Majority subspace clustering (SC) algorithms depend on one or more hyperparameters that need to be tuned for the SC algorithms to achieve high clustering performance. This is often performed using grid-search, assuming that held out set is available. In some domains, such as medicine, this assumption does not hold true in many cases. To address this problem, we propose an approach to label-independent hyperparameter optimization by applying the SC algorithm to the data and use the resulting cluster assignments as pseudo-labels to compute clustering quality metrics (e.g., accuracy (ACC) or normalized mutual information (NMI)) across a predefined hyperparameter grid. Assuming that ACC (or NMI) is a smooth function of hyperparameter values, it is possible to select subintervals of hyperparameters, which are then iteratively further split into halves or thirds until a relative error criterion is satisfied. In principle, the hyperparameters of any SC algorithm can be tuned using the proposed method. We demonstrate this approach on five single-view SC algorithms and two multi-view SC algorithms, comparing the achieved performance with their oracle versions across six datasets for single-view algorithms and three datasets for multi-view algorithms. The proposed method typically achieves clustering performance that is up to 7% lower than that of the oracle versions. We also enhance the interpretability of the proposed method by visualizing subspace bases, estimated from the computed clustering partitions. This aids in the initial selection of the hyperparameter search space.

Kernel methods are widely used in pattern recognition, including subspace clustering (SC). They transform nonlinear problems in the input data space into linear ones in a high-dimensional feature space. This transformation, achieved through the kernel trick, makes computationally tractable nonlinear algorithms possible. However, kernelizing linear algorithms through the kernel trick is infeasible in case of gross sparse corruptions that are modeled by the ℓ1-norm of the error term. To address this, we propose, for the first time, a robust kernel sparse SC (RKSSC) algorithm for data with gross sparse corruptions. We validated the proposed approach on two well-known datasets, using the linear robust SSC algorithm and nonlinear (kernel-based) SSC algorithm as baseline models. According to the Wilcoxon test, the RKSSC's algorithm clustering performance is statistically significantly better than baselines.

Hyperspectral image (HSI) Clustering is an unsupervised task, which segments pixels into different groups without using labeled samples. Low-rank sparse subspace clustering (LRSSC) is often applied to achieve the clustering of high-dimensional data such as HSI. The LRSSC combines low-rank recovery and sparse representation to capture both global and local structures of the data. Nuclear and Li-norm are often used to measure rank and sparsity in LRSSC since minimization of these two norms results in a convex optimization problem. However, the use of Nuclear and L1-norm can only approximate the original problem, and may lead to over-penalization. Thus, the direct solution of a Schatten-0 (So) and Lo quasi-norm regularized objective function has been proposed in the LRSSC for more accurate representation. This paper proposes to use the So/Lo-regulared LRSSC (So/Lo-LRSSC) for hyperspectral image clustering. To accommodate the large data size, an original HSI is pre-partitioned, and the Sn/Ln-LRSSC is implemented in a distributed way. Our experiments show that the performance of the So/Lo-LRSSC in hyperspectral image clustering is better than the original LRSSC and its variants based on Nuclear and L1-norm minimization.

In many applications, high-dimensional data points can be well represented by low-dimensional subspaces. To identify the subspaces, it is important to capture a global and local structure of the data which is achieved by imposing low-rank and sparseness constraints on the data representation matrix. In low-rank sparse subspace clustering (LRSSC), nuclear and ℓ1-norms are used to measure rank and sparsity. However, the use of nuclear and ℓ1-norms leads to an overpenalized problem and only approximates the original problem. In this paper, we propose two ℓ0quasi-norm-based regularizations. First, this paper presents regularization based on multivariate generalization of minimax-concave penalty (GMC-LRSSC), which contains the global minimizers of a ℓ0quasi-norm regularized objective. Afterward, we introduce the Schatten-0 (S0) and ℓ0-regularized objective and approximate the proximal map of the joint solution using a proximal average method (S0/ℓ0-LRSSC). The resulting nonconvex optimization problems are solved using an alternating direction method of multipliers with established convergence conditions of both algorithms. Results obtained on synthetic and four real-world datasets show the effectiveness of GMC-LRSSC and S0/ℓ0-LRSSC when compared to state-of-the-art methods.

