Dual Shared-Specific Multiview Subspace Clustering

Partial Tubal Nuclear Norm-Regularized Multiview Subspace Learning

In this article, a unified multiview subspace learning model, called partial tubal nuclear norm-regularized multiview subspace learning (PTN2MSL), was proposed for unsupervised multiview subspace clustering (MVSC), semisupervised MVSC, and multiview dimension reduction. Unlike most of the existing methods which treat the above three related tasks independently, PTN2MSL integrates the projection learning and the low-rank tensor representation to promote each other and mine their underlying correlations. Moreover, instead of minimizing the tensor nuclear norm which treats all singular values equally and neglects their differences, PTN2MSL develops the partial tubal nuclear norm (PTNN) as a better alternative solution by minimizing the partial sum of tubal singular values. The PTN2MSL method was applied to the above three multiview subspace learning tasks. It demonstrated that these tasks organically benefited from each other and PTN2MSL has achieved better performance in comparison to state-of-the-art methods.

Learning deep representation and discriminative features for clustering of multi-layer networks

The multi-layer network consists of the interactions between different layers, where each layer of the network is depicted as a graph, providing a comprehensive way to model the underlying complex systems. The layer-specific modules of multi-layer networks are critical to understanding the structure and function of the system. However, existing methods fail to characterize and balance the connectivity and specificity of layer-specific modules in networks because of the complicated inter- and intra-coupling of various layers. To address the above issues, a joint learning graph clustering algorithm (DRDF) for detecting layer-specific modules in multi-layer networks is proposed, which simultaneously learns the deep representation and discriminative features. Specifically, DRDF learns the deep representation with deep nonnegative matrix factorization, where the high-order topology of the multi-layer network is gradually and precisely characterized. Moreover, it addresses the specificity of modules with discriminative feature learning, where the intra-class compactness and inter-class separation of pseudo-labels of clusters are explored as self-supervised information, thereby providing a more accurate method to explicitly model the specificity of the multi-layer network. Finally, DRDF balances the connectivity and specificity of layer-specific modules with joint learning, where the overall objective of the graph clustering algorithm and optimization rules are derived. The experiments on ten multi-layer networks showed that DRDF not only outperforms eight baselines on graph clustering but also enhances the robustness of algorithms.

Multiview Subspace Clustering With Multilevel Representations and Adversarial Regularization

Multiview subspace clustering has turned into a promising technique due to its encouraging ability to discover the underlying subspace structure. In recent studies, a lot of subspace clustering methods have been developed to strengthen the clustering performance of multiview data, but these methods rarely consider simultaneously the nonlinear structure and multilevel representation (MLR) information in multiview data as well as the data distribution of latent representation. To address these problems, we develop a new Multiview Subspace Clustering with MLRs and Adversarial Regularization (MvSC-MRAR), where multiple deep auto-encoders are utilized to model nonlinear structure information of multiview data, multiple self-expressive layers are introduced into each deep auto-encoder to extract multilevel latent representations of each view data, and diversity regularizations are designed to preserve complementary information contained in different layers and different views. Furthermore, a universal discriminator based on adversarial training is developed to enforce the output of each encoder to obey a given prior distribution, so that the affinity matrix for spectral clustering (SPC) is more realistic. Comprehensive empirical evaluation with nine real-world multiview datasets indicates that our proposed MvSC-MRAR achieves significant improvements than several state-of-the-art methods in terms of clustering accuracy (ACC) and normalized mutual information (NMI).

