Analysis of histopathological images is critical in cancer diagnosis and treatment. Due to the huge size of histopathological images and the varied number of imaging records per patient, many existing works analyze the Whole Slide Image (WSI) as a bag in which its patches are instances. However, these approaches are limited to analyzing the patches in a fixed shape, while the malignant lesions can form varied shapes. To address this challenge, in this article we propose a Multi-Instance Multi-Shape Support Vector Machine (MIMSSVM) to analyze the multiple images (instances) jointly where each instance consists of multiple patches in various shapes. In our approach, we can identify the different morphologic abnormalities of nuclei shapes from the multiple images. In addition to the multi-instance multi-shape learning capability, we derive an efficient solution algorithm to optimize the proposed model that scales well to a large number of features. Our experimental results show our new method outperforms the existing SVMs and deep learning models in histopathological classification. The proposed model also identifies the tissue segments in an image exhibiting an indication of an abnormality which provides utility in the early detection of malignant tumors. All these promising experimental results have demonstrated the effectiveness of our new method. We anticipate that our new method is of interest to biomedical engineering communities beyond WSI research and have open sourced the code of our method online. The implementation of our proposed MIMSSVM model is publicly available at https://github.com/hoonseo0409/MIMSSVM .

Laplacian embedding (LE) aims to project high-dimensional input data samples, which often contain nonlinear structures, into a low-dimensional space. However, existing distance functions used in the embedding space fail to provide discriminative representations for real-world datasets, especially those related to text analysis or image processing. Cosine similarity measurements are advantageous in dealing with sparse data but are fragile to the impact of outliers and noise from samples or data features. In this work, we propose robust spherical LE (RS-LE), a powerful method that builds the LE on a novel metric that unifies the Euclidean distance and cosine similarity in a spherical space using a robust $\ell _{p,p}$ -norm. We introduce an efficient iterative algorithm, the proximal alternating linearized minimization (ALM) method, to solve the difficult optimization problem that arises from the new metric, which is neither convex nor smooth. This algorithm allows the solution to achieve both global and objective convergence. Our findings are presented in rigorous theoretical analysis and validated in experiments.

Linear discriminant analysis (LDA) is widely used for dimensionality reduction under supervised learning settings. Traditional LDA objective aims to minimize the ratio of the squared Euclidean distances that may not perform optimally on noisy datasets. Multiple robust LDA objectives have been proposed to address this problem, but their implementations have two major limitations. One is that their mean calculations use the squared \(\ell_{2}\) -norm distance to center the data, which is not valid when the objective depends on other distance functions. The second problem is that there is no generalized optimization algorithm to solve different robust LDA objectives. In addition, most existing algorithms can only guarantee that the solution is locally optimal rather than globally optimal. In this article, we review multiple robust loss functions and propose a new and generalized robust objective for LDA. Besides, to remove the mean value within data better, our objective uses an optimal way to center the data through learning. As one important algorithmic contribution, we derive an efficient iterative algorithm to optimize the resulting non-smooth and non-convex objective function. We theoretically prove that our solution algorithm guarantees that both the objective and the solution sequences converge to globally optimal solutions at a sub-linear convergence rate. The results of comprehensive experimental evaluations demonstrate the effectiveness of our new method, achieving significant improvements compared to the other competing methods.

As one of the most popular supervised dimensionality reduction methods, linear discriminant analysis (LDA) has been widely studied in machine learning community and applied to many scientific applications. Traditional LDA minimizes the ratio of squared norms, which is vulnerable to the adversarial examples. In recent studies, many -norm-based robust dimensionality reduction methods are proposed to improve the robustness of model. However, due to the difficulty of -norm ratio optimization and weakness on defending a large number of adversarial examples, so far, scarce works have been proposed to utilize sparsity-inducing norms for LDA objective. In this article, we propose a novel robust discriminative projections learning (rDPL) method based on the -norm trace-ratio minimization optimization algorithm. Minimizing the -norm ratio problem directly is a much more challenging problem than the traditional methods, and there is no existing optimization algorithm to solve such nonsmooth terms ratio problem. We derive a new efficient algorithm to solve this challenging problem and provide a theoretical analysis on the convergence of our algorithm. The proposed algorithm is easy to implement and converges fast in practice. Extensive experiments on both synthetic data and several real benchmark datasets show the effectiveness of the proposed method on defending the adversarial patch attack by comparison with many state-of-the-art robust dimensionality reduction methods.

The COVID-19 pandemic caused by SARS-CoV-2 has emphasized the importance of studying virus-host protein-protein interactions (PPIs) and drug-target interactions (DTIs) to discover effective antiviral drugs. While several computational algorithms have been developed for this purpose, most of them overlook the interplay pathways during infection along PPIs and DTIs. In this paper, we present a novel multipartite graph learning approach to uncover hidden binding affinities in PPIs and DTIs. Our method leverages a comprehensive biomolecular mechanism network that integrates protein-protein, genetic, and virus-host interactions, enabling us to learn a new graph that accurately captures the underlying connected components. Notably, our method identifies clustering structures directly from the new graph, eliminating the need for post-processing steps. To mitigate the detrimental effects of noisy or outlier data in sparse networks, we propose a robust objective function that incorporates the $\ell_{2,p}$-norm and a constraint based on the pth-order Ky-Fan norm applied to the graph Laplacian matrix. Additionally, we present an efficient optimization method tailored to our framework. Experimental results demonstrate the superiority of our approach over existing state-of-the-art techniques, as it successfully identifies potential repurposable drugs for SARS-CoV-2, offering promising therapeutic options for COVID-19 treatment.

Chest X-rays are commonly used for diagnosing and characterizing lung diseases, but the complex morphological patterns in radiographic appearances can challenge clinicians in making accurate diagnoses. To address this challenge, various learning methods have been developed for algorithm-aided disease detection and automated diagnosis. However, most existing methods fail to account for the heterogeneous variability in longitudinal imaging records and the presence of missing or inconsistent temporal data. In this paper, we propose a novel longitudinal learning framework that enriches inconsistent imaging data over sequential time points by leveraging two-dimensional principal component analysis and a robust adaptive loss function. We also derive an efficient solution algorithm that ensures both objective and sequence convergence for the nonconvex optimization problem. Our experiments on the CheXpert dataset demonstrate improved performance in capturing indicative abnormalities in medical images and achieving satisfactory diagnoses. We believe that our method will be of significant interest to the research community working on medical image analysis.

Chest X-ray (CXR) analysis plays an important role in patient treatment. As such, a multitude of machine learning models have been applied to CXR datasets attempting automated analysis. However, each patient has a differing number of images per angle, and multi-modal learning should deal with the missing data for specific angles and times. Furthermore, the large dimensionality of multi-modal imaging data with the shapes inconsistent across the dataset introduces the challenges in training. In light of these issues, we propose the Fast Multi-Modal Support Vector Machine (FMMSVM) which incorporates modality-specific factorization to deal with missing CXRs in the specific angle. Our model is able to adjust the fine-grained details in feature extraction and we provide an efficient optimization algorithm scalable to a large number of features. In our experiments, FMMSVM shows clearly improved classification performance.

Linear discriminant analysis (LDA) is widely used for dimensionality reduction under supervised learning settings. Traditional LDA objective aims to minimize the ratio of squared Euclidean distances that may not perform optimally on noisy data sets. Multiple robust LDA objectives have been proposed to address this problem, but their implementations have two major limitations. One is that their mean calculations use the squared $\ell_{2}$-norm distance to center the data, which is not valid when the objective does not use the Euclidean distance. The second problem is that there is no generalized optimization algorithm to solve different robust LDA objectives. In addition, most existing algorithms can only guarantee the solution to be locally optimal, rather than globally optimal. In this paper, we review multiple robust loss functions and propose a new and generalized robust objective for LDA. Besides, to better remove the mean value within data, our objective uses an optimal way to center the data through learning. As one important algorithmic contribution, we derive an efficient iterative algorithm to optimize the resulting non-smooth and non-convex objective function. We theoretically prove that our solution algorithm guarantees that both the objective and the solution sequences converge to globally optimal solutions at a sub-linear convergence rate. The experimental results demonstrate the effectiveness of our new method, achieving significant improvements compared to the other competing methods.

