex activation functions and are shown to provide a parsimonious structure for processing data in the complex domain and address most of the shortcomings of the traditional approach. The introduction of ETFs, however, raises a new question in the approximation capability of this fully complex MLP. In this letter, three proofs of the approximation capability of the fully complex MLP are provided based on the characteristics of singularity among ETFs. First, the fully complex MLPs with continuous ETFs over a compact set in the complex vector field are shown to be the universal approximator of any continuous complex mappings. The complex universal approximation theorem extends to bounded measurable ETFs possessing a removable singularity. Finally, it is shown that the output of complex MLPs using ETFs with isolated and essential singularities uniformly converges to any nonlinear mapping in the deleted annulus of singularity nearest to the origin.

Functional magnetic resonance imaging (fMRI) is a technique which produces complex data; however the vast majority of functional magnetic resonance imaging analyses utilize only magnitude images. In this paper, we derive a complex-valued independent component analysis (ICA) algorithm using the infomax approach which we then apply to fMRI analysis. Theoretical and empirical results demonstrate an improved sensitivity to functional changes when utilizing the complex data. Additionally, the complex infomax algorithm developed provides a powerful method for exploratory analysis of fMRI data.

Recently, we have presented the ‘fully’ complex feed-forward neural network (FNN) using a subset of complex elementary transcendental functions (ETFs) as the nonlinear activation functions. In this paper, we show that folly complex FNNs can universally approximate any complex mapping to an arbitrary accuracy on a compact set of input patterns with probability 1. The proof is extended to a new family of complex activation functions possessing essential singularities. We discuss properties of the complex activation functions based on the types of their singularity and the implications of these to the efficiency and the domain of convergence in their applications.

We show that electrical domain (post-detection) approaches hold great promise for mitigating distortions such as polarization mode dispersion (PMD) in optical communication systems, when they are used by taking the physical characteristics of the distortion into account. We present a polarization diversity receiver for PMD mitigation and show its effectiveness by simulation results using accurate modeling of the PMD distortion. We also note that by incorporating electronic equalization into the diversity receiver structure further performance improvements can be achieved. We evaluate the system outage probability by calculating the power penalty due to PMD distortion and show its agreement with the simulation results.

Designing a neural network (NN) for processing complex signals is a challenging task due to the lack of bounded and differentiable nonlinear activation functions in the entire complex domain C. To avoid this difficulty, 'splitting', i.e., using uncoupled real sigmoidal functions for the real and imaginary components has been the traditional approach, and a number of fully complex activation functions introduced can only correct for magnitude distortion but can not handle phase distortion. We have previously introduced a fully complex NN that uses a hyperbolic tangent function defined in the entire complex domain and showed that for most practical signal processing problems, it is sufficient to have an activation function that is bounded and differentiable almost everywhere in the complex domain. In this paper, the fully complex NN design is extended to employ other complex activation functions of the hyperbolic, circular, and their inverse function family. They are shown to successfully restore the nonlinear amplitude and phase distortions of non-constant modulus modulated signals.

We address the problem of on-line order determination for communications and show that the penalized partial likelihood criterion provides a suitable likelihood framework for the problem by allowing correlations among samples and online processing ability. An on-line, efficient order selection scheme is developed assuming that the observations can be modeled by a finite normal mixture model without imposing any additional conditions on the unknown system, such as linearity. Channel equalization by finite normal mixtures is considered as an example for which correct order determination is critical and examples are presented to show the application and effectiveness of the approach.

Quantitative analysis of magnetic resonance (MR) images is a powerful tool for image-guided diagnosis, monitoring, and intervention. The major tasks involve tissue quantification and image segmentation where both the pixel and context images are considered. To extract clinically useful information from images that might be lacking in prior knowledge, we introduce an unsupervised tissue characterization algorithm that is both statistically principled and patient specific. The method uses adaptive standard finite normal mixture and inhomogeneous Markov random field models, whose parameters are estimated using expectation-maximization and relaxation labeling algorithms under information theoretic criteria. We demonstrate the successful applications of the approach with synthetic data sets and then with real MR brain images.