Consistency-Induced Multiview Subspace Clustering

Multiview clustering has received great attention and numerous subspace clustering algorithms for multiview data have been presented. However, most of these algorithms do not effectively handle high-dimensional data and fail to exploit consistency for the number of the connected components in similarity matrices for different views. In this article, we propose a novel consistency-induced multiview subspace clustering (CiMSC) to tackle these issues, which is mainly composed of structural consistency (SC) and sample assignment consistency (SAC). To be specific, SC aims to learn a similarity matrix for each single view wherein the number of connected components equals to the cluster number of the dataset. SAC aims to minimize the discrepancy for the number of connected components in similarity matrices from different views based on the SAC assumption, that is, different views should produce the same number of connected components in similarity matrices. CiMSC also formulates cluster indicator matrices for different views, and shared similarity matrices simultaneously in an optimization framework. Since each column of similarity matrix can be used as a new representation of the data point, CiMSC can learn an effective subspace representation for the high-dimensional data, which is encoded into the latent representation by reconstruction in a nonlinear manner. We employ an alternating optimization scheme to solve the optimization problem. Experiments validate the advantage of CiMSC over 12 state-of-the-art multiview clustering approaches, for example, the accuracy of CiMSC is 98.06% on the BBCSport dataset.

Adaptive risk-aware sharable and individual subspace learning for cancer survival analysis with multi-modality data

Biomedical multi-modality data (also named multi-omics data) refer to data that span different types and derive from multiple sources in clinical practices (e.g. gene sequences, proteomics and histopathological images), which can provide comprehensive perspectives for cancers and generally improve the performance of survival models. However, the performance improvement of multi-modality survival models may be hindered by two key issues as follows: (1) how to learn and fuse modality-sharable and modality-individual representations from multi-modality data; (2) how to explore the potential risk-aware characteristics in each risk subgroup, which is beneficial to risk stratification and prognosis evaluation. Additionally, learning-based survival models generally refer to numerous hyper-parameters, which requires time-consuming parameter setting and might result in a suboptimal solution. In this paper, we propose an adaptive risk-aware sharable and individual subspace learning method for cancer survival analysis. The proposed method jointly learns sharable and individual subspaces from multi-modality data, whereas two auxiliary terms (i.e. intra-modality complementarity and inter-modality incoherence) are developed to preserve the complementary and distinctive properties of each modality. Moreover, it equips with a grouping co-expression constraint for obtaining risk-aware representation and preserving local consistency. Furthermore, an adaptive-weighted strategy is employed to efficiently estimate crucial parameters during the training stage. Experimental results on three public datasets demonstrate the superiority of our proposed model.

Consistency and Diversity Induced Human Motion Segmentation

Subspace clustering is a classical technique that has been widely used for human motion segmentation and other related tasks. However, existing segmentation methods often cluster data without guidance from prior knowledge, resulting in unsatisfactory segmentation results. To this end, we propose a novel Consistency and Diversity induced human Motion Segmentation (CDMS) algorithm. Specifically, our model factorizes the source and target data into distinct multi-layer feature spaces, in which transfer subspace learning is conducted on different layers to capture multi-level information. A multi-mutual consistency learning strategy is carried out to reduce the domain gap between the source and target data. In this way, the domain-specific knowledge and domain-invariant properties can be explored simultaneously. Besides, a novel constraint based on the Hilbert Schmidt Independence Criterion (HSIC) is introduced to ensure the diversity of multi-level subspace representations, which enables the complementarity of multi-level representations to be explored to boost the transfer learning performance. Moreover, to preserve the temporal correlations, an enhanced graph regularizer is imposed on the learned representation coefficients and the multi-level representations of the source data. The proposed model can be efficiently solved using the Alternating Direction Method of Multipliers (ADMM) algorithm. Extensive experimental results on public human motion datasets demonstrate the effectiveness of our method against several state-of-the-art approaches.