Principal Component Analysis (PCA) is a powerful approach that can reduce the dimensionality of input data and increase the ease of data interpretation. One major obstacle for using the traditional PCA is its dependence on the squared ℓ2-norm distance that is highly sensitive to outliers and noisy data. This significantly limits the applicability of the PCA when it is applied to large or high-dimensional datasets. In this paper, we review previous efforts of how to overcome this problem and further propose a novel adaptive PCA model. One broadly used hypothesis is that small losses of most data follow the Gaussian distribution and large losses of a few data follow the Laplacian distribution. With this recognition, we choose to use the adaptive loss function that integrates both ℓ1-norm and squared ℓ2-norm distances into a single loss function. To solve the resulted non-convex optimization problem, we derive an efficient iterative algorithm that guarantees that both the objective and solution sequences converge to global optimal solutions at a sub-linear convergence rate. The theoretical convergence analysis of our model is not trivial and comprehensively presented in our work. In comparison to other commonly used dimensionality reduction methods, our experiments on seven real-world datasets showed a great advantage of our model regardless of whether the data was noisy or not. We thus anticipate that our method will have broad usage for a wide range of real-world applications.

MOTIVATION: Breast cancer is a type of cancer that develops in breast tissues, and, after skin cancer, it is the most commonly diagnosed cancer in women in the United States. Given that an early diagnosis is imperative to prevent breast cancer progression, many machine learning models have been developed in recent years to automate the histopathological classification of the different types of carcinomas. However, many of them are not scalable to large-scale datasets. RESULTS: In this study, we propose the novel Primal-Dual Multi-Instance Support Vector Machine to determine which tissue segments in an image exhibit an indication of an abnormality. We derive an efficient optimization algorithm for the proposed objective by bypassing the quadratic programming and least-squares problems, which are commonly employed to optimize Support Vector Machine models. The proposed method is computationally efficient, thereby it is scalable to large-scale datasets. We applied our method to the public BreaKHis dataset and achieved promising prediction performance and scalability for histopathological classification. AVAILABILITY AND IMPLEMENTATION: Software is publicly available at: https://1drv.ms/u/s!AiFpD21bgf2wgRLbQq08ixD0SgRD?e=OpqEmY. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Alzheimer’s Disease (AD) is a chronic neurodegenerative disease that causes severe problems in patients’ thinking, memory, and behavior. An early diagnosis is crucial to prevent AD progression; to this end, many algorithmic approaches have recently been proposed to predict cognitive decline. However, these predictive models often fail to integrate heterogeneous genetic and neuroimaging biomarkers and struggle to handle missing data. In this work we propose a novel objective function and an associated optimization algorithm to identify cognitive decline related to AD. Our approach is designed to incorporate dynamic neuroimaging data by way of a participant-specific augmentation combined with multimodal data integration aligned via a regression task. Our approach, in order to incorporate additional side-information, utilizes structured regularization techniques popularized in recent AD literature. Armed with the fixed-length vector representation learned from the multimodal dynamic and static modalities, conventional machine learning methods can be used to predict the clinical outcomes associated with AD. Our experimental results show that the proposed augmentation model improves the prediction performance on cognitive assessment scores for a collection of popular machine learning algorithms. The results of our approach are interpreted to validate existing genetic and neuroimaging biomarkers that have been shown to be predictive of cognitive decline.

Alzheimer’s Disease (AD) is a progressive memory disorder that causes irreversible cognitive declines, therefore early diagnosis is imperative to prevent the progression of AD. To this end, many biomarker analysis models have been presented for early AD detection. However, these models may not realize the full data potential due to their failure to integrate longitudinal (dynamic) phenotypic data with (static) genetic data. Sometimes, they may not fully utilize both labeled and unlabeled samples either. To overcome these limitations, we propose a semi-supervised enrichment learning method to learn a fixed-length vectorial representation for each participant, by which the static data record can be integrated with the dynamic data records. We have applied our new method on the Alzheimer’s Disease Neuroimaging Initiative (ADNI) cohort and achieved 75% accuracy on multiclass AD progression prediction by one year in advance.

Multi-instance learning (MIL) is an area of machine learning that handles data that is organized into sets of instances known as bags. Traditionally, MIL is used in the supervised-learning setting and is able to classify bags which can contain any number of instances. This property allows MIL to be naturally applied to solve the problems in a wide variety of real-world applications from computer vision to healthcare. However, many traditional MIL algorithms do not scale efficiently to large datasets. In this paper we present a novel Primal-Dual Multi-Instance Support Vector Machine (pdMISVM) derivation and implementation that can operate efficiently on large scale data. Our method relies on an algorithm derived using a multi-block variation of the alternating direction method of multipliers (ADMM). The approach presented in this work is able to scale to large-scale data since it avoids iteratively solving quadratic programming problems which are generally used to optimize MIL algorithms based on SVMs. In addition, we modify our derivation to include an additional optimization designed to avoid solving a least-squares problem during our algorithm; this optimization increases the utility of our approach to handle a large number of features as well as bags. Finally, we apply our approach to synthetic and real-world multi-instance datasets to illustrate the scalability, promising predictive performance, and interpretability of our proposed method. We end our discussion with an extension of our approach to handle non-linear decision boundaries. Code and data for our methods are available online at: https://github.com/minds-mines/pdMISVM.jl.

Nonnegative Matrix Factorization (NMF) is broadly used to determine class membership in a variety of clustering applications. From movie recommendations and image clustering to visual feature extractions, NMF has applications to solve a large number of knowledge discovery and data mining problems. Traditional optimization methods, such as the Multiplicative Updating Algorithm (MUA), solves the NMF problem by utilizing an auxiliary function to ensure that the objective monotonically decreases. Although the objective in MUA converges, there exists no proof to show that the learned matrix factors converge as well. Without this rigorous analysis, the clustering performance and stability of the NMF algorithms cannot be guaranteed. To address this knowledge gap, in this article, we study the factor-bounded NMF problem and provide a solution algorithm with proven convergence by rigorous mathematical analysis, which ensures that both the objective and matrix factors converge. In addition, we show the relationship between MUA and our solution followed by an analysis of the convergence of MUA. Experiments on both toy data and real-world datasets validate the correctness of our proposed method and its utility as an effective clustering algorithm.

A critical challenge in using longitudinal neuroimaging data to study the progressions of Alzheimer's Disease (AD) is the varied number of missing records of the patients during the course when AD develops. To tackle this problem, in this paper we propose a novel formulation to learn an enriched representation with fixed length for imaging biomarkers, which aims to simultaneously capture the information conveyed by both baseline neuroimaging record and progressive variations characterized by varied counts of available follow-up records over time. Because the learned biomarker representations are a set of fixedlength vectors, they can be readily used by traditional machine learning models to study AD developments. Take into account that the missing brain scans are not aligned in terms of time in a studied cohort, we develop a new objective that maximizes the ratio of the summations of a number of ℓ1-norm distances for improved robustness, which, though, is difficult to efficiently solve in general. Thus, we derive a new efficient and non-greedy iterative solution algorithm and rigorously prove its convergence. We have performed extensive experiments on the Alzheimer's Disease Neuroimaging Initiative (ADNI) cohort. A clear performance gain has been achieved in predicting ten different cognitive scores when we compare the original baseline biomarker representations against the learned representations with longitudinal enrichments. We further observe that the top selected biomarkers by our new method are in accordance with known knowledge in AD studies. These promising results have demonstrated improved performances of our new method that validate its effectiveness.