The main source of errors for solitons when propagating in optical fibers is the timing jitter. The acoustic effect, unlike other sources of timing jitter such as the Gordon-Haus effect and the polarization effect that are stochastic in nature, is deterministic and is a source of intersymbol interference (ISI). We introduce an adaptive phase equalizer to compensate for the acoustically induced timing jitter (AITJ). We show that the equalizer can be trained in a "semi-blind" fashion by controlling the probability of "1"s in the transmitted sequence and can successfully decrease the AITJ. We demonstrate application of the scheme by simulations and discuss implementation issues.

In discrete multitone (DMT) transceivers, a time domain equalizer (TEQ) is used to shorten the effective channel impulse response such that a shorter cyclic prefix can be used. We pose the TEQ design problem completely in the frequency-domain by defining a frequency-domain weighted least squares cost function. The definition of the frequency-domain TEQ design criterion, we show, allows for the introduction of a weighting function to control the spectral shape of the TEQ, and facilitates important extensions particularly useful for the DMT system. The TEQ can be used to suppress the noise and interference in the DMT system, a feature especially useful in the frequency division multiplexing based DMT system. Also, in the echo-cancellation based DMT system, the TEQ can be used to jointly shorten the echo response thus reducing the complexity of the echo canceler.

In discrete multitone (DMT) transceivers, a cyclic prefix of length /spl gamma/ is inserted between transmitted symbols. If the channel impulse response is of length /spl gamma/+1 or shorter, the intersymbol interference can be avoided. To reduce the inefficiency due to the use of a long cyclic prefix, the use of a time-domain equalizer (TEQ) to shorten the effective channel impulse response has been the most popular equalization approach in DMT receivers. In this paper, we pose the TEQ design problem completely in the frequency domain by minimizing the least squares cost function defined in the frequency-domain. We also show the connection between the frequency-domain least squares cost function and its time-domain counterpart for the TEQ design. Furthermore, we extend this frequency-domain least squares approach by incorporating noise suppression into the cost function and derive a new learning algorithm such that the channel impulse response can be shortened and noise and interference can be suppressed.

Partial likelihood (PL) provides a unified statistical framework for developing and studying adaptive techniques for nonlinear signal processing. In this paper, we present the general formulation for learning posterior probabilities on the PL cost for multi-class classifier design. We show that the fundamental information-theoretic relationship for learning on the PL cost, the equivalence of likelihood maximization and relative entropy minimization, is satisfied for the multiclass case for the perceptron probability model using softmax normalization. We note the inefficiency of training a softmax network and propose an efficient multiclass equalizer structure based on binary coding of the output classes. We show that the well-formed property of the PL cost is satisfied for the softmax and the new multiclass classifier. We present simulation results to demonstrate this fact and note that though the traditional mean square error (MSE) cost uses the available information more efficiently than the PL cost for the multi-class case, the new multi-class equalizer based on binary coding is much more effective in tracking abrupt changes due to the well-formed property of the cost that it uses.

A new algorithm, the joint network and data density estimation (JNDDE), is proposed to estimate the 'a posteriori' probabilities of the targets with neural networks in multiple classes problems. It is based on the estimation of conditional density functions for each class with some restrictions or constraints imposed by the classifier structure and the use Bayes rule to force the a posteriori probabilities at the output of the network, known here as a implicit set. The method is applied to train perceptrons by means of Gaussian mixture inputs, as a particular example for the generalized Softmax perceptron (GSP) network. The method has the advantage of providing a clear distinction between the network architecture and the model of the data constraints, giving network parameters or weights on one side and data over parameters on the other. MLE stochastic gradient based rules are obtained for JNDDE. This algorithm can be applied to hybrid labeled and unlabeled learning in a natural fashion.

In time series problems, where time ordering is a crucial issue, the use of partial likelihood estimation (PLE) represents a specially suitable method for the estimation of parameters in the model. We propose a general supervised neural network algorithm, joint network and data density estimation (JNDDE), that employs PLE to approximate conditional probability density functions for multi-class classification problems. The logistic regression analysis is generalized to multiple class problems with a softmax regression neural network used to model the a posteriori probabilities such that they are approximated by the network outputs. Constraints to the network architecture, as well as to the model of data, are imposed, resulting in both a flexible network architecture and distribution modeling. We consider application of JNDDE to channel equalization and present simulation results.