Multiview Subspace Clustering Using Low-Rank Representation

Multiview subspace clustering is one of the most widely used methods for exploiting the internal structures of multiview data. Most previous studies have performed the task of learning multiview representations by individually constructing an affinity matrix for each view without simultaneously exploiting the intrinsic characteristics of multiview data. In this article, we propose a multiview low-rank representation (MLRR) method to comprehensively discover the correlation of multiview data for multiview subspace clustering. MLRR considers symmetric low-rank representations (LRRs) to be an approximately linear spatial transformation under the new base, that is, the multiview data themselves, to fully exploit the angular information of the principal directions of LRRs, which is adopted to construct an affinity matrix for multiview subspace clustering, under a symmetric condition. MLRR takes full advantage of LRR techniques and a diversity regularization term to exploit the diversity and consistency of multiple views, respectively, and this method simultaneously imposes a symmetry constraint on LRRs. Hence, the angular information of the principal directions of rows is consistent with that of columns in symmetric LRRs. The MLRR model can be efficiently calculated by solving a convex optimization problem. Moreover, we present an intuitive fusion strategy for symmetric LRRs from the perspective of spectral clustering to obtain a compact representation, which can be shared by multiple views and comprehensively represents the intrinsic features of multiview data. Finally, the experimental results based on benchmark datasets demonstrate the effectiveness and robustness of MLRR compared with several state-of-the-art multiview subspace clustering algorithms.

Progressive Self-Supervised Clustering With Novel Category Discovery

These days, clustering is one of the most classical themes to analyze data structures in machine learning and pattern recognition. Recently, the anchor-based graph has been widely adopted to promote the clustering accuracy of plentiful graph-based clustering techniques. In order to achieve more satisfying clustering performance, we propose a novel clustering approach referred to as the progressive self-supervised clustering method with novel category discovery (PSSCNCD), which consists of three separate procedures specifically. First, we propose a new semisupervised framework with novel category discovery to guide label propagation processing, which is reinforced by the parameter-insensitive anchor-based graph obtained from balanced K -means and hierarchical K -means (BKHK). Second, we design a novel representative point selected strategy based on our semisupervised framework to discover each representative point and endow pseudolabel progressively, where every pseudolabel hypothetically corresponds to a real category in each self-supervised label propagation. Third, when sufficient representative points have been found, the labels of all samples will be finally predicted to obtain terminal clustering results. In addition, the experimental results on several toy examples and benchmark data sets comprehensively demonstrate that our method outperforms other clustering approaches.

Adversarial Incomplete Multiview Subspace Clustering Networks

Multiview clustering aims to leverage information from multiple views to improve the clustering performance. Most previous works assumed that each view has complete data. However, in real-world datasets, it is often the case that a view may contain some missing data, resulting in the problem of incomplete multiview clustering (IMC). Previous approaches to this problem have at least one of the following drawbacks: 1) employing shallow models, which cannot well handle the dependence and discrepancy among different views; 2) ignoring the hidden information of the missing data; and 3) being dedicated to the two-view case. To eliminate all these drawbacks, in this work, we present the adversarial IMC (AIMC) framework. In particular, AIMC seeks the common latent representation of multiview data for reconstructing raw data and inferring missing data. The elementwise reconstruction and the generative adversarial network are integrated to evaluate the reconstruction. They aim to capture the overall structure and get a deeper semantic understanding, respectively. Moreover, the clustering loss is designed to obtain a better clustering structure. We explore two variants of AIMC, namely: 1) autoencoder-based AIMC (AAIMC) and 2) generalized AIMC (GAIMC), with different strategies to obtain the multiview common representation. Experiments conducted on six real-world datasets show that AAIMC and GAIMC perform well and outperform the baseline methods.

Large-Scale Subspace Clustering by Independent Distributed and Parallel Coding

Subspace clustering is a popular method to discover underlying low-dimensional structures of high-dimensional multimedia data (e.g., images, videos, and texts). In this article, we consider a large-scale subspace clustering (LS²C) problem, that is, partitioning million data points with a millon dimensions. To address this, we explore an independent distributed and parallel framework by dividing big data/variable matrices and regularization by both columns and rows. Specifically, LS²C is independently decomposed into many subproblems by distributing those matrices into different machines by columns since the regularization of the code matrix is equal to a sum of that of its submatrices (e.g., square-of-Frobenius/ l₁ -norm). Consensus optimization is designed to solve these subproblems in a parallel way for saving communication costs. Moreover, we provide theoretical guarantees that LS²C can recover consensus subspace representations of high-dimensional data points under broad conditions. Compared with the state-of-the-art LS²C methods, our approach achieves better clustering results in public datasets, including a million images and videos.