Alzheimer's Disease (AD) is a chronic neurodegenerative disease that severely impacts patients' thinking, memory and behavior. To aid automatic AD diagnoses, many longitudinal learning models have been proposed to predict clinical outcomes and/or disease status, which, though, often fail to consider missing temporal phenotypic records of the patients that can convey valuable information of AD progressions. Another challenge in AD studies is how to integrate heterogeneous genotypic and phenotypic biomarkers to improve diagnosis prediction. To cope with these challenges, in this paper we propose a longitudinal multi-modal method to learn enriched genotypic and phenotypic biomarker representations in the format of fixed-length vectors that can simultaneously capture the baseline neuroimaging measurements of the entire dataset and progressive variations of the varied counts of follow-up measurements over time of every participant from different biomarker sources. The learned global and local projections are aligned by a soft constraint and the structured-sparsity norm is used to uncover the multi-modal structure of heterogeneous biomarker measurements. While the proposed objective is clearly motivated to characterize the progressive information of AD developments, it is a nonsmooth objective that is difficult to efficiently optimize in general. Thus, we derive an efficient iterative algorithm, whose convergence is rigorously guaranteed in mathematics. We have conducted extensive experiments on the Alzheimer's Disease Neuroimaging Initiative (ADNI) data using one genotypic and two phenotypic biomarkers. Empirical results have demonstrated that the learned enriched biomarker representations are more effective in predicting the outcomes of various cognitive assessments. Moreover, our model has successfully identified disease-relevant biomarkers supported by existing medical findings that additionally warrant the correctness of our method from the clinical perspective.

The social and financial costs associated with Alzheimer's disease (AD) result in significant burdens on our society. In order to understand the causes of this disease, public-private partnerships such as the Alzheimer's Disease Neuroimaging Initiative (ADNI) release data into the scientific community. These data are organized into various modalities (genetic, brain-imaging, cognitive scores, diagnoses, etc.) for analysis. Many statistical learning approaches used in medical image analysis do not explicitly take advantage of this multimodal data structure. In this work we propose a novel objective function and optimization algorithm that is designed to handle multimodal information for the prediction and analysis of AD. Our approach relies on robust matrix-factorization and row-wise sparsity provided by the ℓ2,1- norm in order to integrate multimodal data provided by the ADNI. These techniques are jointly optimized with a classification task to guide the feature selection in our proposed Task Balanced Multimodal Feature Selection method. Our results, when compared against some widely used machine learning algorithms, show improved balanced accuracies, precision, and Matthew's correlation coefficients for identifying cognitive decline. In addition to the improved prediction performance, our method is able to identify brain and genetic biomarkers that are of interest to the clinical research community. Our experiments validate existing brain biomarkers and single nucleotide polymorphisms located on chromosome 11 and detail novel polymorphisms on chromosome 10 that, to the best of the authors' knowledge, have not previously been reported. We anticipate that our method will be of interest to the greater research community and have released our method's code online.11Code is provided at: https://github.com/minds-mines/TBMFSjl

Alzheimer's Disease (AD) is a progressive memory disorder that causes irreversible cognitive decline. Recently, many statistical learning methods have been presented to predict cognitive declines by using longitudinal imaging data. However, missing records that broadly exist in the longitudinal neuroimaging data have posed a critical challenge for effectively using these data in machine learning models. To tackle this difficulty, in this paper we propose a novel approach to integrate longitudinal (dynamic) phenotypic data and static genetic data to learn a fixed-length biomarker representation using the enrichment learned from the temporal data in multiple imaging modalities. Armed with this enriched biomarker representation, as a fixed-length vector per participant, conventional machine learning models can be used to predict clinical outcomes associated with AD. We have applied our new method on the Alzheimer's Disease Neruoimaging Initiative (ADNI) cohort and achieved promising experimental results that validate its effectiveness.

With rapid progress in high-throughput genotyping and neuroimaging, researches of complex brain disorders, such as Alzheimer's Disease (AD), have gained significant attention in recent years. Many prediction models have been studied to relate neuroimaging measures to cognitive status over the progressions when these disease develops. Missing data is one of the biggest challenge in accurate cognitive score prediction of subjects in longitudinal neuroimaging studies. To tackle this problem, in this paper we propose a novel formulation to learn an enriched representation for imaging biomarkers that can simultaneously capture both the information conveyed by baseline neuroimaging records and that by progressive variations of varied counts of available follow-up records over time. While the numbers of the brain scans of the participants vary, the learned biomarker representation for every participant is a fixed-length vector, which enable us to use traditional learning models to study AD developments. Our new objective is formulated to maximize the ratio of the summations of a number of ℓ1-norm distances for improved robustness, which, though, is difficult to efficiently solve in general. Thus we derive a new efficient iterative solution algorithm and rigorously prove its convergence. We have performed extensive experiments on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset. A performance gain has been achieved to predict four different cognitive scores, when we compare the original baseline representations against the learned representations with enrichments. These promising empirical results have demonstrated improved performances of our new method that validate its effectiveness.

Alzheimer's disease (AD) is a serious neurodegenerative condition that affects millions of individuals across the world. As the average age of individuals in the United States and the world increases, the prevalence of AD will continue to grow. To address this public health problem, the research community has developed computational approaches to sift through various aspects of clinical data and uncover their insights, among which one of the most challenging problem is to determine the biological mechanisms that cause AD to develop. To study this problem, in this paper we present a novel Joint Multi-Modal Longitudinal Regression and Classification method and show how it can be used to identify the cognitive status of the participants in the Alzheimer's Disease Neuroimaging Initiative (ADNI) cohort and the underlying biological mechanisms. By intelligently combining clinical data of various modalities (i.e., genetic information and brain scans) using a variety of regularizations that can identify AD-relevant biomarkers, we perform the regression and classification tasks simultaneously. Because the proposed objective is a non-smooth optimization problem that is difficult to solve in general, we derive an efficient iterative algorithm and rigorously prove its convergence. To validate our new method in predicting the cognitive scores of patients and their clinical diagnosis, we conduct comprehensive experiments on the ADNI cohort. Our promising results demonstrate the benefits and flexibility of the proposed method. We anticipate that our new method is of interest to clinical communities beyond AD research and have open-sourced the code of our method online.11 The code package for the proposed Joint Multi-Modal Longitudinal Regression and Classification model have been made publicly available online at https://github.com/minds-mines/jmmlrc.

Visual place recognition is essential for large-scale simultaneous localization and mapping (SLAM). Long-term robot operations across different time of the days, months, and seasons introduce new challenges from significant environment appearance variations. In this paper, we propose a novel method to learn a location representation that can integrate the semantic landmarks of a place with its holistic representation. To promote the robustness of our new model against the drastic appearance variations due to long-term visual changes, we formulate our objective to use non-squared ℓ2-norm distances, which leads to a difficult optimization problem that minimizes the ratio of the ℓ2,1-norms of matrices. To solve our objective, we derive a new efficient iterative algorithm, whose convergence is rigorously guaranteed by theory. In addition, because our solution is strictly orthogonal, the learned location representations can have better place recognition capabilities. We evaluate the proposed method using two large-scale benchmark data sets, the CMU-VL and Nordland data sets. Experimental results have validated the effectiveness of our new method in long-term visual place recognition applications.