As an unsupervised task, hyperspectral image (HSI) clustering separates pixels into different groups. In this paper, an orthogonal graph-regularized non-negative matrix factorization (OGNMF) algorithm is proposed for HSI clustering. Because of large size of HSI, the HSI clustering problem is computational consuming. On the other hand, non-negative matrix factorization (NMF), which is a popular multivariate analysis method, has related to light computation budget. Furthermore, the orthogonal and graph regularization, which can improve the clustering performance and capture the local structure features, are applied to NMF for better performance in HSI. Moreover, both spatial and spectral information are extracted and utilized. Our experiments show that the performance of the proposed OGNMF is better than the NMF and ONMF algorithms in HSI clustering.

Hyperspectral image (HSI) Clustering is an unsupervised task, which segments pixels into different groups without using labeled samples. In this paper, spatial-spectral based multi-view low-rank sparse subspace clustering (SSMLC) algorithm is proposed. Due to significant number of spectra bands HSI contains much more information than a regular image. These spectral information can be considered as multiview. In this paper, the spectral partitioning is applied to generate spectral views which contain correlated bands. Morphological features of the original HSI are taken as another view which contains spatial features. Principal components construct another view, which eliminates the noise in the original dataset. After the multi-view dataset is formed, multi-view low-rank sparse subspace clustering is applied to segment HSI. Our experiments show that the performance of the proposed SSMLC is better than other that of clustering algorithms such as sparse subspace clustering and low-rank sparse subspace clustering.

In this paper, the tensor-based offset-sparsity decomposition (TOSD) method, or low-rank and sparse decomposition, is applied to hyperspectral imagery, where the low-rank tensor is considered to be enhanced or pruned data and used for classification. In the tensor form of dataset, all the information of the original 3D data cube, includes spatial and spectral information, can be better reserved. To make the low-rank assumption more possibly true, spatial and spectral segmentations are conducted in a preprocessing step for the TOSD. The experimental results demonstrate the TOSD offers better performance than the matrix-based one, and the spatial-spectral segmentation can further improve the performance.

In this paper, we propose a novel method for single-channel blind separation of nonoverlapped sources and, to the best of our knowledge, apply it for the first time to automatic segmentation of lung tumors in positron emission tomography (PET) images. Our approach first converts a 3-D PET image into a pseudo-multichannel image. Afterward, regularization free sparseness constrained non-negative matrix factorization is used to separate tumor from other tissues. By using complexity based criterion, we select tumor component as the one with minimal complexity. We have compared the proposed method with threshold based on 40% and 50% maximum standardized uptake value (SUV), graph cuts (GC), random walks (RW), and affinity propagation (AP) algorithms on 18 nonsmall cell lung cancer datasets with respect to ground truth (GT) provided by two radiologists. Dice similarity coefficient averaged with respect to two GTs is: 0.78 ± 0.12 by the proposed algorithm, 0.78 ± 0.1 by GC, 0.77 ± 0.13 by AP, 0.77 ± 0.07 by RW, and 0.75 ± 0.13 by 50% maximum SUV threshold. Since the proposed method achieved performance comparable with interactive methods, considering the unique challenges of lung tumor segmentation from PET images, our findings support possibility of using our fully automated method in routine clinics. The source codes will be available at www.mipav.net/English/research/research.html.

In this paper, the extended offset-sparsity decomposition (OSD) method is applied to multispectral image enhancement. Both principle component analysis (PCA) and hue-saturation-value (HSV) transform are considered before the single-band-based OSD is deployed. The objective is to enhance image details while maintaining the original spectral information. Spectral angle is used to evaluate spectral fidelity, while the extended sharpness and contrast quality measurements are for spatial quality assessment. The experimental results demonstrate that extended OSD with HSV offers better performance of enhancement with acceptable spectral distortion.

In the above-named work, the spelling of the second author’s name was incorrect. The correct spelling is given.