The aim of the work is to develop a flexible and efficient approach to the classification of the ratio of voiced to unvoiced excitation sources in continuous speech. To achieve this aim we adopt a probabilistic neural network approach. This is accomplished by designing a multilayer perceptron classifier trained by steepest descent minimization of the least relative entropy (LRE) cost function. By using the LRE cost function we can directly output the ratio, as a probability, of excitation source, voiced to unvoiced, for a given speech segment. These output probabilities can then be used directly in other applications, such as low bit rate coders.

The maintenance of equipment, machinery and facilities is a vital part of the industrial process and requires millions of man-hours of technician time. A significant portion of this time is devoted to troubleshooting system malfunctions. We develop an automated system that uses Bayesian belief networks (BBNs) for effective troubleshooting. BBNs are ideal paradigms to represent the causality and uncertainty involved in troubleshooting problems. The automated system we develop generates a cost-effective sequence of testing operations. This optimal sequence generation algorithm is a unique blend of the graphical capabilities of the BBN and older constrained sequence generation algorithms. The test sequence takes into consideration the cost of testing a component and the probability of that component being faulty. An efficient graphical user interface is used to enable the user to develop the BBN and perform decision analysis. We use concepts of qualitative probability networks (QPNs), verbal mapping functions, and automated probability matrix generation to reduce the amount of input required.

We use partial likelihood (PL) theory to introduce a general formulation for learning multi-class posterior probabilities. The formulation establishes a fundamental information-theoretic connection, the equivalence of partial likelihood maximization and relative entropy minimization, without making the common assumption of independent data samples. We further show that this fundamental information-theoretic relationship is satisfied for the basic class of probability models, the exponential family, which includes many important neural network probability models. Thus we provide the prospect of learning the multi-class probabilities on the PL cost using different models. We note the inefficiency of training a Softmax network and propose a modified multi-level classifier structure based on binary coding of the classes. We demonstrate the efficiency of our reduced complexity multi-level classifier by simulation results.

We introduce a signal processing approach to compensate for the timing jitter produced by the acoustic effect in soliton communications. The other main sources of timing jitter, the Gordon-Haus effect and the polarization effect, are inherently stochastic. By contrast, the acoustic effect is deterministic and becomes the dominant source of bit error rates in standard soliton systems when the bit rates are more than 10 Gbits/s and the transmission distance is more than several thousand kilometers. We exploit the deterministic nature of the acoustic effect to introduce a scheme that predicts the amount of timing jitter as a function of the previous transmitted bits and uses the information to adjust the sampling period of the received soliton pulses. We demonstrate successful application of the scheme by simulations and discuss implementation issues.

We present a piecewise linear recurrent neural network (PL-RNN) structure by combining the canonical piecewise linear function with the autoregressive moving average (ARMA) model such that an augmented input space is partitioned into regions where an ARMA model is used in each. The piecewise linear structure allows for easy implementation, and in training, allows for use of standard linear adaptive filtering techniques based on gradient optimization and description of convergence regions for the step-size. We study the dynamics of PL-RNN and show that it defines a contractive mapping and is bounded input bounded output stable. We introduce application of PL-RNN to channel equalization and show that it closely approximates the performance of the traditional RNN that uses sigmoidal activation functions.

This paper presents a probabilistic neural network based technique for unsupervised quantification and segmentation of brain tissues from magnetic resonance images. It is shown that this problem can be solved by distribution learning and relaxation labeling, resulting in an efficient method that may be particularly useful in quantifying and segmenting abnormal brain tissues where the number of tissue types is unknown and the distributions of tissue types heavily overlap. The new technique uses suitable statistical models for both the pixel and context images and formulates the problem in terms of model-histogram fitting and global consistency labeling. The quantification is achieved by probabilistic self-organizing mixtures and the segmentation by a probabilistic constraint relaxation network. The experimental results show the efficient and robust performance of the new algorithm and that it outperforms the conventional classification based approaches.