Metric Learning, which aims at learning a distance metric for a given data set, plays an important role in measuring the distance or similarity between data objects. Due to its broad usefulness, it has attracted a lot of interest in machine learning and related areas in the past few decades. This paper proposes to learn the distance metric from the side information in the forms of must-links and cannot-links. Given the pairwise constraints, our goal is to learn a Mahalanobis distance that minimizes the ratio of the distances of the data pairs in the must-links to those in the cannot-links. Different from many existing papers that use the traditional squared L2-norm distance, we develop a robust model that is less sensitive to data noise or outliers by using the not-squared L2-norm distance. In our objective, the orthonormal constraint is enforced to avoid degenerate solutions. To solve our objective, we have derived an efficient iterative solution algorithm. We have conducted extensive experiments, which demonstrated the superiority of our method over state-of-the-art.

Laplacian Embedding (LE) is a powerful method to reveal the intrinsic geometry of high-dimensional data by using graphs. Imposing the orthogonal and nonnegative constraints onto the LE objective has proved to be effective to avoid degenerate and negative solutions, which, though, are challenging to achieve simultaneously because they are nonlinear and nonconvex. In addition, recent studies have shown that using the p-th order of the L2-norm distances in LE can find the best solution for clustering and promote the robustness of the embedding model against outliers, although this makes the optimization objective nonsmooth and difficult to efficiently solve in general. In this work, we study LE that uses the p-th order of the L2-norm distances and satisfies both orthogonal and nonnegative constraints. We introduce a novel smoothed iterative reweighted method to tackle this challenging optimization problem and rigorously analyze its convergence. We demonstrate the effectiveness and potential of our proposed method by extensive empirical studies on both synthetic and real data sets.

Principal Component Analysis (PCA) is one of the most broadly used methods to analyze high-dimensional data. However, most existing studies on PCA aim to minimize the reconstruction error measured by the Euclidean distance, although in some fields, such as text analysis in information retrieval, analysis using the angle distance is known to be more effective. In this paper, we propose a novel PCA formulation by adding a constraint on the factors to unify the Euclidean distance and the angle distance. Because the objective and constraints are nonconvex, the optimization problem is difficult to solve in general. To tackle the optimization problem, we propose an alternating linearized minimization method with guaranteed convergence and provable convergence rate. Experiments on synthetic data and real-world data sets have validated the effectiveness of our new method and demonstrated its advantages over state-of-art competing methods.

Loop closure detection is a critical component of large-scale simultaneous localization and mapping (SLAM) in loopy environments. This capability is challenging to achieve in long-term SLAM, when the environment appearance exhibits significant long-term variations across various time of the day, months, and even seasons. In this paper, we introduce a novel formulation to learn an integrated long-term representation based upon both holistic and landmark information, which integrates two previous insights under a unified framework: (1) holistic representations outperform keypoint-based representations, and (2) landmarks as an intermediate representation provide informative cues to detect challenging locations. Our new approach learns the representation by projecting input visual data into a low-dimensional space, which preserves both the global consistency (to minimize representation error) and the local consistency (to preserve landmarks’ pairwise relationship) of the input data. To solve the formulated optimization problem, a new algorithm is developed with theoretically guaranteed convergence. Extensive experiments have been conducted using two large-scale public benchmark data sets, in which the promising performances have demonstrated the effectiveness of the proposed approach.

Multi-instance learning (MIL) has demonstrated its usefulness in many real-world image applications in recent years. However, two critical challenges prevent one from effectively using MIL in practice. First, existing MIL methods routinely model the predictive targets using the instances of input images, but rarely utilize an input image as a whole. As a result, the useful information conveyed by the holistic representation of an input image could be potentially lost. Second, the varied numbers of the instances of the input images in a data set make it infeasible to use traditional learning models that can only deal with single-vector inputs. To tackle these two challenges, in this paper we propose a novel image representation learning method that can integrate the local patches (the instances) of an input image (the bag) and its holistic representation into one single-vector representation. Our new method first learns a projection to preserve both global and local consistencies of the instances of an input image. It then projects the holistic representation of the same image into the learned subspace for information enrichment. Taking into account the content and characterization variations in natural scenes and photos, we develop an objective that maximizes the ratio of the summations of a number of ℓ1-norm distances, which is difficult to solve in general. To solve our objective, we derive a new efficient non-greedy iterative algorithm and rigorously prove its convergence. Promising results in extensive experiments have demonstrated improved performances of our new method that validate its effectiveness.

Different to traditional clustering methods that deal with one single type of data, High-Order Co- Clustering (HOCC) aims to cluster multiple types of data simultaneously by utilizing the inter- or/and intra-type relationships across different data types. In existing HOCC methods, data points routinely enter the objective functions with squared residual errors. As a result, outlying data samples can dominate the objective functions, which may lead to incorrect clustering results. Moreover, existing methods usually suffer from soft clustering, where the probabilities to different groups can be very close. In this paper, we propose an L1 -norm symmetric nonnegative matrix tri-factorization method to solve the HOCC problem. Due to the orthogonal constraints and the symmetric L1 -norm formulation in our new objective, conventional auxiliary function approach no longer works. Thus we derive the solution algorithm using the alternating direction method of multipliers. Extensive experiments have been conducted on a real world data set, in which promising empirical results, including less time consumption, strictly orthogonal membership matrix, lower local minima etc., have demonstrated the effectiveness of our proposed method.

Transductive semi-supervised learning can only predict labels for unlabeled data appearing in training data, and can not predict labels for testing data never appearing in training set. To handle this out-of-sample problem, many inductive methods make a constraint such that the predicted label matrix should be exactly equal to a linear model. In practice, this constraint might be too rigid to capture the manifold structure of data. In this paper, we relax this rigid constraint and propose to use an elastic constraint on the predicted label matrix such that the manifold structure can be better explored. Moreover, since unlabeled data are often very abundant in practice and usually there are some outliers, we use a non-squared loss instead of the traditional squared loss to learn a robust model. The derived problem, although is convex, has so many nonsmooth terms, which make it very challenging to solve. In the paper, we propose an efficient optimization algorithm to solve a more general problem, based on which we find the optimal solution to the derived problem.

Sequence describes the primary structure of a protein, which contains important structural, characteristic, and genetic information and thereby motivates many sequence-based computational approaches to infer protein function. Among them, feature-base approaches attract increased attention because they make prediction from a set of transformed and more biologically meaningful sequence features. However, original features extracted from sequence are usually of high dimensionality and often compromised by irrelevant patterns, therefore dimension reduction is necessary prior to classification for efficient and effective protein function prediction. A protein usually performs several different functions within an organism, which makes protein function prediction amulti-label classificationproblem. In machine learning, multi-label classification deals with problems where each object may belong to more than one class. As a well-known feature reduction method, linear discriminant analysis (LDA) has been successfully applied in many practical applications. It, however, by nature is designed forsingle-label classification, in which each object can belong to exactly one class. Because directly applying LDA in multi-label classification causes ambiguity when computing scatters matrices, we apply a new Multi-label Linear Discriminant Analysis (MLDA) approach to address this problem and meanwhile preserve powerful classification capability inherited from classical LDA. We further extend MLDA by$\ell _1$-normalization to overcome the problem of over-counting data points with multiple labels. In addition, we incorporate biological network data using Laplacian embedding into our method, and assess the reliability of predicted putative functions. Extensive empirical evaluations demonstrate promising results of our methods.