Estimation of pure spectral signatures, called endmembers, is a key step in hyperspectral image (HI) analysis. We propose endmembers estimation method that uses Gabor Filter Banks (GFBs) to filter HI into set of HIs with different resolutions and orientations. Afterwards, set of approximate pure pixels is identified from each filtered HI by means of directivity based criterion. Hierarchical clustering is used to estimate candidate endmembers from sets of approximate pure pixels. Final estimate of endmembers is obtained after annotation of candidate endmembers with library of pure spectral signatures. Thereby, candidate with the smallest angular deviation with respect to corresponding pure spectra is selected as endmember estimate. Proposed method is compared favorably with five endmembers estimation methods using well-understood experimental AVIRIS Cuprite Nevada dataset.

Accurate lung tumor delineation plays an important role in radiotherapy treatment planning. Since the lung tumor has poor boundary in positron emission tomography (PET) images and low contrast in computed tomography (CT) images, segmentation of tumor in the PET and CT images is a challenging task. In this paper, we effectively integrate the two modalities by making fully use of the superior contrast of PET images and superior spatial resolution of CT images. Random walk and graph cut method is integrated to solve the segmentation problem, in which random walk is utilized as an initialization tool to provide object seeds for graph cut segmentation on the PET and CT images. The co-segmentation problem is formulated as an energy minimization problem which is solved by max-flow/min-cut method. A graph, including two sub-graphs and a special link, is constructed, in which one sub-graph is for the PET and another is for CT, and the special link encodes a context term which penalizes the difference of the tumor segmentation on the two modalities. To fully utilize the characteristics of PET and CT images, a novel energy representation is devised. For the PET, a downhill cost and a 3D derivative cost are proposed. For the CT, a shape penalty cost is integrated into the energy function which helps to constrain the tumor region during the segmentation. We validate our algorithm on a data set which consists of 18 PET-CT images. The experimental results indicate that the proposed method is superior to the graph cut method solely using the PET or CT is more accurate compared with the random walk method, random walk co-segmentation method, and non-improved graph cut method.

In tensor factorization approach to blind separation of multidimensional sources two formulas for calculating the source tensor have emerged. In practice, it is observed that these two schemes exhibit different levels of robustness against perturbations of the factors involved in the tensor model. Motivated by both practical reasons and the will to better figure this out, we present error analyses in source tensor estimation performed by low-rank factorization of three-way tensors. To that aim, computer simulations as well as the analytical calculation of the theoretical error are carried out. The conclusions drawn from these numerical and analytical error analyses are supported by the results obtained thanks to the tensor factorization based blind decomposition of an experimental multispectral image of a skin tumor.

BACKGROUND: Bioinformatics data analysis is often using linear mixture model representing samples as additive mixture of components. Properly constrained blind matrix factorization methods extract those components using mixture samples only. However, automatic selection of extracted components to be retained for classification analysis remains an open issue. RESULTS: The method proposed here is applied to well-studied protein and genomic datasets of ovarian, prostate and colon cancers to extract components for disease prediction. It achieves average sensitivities of: 96.2 (sd = 2.7%), 97.6% (sd = 2.8%) and 90.8% (sd = 5.5%) and average specificities of: 93.6% (sd = 4.1%), 99% (sd = 2.2%) and 79.4% (sd = 9.8%) in 100 independent two-fold cross-validations. CONCLUSIONS: We propose an additive mixture model of a sample for feature extraction using, in principle, sparseness constrained factorization on a sample-by-sample basis. As opposed to that, existing methods factorize complete dataset simultaneously. The sample model is composed of a reference sample representing control and/or case (disease) groups and a test sample. Each sample is decomposed into two or more components that are selected automatically (without using label information) as control specific, case specific and not differentially expressed (neutral). The number of components is determined by cross-validation. Automatic assignment of features (m/z ratios or genes) to particular component is based on thresholds estimated from each sample directly. Due to the locality of decomposition, the strength of the expression of each feature across the samples can vary. Yet, they will still be allocated to the related disease and/or control specific component. Since label information is not used in the selection process, case and control specific components can be used for classification. That is not the case with standard factorization methods. Moreover, the component selected by proposed method as disease specific can be interpreted as a sub-mode and retained for further analysis to identify potential biomarkers. As opposed to standard matrix factorization methods this can be achieved on a sample (experiment)-by-sample basis. Postulating one or more components with indifferent features enables their removal from disease and control specific components on a sample-by-sample basis. This yields selected components with reduced complexity and generally, it increases prediction accuracy.