One-Step Multiview Subspace Segmentation via Joint Skinny Tensor Learning and Latent Clustering

Multiview subspace clustering (MSC) has attracted growing attention due to the extensive value in various applications, such as natural language processing, face recognition, and time-series analysis. In this article, we are devoted to address two crucial issues in MSC: 1) high computational cost and 2) cumbersome multistage clustering. Existing MSC approaches, including tensor singular value decomposition (t-SVD)-MSC that has achieved promising performance, generally utilize the dataset itself as the dictionary and regard representation learning and clustering process as two separate parts, thus leading to the high computational overhead and unsatisfactory clustering performance. To remedy these two issues, we propose a novel MSC model called joint skinny tensor learning and latent clustering (JSTC), which can learn high-order skinny tensor representations and corresponding latent clustering assignments simultaneously. Through such a joint optimization strategy, the multiview complementary information and latent clustering structure can be exploited thoroughly to improve the clustering performance. An alternating direction minimization algorithm, which owns low computational complexity and can be run in parallel when solving several key subproblems, is carefully designed to optimize the JSTC model. Such a nice property makes our JSTC an appealing solution for large-scale MSC problems. We conduct extensive experiments on ten popular datasets and compare our JSTC with 12 competitors. Five commonly used metrics, including four external measures (NMI, ACC, F-score, and RI) and one internal metric (SI), are adopted to evaluate the clustering quality. The experimental results with the Wilcoxon statistical test demonstrate the superiority of the proposed method in both clustering performance and operational efficiency.

Multiview Subspace Clustering With Grouping Effect

Multiview subspace clustering (MVSC) is a recently emerging technique that aims to discover the underlying subspace in multiview data and thereby cluster the data based on the learned subspace. Though quite a few MVSC methods have been proposed in recent years, most of them cannot explicitly preserve the locality in the learned subspaces and also neglect the subspacewise grouping effect, which restricts their ability of multiview subspace learning. To address this, in this article, we propose a novel MVSC with grouping effect (MvSCGE) approach. Particularly, our approach simultaneously learns the multiple subspace representations for multiple views with smooth regularization, and then exploits the subspacewise grouping effect in these learned subspaces by means of a unified optimization framework. Meanwhile, the proposed approach is able to ensure the cross-view consistency and learn a consistent cluster indicator matrix for the final clustering results. Extensive experiments on several benchmark datasets have been conducted to validate the superiority of the proposed approach.

Improving EEG Decoding via Clustering-Based Multitask Feature Learning

Accurate electroencephalogram (EEG) pattern decoding for specific mental tasks is one of the key steps for the development of brain-computer interface (BCI), which is quite challenging due to the considerably low signal-to-noise ratio of EEG collected at the brain scalp. Machine learning provides a promising technique to optimize EEG patterns toward better decoding accuracy. However, existing algorithms do not effectively explore the underlying data structure capturing the true EEG sample distribution and, hence, can only yield a suboptimal decoding accuracy. To uncover the intrinsic distribution structure of EEG data, we propose a clustering-based multitask feature learning algorithm for improved EEG pattern decoding. Specifically, we perform affinity propagation-based clustering to explore the subclasses (i.e., clusters) in each of the original classes and then assign each subclass a unique label based on a one-versus-all encoding strategy. With the encoded label matrix, we devise a novel multitask learning algorithm by exploiting the subclass relationship to jointly optimize the EEG pattern features from the uncovered subclasses. We then train a linear support vector machine with the optimized features for EEG pattern decoding. Extensive experimental studies are conducted on three EEG data sets to validate the effectiveness of our algorithm in comparison with other state-of-the-art approaches. The improved experimental results demonstrate the outstanding superiority of our algorithm, suggesting its prominent performance for EEG pattern decoding in BCI applications.