In recent data mining research, the graph clustering methods, such as normalized cut and ratio cut, have been well studied and applied to solve many unsupervised learning applications. The original graph clustering methods are NP-hard problems. Traditional approaches used spectral relaxation to solve the graph clustering problems. The main disadvantage of these approaches is that the obtained spectral solutions could severely deviate from the true solution. To solve this problem, in this paper, we propose a new relaxation mechanism for graph clustering methods. Instead of minimizing the squared distances of clustering results, we use the l1-norm distance. More important, considering the normalized consistency, we also use the l1-norm for the normalized terms in the new graph clustering relaxations. Due to the sparse result from the l1-norm minimization, the solutions of our new relaxed graph clustering methods get discrete values with many zeros, which are close to the ideal solutions. Our new objectives are difficult to be optimized, because the minimization problem involves the ratio of nonsmooth terms. The existing sparse learning optimization algorithms cannot be applied to solve this problem. In this paper, we propose a new optimization algorithm to solve this difficult non-smooth ratio minimization problem. The extensive experiments have been performed on three two-way clustering and eight multi-way clustering benchmark data sets. All empirical results show that our new relaxation methods consistently enhance the normalized cut and ratio cut clustering results.

Recent developments in biologyhave produced a large number of gene expression patterns, many of which have been annotated textually with anatomical and developmental terms. These terms spatially correspond to local regions of the images, which are attached collectively to groups of images. Because one does not know which term is assigned to which region of which image in the group, the developmental stage classification and anatomical term annotation turn out to be a multi-instance learning (MIL) problem, which considers input as bags of instances and labels are assigned to the bags. Most existing MIL methods routinely use the Bag-to-Bag (B2B) distances, which, however, are often computationally expensive and may not truly reflect the similarities between the anatomical and developmental terms. In this paper, we approach the MIL problem from a new perspective using the Class-to-Bag (C2B) distances, which directly assesses the relations between annotation terms and image panels. Taking into account the two challenging properties of multi-instance gene expression data, high heterogeneity and weak label association, we computes the C2B distance by introducing class specific distance metrics and locally adaptive significance coefficients.We apply our new approach to automatic gene expression pattern classification and annotation on the Drosophila melanogaster species. Extensive experiments have demonstrated the effectiveness of our new method.

Locality preserving projection (LPP) is an effective dimensionality reduction method based on manifold learning, which is defined over the graph weighted squared L2-norm distances in the projected subspace. Since squared L2-norm distance is prone to outliers, it is desirable to develop a robust LPP method. In this paper, motivated by existing studies that improve the robustness of statistical learning models via L1-norm or not-squared L2-norm formulations, we propose a robust LPP (rLPP) formulation to minimize the p-th order of the L2-norm distances, which can better tolerate large outlying data samples because it suppress the introduced biased more than the L1-norm or not squared L2-norm minimizations. However, solving the formulated objective is very challenging because it not only non-smooth but also non-convex. As an important theoretical contribution of this work, we systematically derive an efficient iterative algorithm to solve the general p-th order L2-norm minimization problem, which, to the best of our knowledge, is solved for the first time in literature. Extensive empirical evaluations on the proposed rLPP method have been performed, in which our new method outperforms the related state-of-the-art methods in a variety of experimental settings and demonstrate its effectiveness in seeking better subspaces on both noiseless and noisy data.

With the rapid growth of modern technologies, Internet has reached almost every corner of the world. As a result, it becomes more and more important to manage and mine information contained in Web pages in different languages. Traditional supervised learning methods usually require a large amount of training data to obtain accurate and robust classification models. However, labeled Web pages did not increase as fast as the growth of Internet. The lack of sufficient training Web pages in many languages, especially for those in uncommonly used languages, makes it a challenge for traditional classification algorithms to achieve satisfactory performance. To address this, we observe that Web pages for a same topic from different languages usually share some common semantic patterns, though in different representation forms. In addition, we also observe that the associations between word clusters and Web page classes are another type of reliable carriers to transfer knowledge across languages. With these recognitions, in this article we propose a novel joint nonnegative matrix trifactorization (NMTF) based Dual Knowledge Transfer (DKT) approach for cross-language Web page classification. Our approach transfers knowledge from the auxiliary language, in which abundant labeled Web pages are available, to the target languages, in which we want to classify Web pages, through two different paths: word cluster approximation and the associations between word clusters and Web page classes. With the reinforcement between these two different knowledge transfer paths, our approach can achieve better classification accuracy. In order to deal with the large-scale real world data, we further develop the proposed DKT approach by constraining the factor matrices of NMTF to be cluster indicator matrices. Due to the nature of cluster indicator matrices, we can decouple the proposed optimization objective and the resulted subproblems are of much smaller sizes involving much less matrix multiplications, which make our new approach much more computationally efficient. We evaluate the proposed approach in extensive experiments using a real world cross-language Web page data set. Promising results have demonstrated the effectiveness of our approach that are consistent with our theoretical analyses.

In this paper, we propose an unsupervised projection method for feature extraction to preserve both global and local consistencies of the input data in the projected space. Traditional unsupervised feature extraction methods, such as principal component analysis (PCA) and locality preserving projections (LPP), can only explore either the global or local geometric structures of the input data, but not the both at the same time. In our new method, we introduce a new measurement using the neighborhood data variances to assess the data locality, by which we propose to learn an optimal projection by rewarding both the global and local structures of the input data. The formulated optimization problem is challenging to solve, because it ends up a trace ratio minimization problem. In this paper, as an important theoretical contribution, we propose a simple yet efficient optimization algorithm to solve the trace ratio problem with theoretically proved convergence. Extensive experiments have been performed on six benchmark data sets, where the promising results validate the proposed method.

Video completion is a computer vision technique to recover the missing values in video sequences by filling the unknown regions with the known information. In recent research, tensor completion, a generalization of matrix completion for higher order data, emerges as a new solution to estimate the missing information in video with the assumption that the video frames are homogenous and correlated. However, each video clip often stores the heterogeneous episodes and the correlations among all video frames are not high. Thus, the regular tenor completion methods are not suitable to recover the video missing values in practical applications. To solve this problem, we propose a novel spatially-temporally consistent tensor completion method for recovering the video missing data. Instead of minimizing the average of the trace norms of all matrices unfolded along each mode of a tensor data, we introduce a new smoothness regularization along video time direction to utilize the temporal information between consecutive video frames. Meanwhile, we also minimize the trace norm of each individual video frame to employ the spatial correlations among pixels. Different to previous tensor completion approaches, our new method can keep the spatio-temporal consistency in video and do not assume the global correlation in video frames. Thus, the proposed method can be applied to the general and practical video completion applications. Our method shows promising results in all evaluations on both 3D biomedical image sequence and video benchmark data sets.

Traditional distance metric learning with side information usually formulates the objectives using the covariance matrices of the data point pairs in the two constraint sets of must-links and cannot-links. Because the covariance matrix computes the sum of the squared L2-norm distances, it is prone to both outlier samples and outlier features. To develop a robust distance metric learning method, in this paper we propose a new objective for distance metric learning using the L1-norm distances. However, the resulted objective is very challenging to solve, because it simultaneously minimizes and maximizes (minmax) a number of non-smooth L1-norm terms. As an important theoretical contribution of this paper, we systematically derive an efficient iterative algorithm to solve the general L1-norm minmax problem, which is rarely studied in literature. We have performed extensive empirical evaluations, where our new distance metric learning method outperforms related state-of-the-art methods in a variety of experimental settings to cluster both noiseless and noisy data.

To better understand, search, and classify image and video information, many visual feature descriptors have been proposed to describe elementary visual characteristics, such as the shape, the color, the texture, etc. How to integrate these heterogeneous visual features and identify the important ones from them for specific vision tasks has become an increasingly critical problem. In this paper, We propose a novel Sparse Multimodal Learning (SMML) approach to integrate such heterogeneous features by using the joint structured sparsity regularizations to learn the feature importance of for the vision tasks from both group-wise and individual point of views. A new optimization algorithm is also introduced to solve the non-smooth objective with rigorously proved global convergence. We applied our SMML method to five broadly used object categorization and scene understanding image data sets for both single-label and multi-label image classification tasks. For each data set we integrate six different types of popularly used image features. Compared to existing scene and object categorization methods using either single modality or multi-modalities of features, our approach always achieves better performances measured.