We consider the problem of magnetic resonance (MR) image reconstruction from non-uniformly sampled data acquired by echo-planar imaging (EPI) and spiral scan imaging techniques. In EPI, mismatches in the timings of the odd and even echoes collected with readout gradients of alternating polarity will result in "N/2" ghosting in the reconstructed images. We propose a new method using a calibration data set to correct this mismatch and hence to calculate accurate k-space trajectories. In order to reconstruct images at real-time speeds, we utilize a high speed optoelectronic device to perform two-dimensional discrete Fourier transform (DFT). Images reconstructed from EPI data, are presented to demonstrate that our method can successfully suppress the "N/2" ghosting and provide good contrast at real-time speeds. Image reconstructed from SSI data is also presented to show that our method can provide better sharp features and more detail in the reconstructed images.

The recurrent canonical piecewise linear (RCPL) network is applied to nonlinear blind equalization by generalizing Donoho's minimum entropy deconvolution approach. We first study the approximation ability of the canonical piecewise linear (CPL) network and the CPL based distribution learning for blind equalization. We then generalize these conclusions to the RCPL network. We show that nonlinear blind equalization can be achieved by matching the distribution of the channel input with that of the RCPL equalizer output. A new blind equalizer structure is constructed by using RCPL network and decision feedback. We discuss application of various cost functions to RCPL based equalization and present experimental results that demonstrate the successful application of RCPL network to blind equalization.

A finite-element deformable surface-spine model is developed in this paper to register two surfaces by recovering the nonlinear deformation with respect to each other. The deformable surface-spine model is a dynamic model governed by Lagrangian motion equations. A 9 degree-of-freedom (dof) finite-element surface element and a 4-dof spine element are developed to iteratively solve Lagrangian equations for computing the deformation between two surfaces. The method has been applied to registration of computerized surgical prostate models. Experimental results have demonstrated that the new registration method can successfully match complex-structured surfaces by recovering the nonlinear deformation.

We introduce a unified statistical framework for real-time signal processing with neural networks by using a recent extension of maximum likelihood (ML) estimation, partial likelihood (PL) estimation theory, which allows for (i) dependent observations, and (ii) processing of data using only the information that is available at the time of processing. For a general neural network conditional distribution model, we establish a fundamental information-theoretic relationship for PL estimation, and obtain large sample properties of PL for the general case of dependent observations. We consider applications of PL to prediction and channel equalization.

This paper presents an efficient on-line distribution learning procedure of standard finite normal mixtures for image quantification. Based on the standard finite normal mixture (SFNM) model, we formulate image quantification as a distribution learning problem, and derive the probabilistic self-organizing map (PSOM) algorithm by minimizing the relative entropy between the SFNM distribution and the image histogram. We justify our formulation and hence provide a basis for the use of SFNM, in pixel image modeling in terms of large sample properties of the maximum likelihood estimator. We then establish convergence properties of the PSOM which simulates a Bayesian rule network structure with Gaussian activation functions forming soft splits of the data, and thus providing unbiased estimates. It is shown that by incorporating learning rate adaptation in a sequential mode, PSOM achieves fast convergence and has efficient learning capabilities which make it very attractive for many practical image quantification applications; such as unsupervised image segmentation and diagnosis by medical images.

Information geometry of partial likelihood is constructed and is used to derive the em-algorithm for learning parameters of a conditional distribution model through information-theoretic projections. To construct the coordinates of the information geometry, an expectation maximization (EM) framework is described for the distribution learning problem using the Gaussian mixture probability model. It is shown that the information-geometric em-algorithm is equivalent to EM to establish its convergence. The algorithm is applied to channel equalization by distribution learning and its rapid convergence characteristics are demonstrated through simulation studies.