DMIB: Dual-Correlated Multivariate Information Bottleneck for Multiview Clustering

Multiview clustering (MVC) has recently been the focus of much attention due to its ability to partition data from multiple views via view correlations. However, most MVC methods only learn either interfeature correlations or intercluster correlations, which may lead to unsatisfactory clustering performance. To address this issue, we propose a novel dual-correlated multivariate information bottleneck (DMIB) method for MVC. DMIB is able to explore both interfeature correlations (the relationship among multiple distinct feature representations from different views) and intercluster correlations (the close agreement among clustering results obtained from individual views). For the former, we integrate both view-shared feature correlations discovered by learning a shared discriminative feature subspace and view-specific feature information to fully explore the interfeature correlation. This allows us to attain multiple reliable local clustering results of different views. Following this, we explore the intercluster correlations by learning the shared mutual information over different local clusterings for an improved global partition. By integrating both correlations, we formulate the problem as a unified information maximization function and further design a two-step method for optimization. Moreover, we theoretically prove the convergence of the proposed algorithm, and discuss the relationships between our method and several existing clustering paradigms. The experimental results on multiple datasets demonstrate the superiority of DMIB compared to several state-of-the-art clustering methods.

High-Order Correlation Preserved Incomplete Multi-View Subspace Clustering

Incomplete multi-view clustering aims to exploit the information of multiple incomplete views to partition data into their clusters. Existing methods only utilize the pair-wise sample correlation and pair-wise view correlation to improve the clustering performance but neglect the high-order correlation of samples and that of views. To address this issue, we propose a high-order correlation preserved incomplete multi-view subspace clustering (HCP-IMSC) method which effectively recovers the missing views of samples and the subspace structure of incomplete multi-view data. Specifically, multiple affinity matrices constructed from the incomplete multi-view data are treated as a third-order low rank tensor with a tensor factorization regularization which preserves the high-order view correlation and sample correlation. Then, a unified affinity matrix can be obtained by fusing the view-specific affinity matrices in a self-weighted manner. A hypergraph is further constructed from the unified affinity matrix to preserve the high-order geometrical structure of the data with incomplete views. Then, the samples with missing views are restricted to be reconstructed by their neighbor samples under the hypergraph-induced hyper-Laplacian regularization. Furthermore, the learning of view-specific affinity matrices as well as the unified one, tensor factorization, and hyper-Laplacian regularization are integrated into a unified optimization framework. An iterative algorithm is designed to solve the resultant model. Experimental results on various benchmark datasets indicate the superiority of the proposed method. The code is implemented by using MATLAB R2018a and MindSpore library: https://github.com/ChangTang/HCP-IMSC.

Smoothness Regularized Multiview Subspace Clustering With Kernel Learning

Multiview subspace clustering has attracted an increasing amount of attention in recent years. However, most of the existing multiview subspace clustering methods assume linear relations between multiview data points when learning the affinity representation by means of the self-expression or fail to preserve the locality property of the original feature space in the learned affinity representation. To address the above issues, in this article, we propose a new multiview subspace clustering method termed smoothness regularized multiview subspace clustering with kernel learning (SMSCK). To capture the nonlinear relations between multiview data points, the proposed model maps the concatenated multiview observations into a high-dimensional kernel space, in which the linear relations reflect the nonlinear relations between multiview data points in the original space. In addition, to explicitly preserve the locality property of the original feature space in the learned affinity representation, the smoothness regularization is deployed in the subspace learning in the kernel space. Theoretical analysis has been provided to ensure that the optimal solution of the proposed model meets the grouping effect. The unique optimal solution of the proposed model can be obtained by an optimization strategy and the theoretical convergence analysis is also conducted. Extensive experiments are conducted on both image and document data sets, and the comparison results with state-of-the-art methods demonstrate the effectiveness of our method.