Representing the raw input of a data set by a set of relevant codes is crucial to many computer vision applications. Due to the intrinsic sparse property of real-world data, dictionary learning, in which the linear decomposition of a data point uses a set of learned dictionary bases, i.e., codes, has demonstrated state-of-the-art performance. However, traditional dictionary learning methods suffer from three weaknesses: sensitivity to noisy and outlier samples, difficulty to determine the optimal dictionary size, and incapability to incorporate supervision information. In this paper, we address these weaknesses by learning a Semi-Supervised Robust Dictionary (SSR-D). Specifically, we use the l2,0+-norm as the loss function to improve the robustness against outliers, and develop a new structured sparse regularization to incorporate the supervision information in dictionary learning, without incurring additional parameters. Moreover, the optimal dictionary size is automatically learned from the input data. Minimizing the derived objective function is challenging because it involves many non-smooth l2,0+-norm terms. We present an efficient algorithm to solve the problem with a rigorous proof of the convergence of the algorithm. Extensive experiments are presented to show the superior performance of the proposed method.

The lack of training data is a common challenge in many machine learning problems, which is often tackled by semi-supervised learning methods or transfer learning methods. The former requires unlabeled images from the same distribution as the labeled ones and the latter leverages labeled images from related homogenous tasks. However, these restrictions often cannot be satisfied. To address this, we propose a novel robust and discriminative self-taught learning approach to utilize any unlabeled data without the above restrictions. Our new approach employs a robust loss function to learn the dictionary, and enforces the structured sparse regularization to automatically select the optimal dictionary basis vectors and incorporate the supervision information contained in the labeled data. We derive an efficient iterative algorithm to solve the optimization problem and rigorously prove its convergence. Promising results in extensive experiments have validated the proposed approach.

Combining information from various data sources has become an important research topic in machine learning with many scientific applications. Most previous studies employ kernels or graphs to integrate different types of features, which routinely assume one weight for one type of features. However, for many problems, the importance of features in one source to an individual cluster of data can be varied, which makes the previous approaches ineffective. In this paper, we propose a novel multi-view learning model to integrate all features and learn the weight for every feature with respect to each cluster individually via new joint structured sparsity-inducing norms. The proposed multi-view learning framework allows us not only to perform clustering tasks, but also to deal with classification tasks by an extension when the labeling knowledge is available. A new efficient algorithm is derived to solve the formulated objective with rigorous theoretical proof on its convergence. We applied our new data fusion method to five broadly used multi-view data sets for both clustering and classification. In all experimental results, our method clearly outperforms other related state-of-the-art methods.

Multi-Instance Learning (MIL) is an emerging topic in machine learning, which has broad applications in computer vision. For example, by considering video classification as a MIL problem where we only need labeled video clips (such as tagged online videos) but not labeled video frames, one can lower down the labeling cost, which is typically very expensive. We propose a novel class specific distance Metrics enhanced Class-to-Bag distance (M-C2B) method to learn a robust and discriminative distance for multi-instance data, which employs the not-squared ℓ2-norm distance to address the most difficult challenge in MIL, i.e., the outlier instances that abound in multi-instance data by nature. As a result, the formulated objective ends up to be a simultaneous ℓ2, 1-norm minimization and maximization (minmax) problem, which is very hard to solve in general due to the non-smoothness of the ℓ2, 1-norm. We thus present an efficient iterative algorithm to solve the general ℓ2, 1-norm minmax problem with rigorously proved convergence. To the best of our knowledge, we are the first to solve a general ℓ2, 1-norm minmax problem in literature. We have conducted extensive experiments to evaluate various aspects of the proposed method, in which promising results validate our new method in cost-effective video classification.

The low-rank matrix completion problem is a fundamental machine learning problem with many important applications. The standard low-rank matrix completion methods relax the rank minimization problem by the trace norm minimization. However, this relaxation may make the solution seriously deviate from the original solution. Meanwhile, most completion methods minimize the squared prediction errors on the observed entries, which is sensitive to outliers. In this paper, we propose a new robust matrix completion method to address these two problems. The joint Schatten p-norm and ℓp-norm are used to better approximate the rank minimization problem and enhance the robustness to outliers. The extensive experiments are performed on both synthetic data and real world applications in collaborative filtering and social network link prediction. All empirical results show our new method outperforms the standard matrix completion methods.

In recent years, several methods have been proposed to exploit image context (such as location) that provides valuable cues complementary to the image content, i.e., image annotations and geotags have been shown to assist the prediction of each other. To exploit the useful interrelatedness between these two heterogeneous prediction tasks, we propose a new correlation guided structured sparse multi-task learning method. We utilize a joint classification and regression model to identify annotation-informative and geotag-relevant image features. We also introduce the tree-structured sparsity regularizations into multi-task learning to integrate the label correlations in multi-label image annotation. Finally we derive an efficient algorithm to optimize our non-smooth objective function. We demonstrate the performance of our method on three real-world geotagged multi-label image data sets for both semantic annotation and geotag prediction.

Alzheimer disease (AD) is a neurodegenerative disorder characterized by progressive impairment of memory and other cognitive functions. Regression analysis has been studied to relate neuroimaging measures to cognitive status. However, whether these measures have further predictive power to infer a trajectory of cognitive performance over time is still an under-explored but important topic in AD research. We propose a novel high-order multi-task learning model to address this issue. The proposed model explores the temporal correlations existing in data features and regression tasks by the structured sparsity-inducing norms. In addition, the sparsity of the model enables the selection of a small number of MRI measures while maintaining high prediction accuracy. The empirical studies, using the baseline MRI and serial cognitive data of the ADNI cohort, have yielded promising results.

MOTIVATION: Staining the mRNA of a gene via in situ hybridization (ISH) during the development of a Drosophila melanogaster embryo delivers the detailed spatio-temporal patterns of the gene expression. Many related biological problems such as the detection of co-expressed genes, co-regulated genes and transcription factor binding motifs rely heavily on the analysis of these image patterns. To provide the text-based pattern searching for facilitating related biological studies, the images in the Berkeley Drosophila Genome Project (BDGP) study are annotated with developmental stage term and anatomical ontology terms manually by domain experts. Due to the rapid increase in the number of such images and the inevitable bias annotations by human curators, it is necessary to develop an automatic method to recognize the developmental stage and annotate anatomical terms. RESULTS: In this article, we propose a novel computational model for jointly stage classification and anatomical terms annotation of Drosophila gene expression patterns. We propose a novel Tri-Relational Graph (TG) model that comprises the data graph, anatomical term graph, developmental stage term graph, and connect them by two additional graphs induced from stage or annotation label assignments. Upon the TG model, we introduce a Preferential Random Walk (PRW) method to jointly recognize developmental stage and annotate anatomical terms by utilizing the interrelations between two tasks. The experimental results on two refined BDGP datasets demonstrate that our joint learning method can achieve superior prediction results on both tasks than the state-of-the-art methods. AVAILABILITY: http://ranger.uta.edu/%7eheng/Drosophila/.