We present the general formulation for the adaptive equalization by distribution learning introduced by Adali (see Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, vol.3, p.297-300, April 1994) In this framework, adaptive equalization can be viewed as a parametrized conditional distribution estimation problem where the parameter estimation is achieved by learning on a multilayer perceptron (MLP). Depending on the definition of the conditioning event set either supervised or unsupervised (blind) algorithms in either recurrent or feedforward networks result. We derive the least relative entropy (LRE) algorithm for binary data communications and analyze its statistical and dynamical properties. Particularly, we show that LRE learning is consistent and asymptotically normal by working in the partial likelihood estimation framework, and that the algorithm can always recover from convergence at the wrong extreme as opposed to the MSE based MLP's by working within an extension of the well-formed cost functions framework of Wittner and Denker (1988). We present simulation examples to demonstrate this fact.

The authors present a method that combines region growing and edge detection for magnetic resonance (MR) brain image segmentation. Starting with a simple region growing algorithm which produces an over segmented image, the authors apply a sophisticated region merging method which is capable of handling complex image structures. Edge information is then integrated to verify and, where necessary, to correct region boundaries. The results show that this method is reliable and efficient for MR brain image segmentation.

We formulate the adaptive channel equalization as a conditional probability distribution learning problem. Conditional probability density function of the transmitted signal given the received signal is parametrized by a sigmoidal perceptron. In this framework, we use relative entropy (Kullback-Leibler distance) between the true and the estimated distributions as the cost function to be minimized. The true probabilities are approximated by their stochastic estimators resulting in a stochastic relative entropy cost function. This function is well-formed in the sense of Wittner and Denker (1988), therefore gradient descent on this cost function is guaranteed to find a solution. The consistency and asymptotic normality of this learning scheme are shown via maximum partial likelihood estimation of logistic models. As a practical example, we demonstrate that the resulting algorithm successfully equalizes multipath channels.>

Graphical block diagram simulation tools with highly interactive plotting and visualization capabilities can accelerate and greatly improve DSP and communications education. In this paper, we present several projects given in graduate and senior level undergraduate courses in DSP and communications which use the graphical simulation tool Capsim, and emphasize the importance of true multi-rate signal processing capability for studying DSP. We present a project on integrated design and simulation of network and physical layers in communications systems which also requires asynchronous data flow capability. This project unifies two topics that are traditionally treated separately, and provides important insight for students on error free transmission over noisy channels.>

A probabilistic neural network structure is designed for estimating the parameters of a standard finite normal mixture (SFNM) model in medical image analysis. This neural network employs an unsupervised learning scheme based on the unification of Bayesian and least relative entropy principles, and has Bayes and maximum likelihood neurons which adaptively update the local fuzzy variables in the classification space with the capability of achieving flexible boundary shapes. The optimal network size and hence the number of regions for the SFNM model are determined by various information theoretic criteria, and their performances are compared for images with different stochastic characterizations. A Lloyd-Max quantizer is used to improve the initialization of this self-learning procedure. The performance of this learning technique is tested with both simulated and real medical images, and is shown to be an efficient learning scheme.>

The authors consider the derivation of a numerically stable multichannel fast least-squares algorithm, the multichannel general-order fast transversal filter (MCGO-FTF). The new algorithm is derived by using a vector space formulation, and it is a general-order algorithm, i.e. the orders of several input channel joint process filters can be independently and arbitrarily specified. The numerical stability is achieved through feedback of numerical errors. The algorithm is tested in the equalization of mobile communication channels, which is an important application area for the algorithm. The decision feedback equalizer (DFE), which is essential for the equalization of a mobile communications channel, requires the use of a general-order algorithm to mitigate the effect of error propagation in the decision directed mode. Also, the choice of a least-squares algorithm for this application is critical because of its superior convergence properties.>

The authors derive the steady-state mean square prediction error expression for the fixed-point RLS (recursive least squares) algorithm for the case of time-varying channel estimation, which is modeled as a first-order Markov tapped delay line. It is shown that the random variable driving the time-varying system taps affects the prediction error in the same way as does the roundoff error term due to weight update. It causes the error to grow linearly with time when the forgetting factor, lambda , is chosen as 1. For lambda>

The steady state mean square prediction error is derived for the fixed-point RLS (recursive least squares) algorithm, both for the exponentially windowed RLS (forgetting factor, gamma>