Exploiting hyperspectral imagery without prior information is a challenge. Under this circumstance, unsupervised target detection becomes an anomaly detection problem. We propose an effective algorithm for target detection and discrimination based on the normalized fourth central moment named kurtosis, which can measure the flatness of a distribution. Small targets in hyperspectral imagery contribute to the tail of a distribution, thus making it heavier. The Gaussian distribution is completely determined by the first two order statistics and has zero kurtosis. Consequently, kurtosis measures the deviation of a distribution from the background and is suitable for anomaly/target detection. When imposing appropriate inequality constraints on the kurtosis to be maximized, the resulting constrained kurtosis maximization (CKM) algorithm will be able to quickly detect small targets with several projections. Compared to the widely used unconstrained kurtosis maximization algorithm, i.e., fast independent component analysis, the CKM algorithm may detect small targets with fewer projections and yield a slightly higher detection rate.

Blind source separation (BSS) problem is commonly solved by means of independent component analysis (ICA) assuming statistically independent and non-Gaussian sources. The strict independence assumption can be relaxed to existence of subbands where signals are less dependent. In this paper, we use dual tree complex wavelets for the subband decomposition of observed signals and small cummulant based approximation of mutual information for finding the most independent subband(s). We compare the proposed method to previously reported shift invariant and decimated wavelet packet based approach, as well as to innovations based approach. We found proposed dual tree wavelets scheme as an efficient and robust solution of the BSS problem of statistically dependent sources. One important application of the proposed method is related to unsupervised segmentation of medical and remotely sensed multispectral images.

Matrix factorization is applied to unsupervised linear unmixing for hyperspectral imagery. The algorithm, called nonnegative matrix factorization, is used. It imposes a constraint on the non-negativity of the amplitudes of the recovered endmember spectral signatures as well as their fractional abundances. This ensures the recovery of physically meaningful endmembers and their abundances. This algorithm is further modified to include the sum-to-one constraint such that the sum of the fractional abundances for each pixel is unity. Several practical implementation issues in hyperspectral image unmixng are discussed. Some preliminary results from AVIRIS experiments are presented. We also discuss the advantages and possible limitations of this method in hyperspectral image analysis.

In multiple access communication, an addressing code - encapsulated information of senders or receivers - is essential for a correct data communication. However, it occupies a part of the data payload which causes a reduction in bandwidth utilization. This may not be a problem provided that the communications channel has a large bandwidth. The code division multiple access (CDMA) can encapsulate the code without occupying any data payload. However, many communication channels have, due to their physical characteristics, a small available bandwidth, which makes them unsuitable for CDMA. The low-frequency-band powerlines (<0.5 MHz) is an example of such a channel because such lines are not designed for data transmission purposes. Usage of the low frequency band, however, makes the system insensitive to the structure of the power grid, where many locations do not lend themselves to modification of the network. This paper describes an idea of communications without addressing in the low-frequency-band powerline network (<0.5 MHz) using finite alphabet signals and underdetermined blind signal separation (uBSS). The paper also presents a possible application of biomimetic intelligence for a surveillance system and a smart sensor web in the legacy powerlines.

We revisited the Cauchy machine for solving blind space-variant imaging problem on the pixel-by-pixel basis. Under-determinacy of the pixel by pixel blind matrix inversion was accomplished non-statistically by a dynamic balance by minimizing the thermodynamics free energy H = U-T/sub 0/S where U is estimation error energy, T/sub 0/ is temperature and S is the entropy. Solution was found through algorithm that computes the unknown source vector and unknown mixing matrix using Cauchy machine to find the global minimum of H for each pixel. We demonstrated the algorithm capability to perfectly recover images from the noise free linear mixture of images. Capability of the Cauchy machine to find the global minimum of the 'golf hole' type of landscape has been demonstrated in higher dimensions with a less computation complexity than an exhaustive search algorithm.