MOTIVATION: Recent advances in high-throughput genotyping and brain imaging techniques enable new approaches to study the influence of genetic variation on brain structures and functions. Traditional association studies typically employ independent and pairwise univariate analysis, which treats single nucleotide polymorphisms (SNPs) and quantitative traits (QTs) as isolated units and ignores important underlying interacting relationships between the units. New methods are proposed here to overcome this limitation. RESULTS: Taking into account the interlinked structure within and between SNPs and imaging QTs, we propose a novel Group-Sparse Multi-task Regression and Feature Selection (G-SMuRFS) method to identify quantitative trait loci for multiple disease-relevant QTs and apply it to a study in mild cognitive impairment and Alzheimer's disease. Built upon regression analysis, our model uses a new form of regularization, group ℓ(2,1)-norm (G(2,1)-norm), to incorporate the biological group structures among SNPs induced from their genetic arrangement. The new G(2,1)-norm considers the regression coefficients of all the SNPs in each group with respect to all the QTs together and enforces sparsity at the group level. In addition, an ℓ(2,1)-norm regularization is utilized to couple feature selection across multiple tasks to make use of the shared underlying mechanism among different brain regions. The effectiveness of the proposed method is demonstrated by both clearly improved prediction performance in empirical evaluations and a compact set of selected SNP predictors relevant to the imaging QTs. AVAILABILITY: Software is publicly available at: http://ranger.uta.edu/%7eheng/imaging-genetics/.

MOTIVATION: Recent advances in brain imaging and high-throughput genotyping techniques enable new approaches to study the influence of genetic and anatomical variations on brain functions and disorders. Traditional association studies typically perform independent and pairwise analysis among neuroimaging measures, cognitive scores and disease status, and ignore the important underlying interacting relationships between these units. RESULTS: To overcome this limitation, in this article, we propose a new sparse multimodal multitask learning method to reveal complex relationships from gene to brain to symptom. Our main contributions are three-fold: (i) introducing combined structured sparsity regularizations into multimodal multitask learning to integrate multidimensional heterogeneous imaging genetics data and identify multimodal biomarkers; (ii) utilizing a joint classification and regression learning model to identify disease-sensitive and cognition-relevant biomarkers; (iii) deriving a new efficient optimization algorithm to solve our non-smooth objective function and providing rigorous theoretical analysis on the global optimum convergency. Using the imaging genetics data from the Alzheimer's Disease Neuroimaging Initiative database, the effectiveness of the proposed method is demonstrated by clearly improved performance on predicting both cognitive scores and disease status. The identified multimodal biomarkers could predict not only disease status but also cognitive function to help elucidate the biological pathway from gene to brain structure and function, and to cognition and disease. AVAILABILITY: Software is publicly available at: http://ranger.uta.edu/%7eheng/multimodal/.

MOTIVATION: Imaging genetic studies typically focus on identifying single-nucleotide polymorphism (SNP) markers associated with imaging phenotypes. Few studies perform regression of SNP values on phenotypic measures for examining how the SNP values change when phenotypic measures are varied. This alternative approach may have a potential to help us discover important imaging genetic associations from a different perspective. In addition, the imaging markers are often measured over time, and this longitudinal profile may provide increased power for differentiating genotype groups. How to identify the longitudinal phenotypic markers associated to disease sensitive SNPs is an important and challenging research topic. RESULTS: Taking into account the temporal structure of the longitudinal imaging data and the interrelatedness among the SNPs, we propose a novel 'task-correlated longitudinal sparse regression' model to study the association between the phenotypic imaging markers and the genotypes encoded by SNPs. In our new association model, we extend the widely used ℓ(2,1)-norm for matrices to tensors to jointly select imaging markers that have common effects across all the regression tasks and time points, and meanwhile impose the trace-norm regularization onto the unfolded coefficient tensor to achieve low rank such that the interrelationship among SNPs can be addressed. The effectiveness of our method is demonstrated by both clearly improved prediction performance in empirical evaluations and a compact set of selected imaging predictors relevant to disease sensitive SNPs. AVAILABILITY: Software is publicly available at: http://ranger.uta.edu/%7eheng/Longitudinal/ CONTACT: [email protected] or [email protected].

Multi-Instance Learning (MIL) deals with problems where each training example is a bag, and each bag contains a set of instances. Multi-instance representation is useful in many real world applications, because it is able to capture more structural information than traditional flat single-instance representation. However, it also brings new challenges. Specifically, the distance between data objects in MIL is a set-to-set distance, which is harder to estimate than vector distances used in single-instance data. Moreover, because in MIL labels are assigned to bags instead of instances, although a bag belongs to a class, some, or even most, of its instances may not be truly related to the class. In order to address these difficulties, in this paper we propose a novel Instance Specific Distance (ISD) method for MIL, which computes the Class-to-Bag (C2B) distance by further considering the relevances of training instances with respect to their labeled classes. Taking into account the outliers caused by the weak label association in MIL, we learn ISD by solving an l0+-norm minimization problem. An efficient algorithm to solve the optimization problem is presented, together with the rigorous proof of its convergence. The promising results on five benchmark multi-instance data sets and two real world multi-instance applications validate the effectiveness of the proposed method.

The rapid growth of Internet and modern technologies has brought data involving objects of multiple types that are related to each other, called as multi-type relational data. Traditional clustering methods for single-type data rarely work well on them, which calls for more advanced clustering techniques to deal with multiple types of data simultaneously to utilize their interrelatedness. A major challenge in developing simultaneous clustering methods is how to effectively use all available information contained in a multi-type relational data set including inter-type and intra-type relationships. In this paper, we propose a Symmetric Nonnegative Matrix Tri-Factorization (S-NMTF) framework to cluster multi-type relational data at the same time. The proposed S-NMTF approach employs NMTF to simultaneously cluster different types of data using their inter-type relationships, and incorporate the intra-type information through manifold regularization. In order to deal with the symmetric usage of the factor matrix in S-NMTF, we present a new generic matrix inequality to derive the solution algorithm, which involves a fourth-order matrix polynomial, in a principled way. Promising experimental results have validated the proposed approach.

Image annotation is usually formulated as a multi-label semi-supervised learning problem. Traditional graph-based methods only utilize the data (images) graph induced from image similarities, while ignore the label (semantic terms) graph induced from label correlations of a multi-label image data set. In this paper, we propose a novel Bi-relational Graph (BG) model that comprises both the data graph and the label graph as subgraphs, and connect them by an additional bipartite graph induced from label assignments. By considering each class and its labeled images as a semantic group, we perform random walk on the BG to produce group-to-vertex relevance, including class-to-image and class-to-class relevances. The former can be used to predict labels for unannotated images, while the latter are new class relationships, called as Causal Relationships (CR), which are asymmetric. CR is learned from input data and has better semantic meaning to enhance the label prediction for unannotated images. We apply the proposed approaches to automatic image annotation and semantic image retrieval tasks on four benchmark multi-label image data sets. The superior performance of our approaches compared to state-of-the-art multi-label classification methods demonstrate their effectiveness.

In this paper, we propose a novel ℓ1-norm graph model to perform unsupervised and semi-supervised learning methods. Instead of minimizing the ℓ2-norm of spectral embedding as traditional graph based learning methods, our new graph learning model minimizes the ℓ1-norm of spectral embedding with well motivation. The sparsity produced by the ℓ1-norm minimization results in the solutions with much clearer cluster structures, which are suitable for both image clustering and classification tasks. We introduce a new efficient iterative algorithm to solve the ℓ1-norm of spectral embedding minimization problem, and prove the convergence of the algorithm. More specifically, our algorithm adaptively re-weight the original weights of graph to discover clearer cluster structure. Experimental results on both toy data and real image data sets show the effectiveness and advantages of our proposed method.

Because manual image annotation is both expensive and labor intensive, in practice we often do not have sufficient labeled images to train an effective classifier for the new image classification tasks. Although multiple labeled image data sets are publicly available for a number of computer vision tasks, a simple mixture of them cannot achieve good performance due to the heterogeneous properties and structures between different data sets. In this paper, we propose a novel nonnegative matrix tri-factorization based transfer learning framework, called as Dyadic Knowledge Transfer (DKT) approach, to transfer cross-domain image knowledge for the new computer vision tasks, such as classifications. An efficient iterative algorithm to solve the proposed optimization problem is introduced. We perform the proposed approach on two benchmark image data sets to simulate the real world cross-domain image classification tasks. Promising experimental results demonstrate the effectiveness of the proposed approach.

Alzheimer's disease (AD) is a neurodegenerative disorder characterized by progressive impairment of memory and other cognitive functions, which makes regression analysis a suitable model to study whether neuroimaging measures can help predict memory performance and track the progression of AD. Existing memory performance prediction methods via regression, however, do not take into account either the interconnected structures within imaging data or those among memory scores, which inevitably restricts their predictive capabilities. To bridge this gap, we propose a novel Sparse Multi-tAsk Regression and feaTure selection (SMART) method to jointly analyze all the imaging and clinical data under a single regression framework and with shared underlying sparse representations. Two convex regularizations are combined and used in the model to enable sparsity as well as facilitate multi-task learning. The effectiveness of the proposed method is demonstrated by both clearly improved prediction performances in all empirical test cases and a compact set of selected RAVLT-relevant MRI predictors that accord with prior studies.

The fast growth of Internet and modern technologies has brought data involving objects of multiple types that are related to each other, called as Multi-Type Relational data. Traditional clustering methods for single-type data rarely work well on them, which calls for new clustering techniques, called as high-order co-clustering (HOCC), to deal with the multiple types of data at the same time. A major challenge in developing HOCC methods is how to effectively make use of all available information contained in a multi-type relational data set, including both inter-type and intra-type relationships. Meanwhile, because many real world data sets are often of large sizes, clustering methods with computationally efficient solution algorithms are of great practical interest. In this paper, we first present a general HOCC framework, named as Orthogonal Nonnegative Matrix Tri-factorization (O-NMTF), for simultaneous clustering of multi-type relational data. The proposed O-NMTF approach employs Nonnegative Matrix Tri-Factorization (NMTF) to simultaneously cluster different types of data using the inter-type relationships, and incorporate intra-type information through manifold regularization, where, different from existing works, we emphasize the importance of the orthogonal ties of the factor matrices of NMTF. Based on O-NMTF, we further develop a novel Fast Nonnegative Matrix Tri-Factorization (F-NMTF) approach to deal with large-scale data. Instead of constraining the factor matrices of NMTF to be nonnegative as in existing methods, F-NMTF constrains them to be cluster indicator matrices, a special type of nonnegative matrices. As a result, the optimization problem of the proposed method can be decoupled, which results in sub problems of much smaller sizes requiring much less matrix multiplications, such that our new algorithm scales well to real world data of large sizes. Extensive experimental evaluations have demonstrated the effectiveness of our new approaches.

Traditional video classification methods typically require a large number of labeled training video frames to achieve satisfactory performance. However, in the real world, we usually only have sufficient labeled video clips (such as tagged online videos) but lack labeled video frames. In this paper, we formalize the video classification problem as a Multi-Instance Learning (MIL) problem, an emerging topic in machine learning in recent years, which only needs bag (video clip) labels. To solve the problem, we propose a novel Parameterized Class-to-Bag (P-C2B) Distance method to learn the relative importance of a training instance with respect to its labeled classes, such that the instance level labeling ambiguity in MIL is tackled and the frame relevances of training video data with respect to the semantic concepts of interest are given. Promising experimental results have demonstrated the effectiveness of the proposed method.

Multi-instance learning (MIL) considers input as bags of instances, in which labels are assigned to the bags. MIL is useful in many real-world applications. For example, in image categorization semantic meanings (labels) of an image mostly arise from its regions (instances) instead of the entire image (bag). Existing MIL methods typically build their models using the Bag-to-Bag (B2B) distance, which are often computationally expensive and may not truly reflect the semantic similarities. To tackle this, in this paper we approach MIL problems from a new perspective using the Class-to-Bag (C2B) distance, which directly assesses the relationships between the classes and the bags. Taking into account the two major challenges in MIL, high heterogeneity on data and weak label association, we propose a novel Maximum Margin Multi-Instance Learning (M3 I) approach to parameterize the C2B distance by introducing the class specific distance metrics and the locally adaptive significance coefficients. We apply our new approach to the automatic image categorization tasks on three (one single-label and two multilabel) benchmark data sets. Extensive experiments have demonstrated promising results that validate the proposed method.

The lack of sufficient labeled Web pages in many languages, especially for those uncommonly used ones, presents a great challenge to traditional supervised classification methods to achieve satisfactory Web page classification performance. To address this, we propose a novel Nonnegative Matrix Tri-factorization (NMTF) based Dual Knowledge Transfer (DKT) approach for cross-language Web page classification, which is based on the following two important observations. First, we observe that Web pages for a same topic from different languages usually share some common semantic patterns, though in different representation forms. Second, we also observe that the associations between word clusters and Web page classes are a more reliable carrier than raw words to transfer knowledge across languages. With these recognitions, we attempt to transfer knowledge from the auxiliary language, in which abundant labeled Web pages are available, to target languages, in which we want classify Web pages, through two different paths: word cluster approximations and the associations between word clusters and Web page classes. Due to the reinforcement between these two different knowledge transfer paths, our approach can achieve better classification accuracy. We evaluate the proposed approach in extensive experiments using a real world cross-language Web page data set. Promising results demonstrate the effectiveness of our approach that is consistent with our theoretical analyses.

Many existing approaches employ one-vs-rest method to decompose a multi-label classification problem into a set of 2- class classification problems, one for each class. This method is valid in traditional single-label classification, it, however, incurs training inconsistency in multi-label classification, because in the latter a data point could belong to more than one class. In order to deal with this problem, in this work, we further develop classicalK-Nearest Neighbor classifier and propose a novel Class Balanced K-Nearest Neighbor approach for multi-label classification by emphasizing balanced usage of data from all the classes. In addition, we also propose a Class Balanced Linear Discriminant Analysis approach to address high-dimensional multi-label input data. Promising experimental results on three broadly used multi-label data sets demonstrate the effectiveness of our approach.

Many real life applications brought by modern technologies often have multiple data sources, which are usually characterized by both attributes and pairwise similarities at the same time. For example in webpage ranking, a webpage is usually represented by a vector of term values, and meanwhile the internet linkages induce pairwise similarities among the webpages. Although both attributes and pairwise similarities are useful for class membership inference, many traditional embedding algorithms only deal with one type of input data. In order to make use of the both types of data simultaneously, in this work, we propose a novel Discriminant Laplacian Embedding (DLE) approach. Supervision information from training data are integrated into DLE to improve the discriminativity of the resulted embedding space. By solving the ambiguity problem in computing the scatter matrices caused by data points with multiple labels, we successfully extend the proposed DLE to multi-label classification. In addition, through incorporating the label correlations, the classification performance using multi-label DLE is further enhanced. Promising experimental results in extensive empirical evaluations have demonstrated the effectiveness of our approaches.

Image annotation has been an active research topic in the recent years due to its potentially large impact on both image understanding and web/database image search. In this paper, we target at solving the automatic image annotation problem in a novel semi-supervised learning framework. A novel multi-label correlated Green's function approach is proposed to annotate images over a graph. The correlations among labels are integrated into the objective function which improves the performance significantly. We also propose a new adaptive decision boundary method for multi-label assignment to deal with the difficulty of label assignment in most of the existing rank-based multi-label classification algorithms. Instead of setting the threshold heuristically or by experience, our method principally compute it upon the prior knowledge in the training data. We perform our methods on three commonly used image annotation testing data sets. Experimental results show significant improvements on classification performance over four other state-of-the-art methods. As a general semi-supervised learning framework, other local feature based image annotation methods could be easily incorporated into our framework to improve the performance.