Multiview Common Subspace Clustering via Coupled Low Rank Representation

Multi-view subspace clustering (MVSC) finds a shared structure in latent low-dimensional subspaces of multi-view data to enhance clustering performance. Nonetheless, we observe that most existing MVSC methods neglect the diversity in multi-view data by considering only the common knowledge to find a shared structure either directly or by merging different similarity matrices learned for each view. In the presence of noise, this predefined shared structure becomes a biased representation of the different views. Thus, in this article, we propose a MVSC method based on coupled low-rank representation to address the above limitation. Our method first obtains a low-rank representation for each view, constrained to be a linear combination of the view-specific representation and the shared representation by simultaneously encouraging the sparsity of view-specific one. Then, it uses the k -block diagonal regularizer to learn a manifold recovery matrix for each view through respective low-rank matrices to recover more manifold structures from them. In this way, the proposed method can find an ideal similarity matrix by approximating clustering projection matrices obtained from the recovery structures. Hence, this similarity matrix denotes our clustering structure with exactly k connected components by applying a rank constraint on the similarity matrix’s relaxed Laplacian matrix to avoid spectral post-processing of the low-dimensional embedding matrix. The core of our idea is such that we introduce dynamic approximation into the low-rank representation to allow the clustering structure and the shared representation to guide each other to learn cleaner low-rank matrices that would lead to a better clustering structure. Therefore, our approach is notably different from existing methods in which the local manifold structure of data is captured in advance. Extensive experiments on six benchmark datasets show that our method outperforms 10 similar state-of-the-art compared methods in six evaluation metrics.

Multi-Class ASD Classification Based on Functional Connectivity and Functional Correlation Tensor via Multi-Source Domain Adaptation and Multi-View Sparse Representation

The resting-state functional magnetic resonance imaging (rs-fMRI) reflects functional activity of brain regions by blood-oxygen-level dependent (BOLD) signals. Up to now, many computer-aided diagnosis methods based on rs-fMRI have been developed for Autism Spectrum Disorder (ASD). These methods are mostly the binary classification approaches to determine whether a subject is an ASD patient or not. However, the disease often consists of several sub-categories, which are complex and thus still confusing to many automatic classification methods. Besides, existing methods usually focus on the functional connectivity (FC) features in grey matter regions, which only account for a small portion of the rs-fMRI data. Recently, the possibility to reveal the connectivity information in the white matter regions of rs-fMRI has drawn high attention. To this end, we propose to use the patch-based functional correlation tensor (PBFCT) features extracted from rs-fMRI in white matter, in addition to the traditional FC features from gray matter, to develop a novel multi-class ASD diagnosis method in this work. Our method has two stages. Specifically, in the first stage of multi-source domain adaptation (MSDA), the source subjects belonging to multiple clinical centers (thus called as source domains) are all transformed into the same target feature space. Thus each subject in the target domain can be linearly reconstructed by the transformed subjects. In the second stage of multi-view sparse representation (MVSR), a multi-view classifier for multi-class ASD diagnosis is developed by jointly using both views of the FC and PBFCT features. The experimental results using the ABIDE dataset verify the effectiveness of our method, which is capable of accurately classifying each subject into a respective ASD sub-category.

Hi-Net: Hybrid-Fusion Network for Multi-Modal MR Image Synthesis

Magnetic resonance imaging (MRI) is a widely used neuroimaging technique that can provide images of different contrasts (i.e., modalities). Fusing this multi-modal data has proven particularly effective for boosting model performance in many tasks. However, due to poor data quality and frequent patient dropout, collecting all modalities for every patient remains a challenge. Medical image synthesis has been proposed as an effective solution, where any missing modalities are synthesized from the existing ones. In this paper, we propose a novel Hybrid-fusion Network (Hi-Net) for multi-modal MR image synthesis, which learns a mapping from multi-modal source images (i.e., existing modalities) to target images (i.e., missing modalities). In our Hi-Net, a modality-specific network is utilized to learn representations for each individual modality, and a fusion network is employed to learn the common latent representation of multi-modal data. Then, a multi-modal synthesis network is designed to densely combine the latent representation with hierarchical features from each modality, acting as a generator to synthesize the target images. Moreover, a layer-wise multi-modal fusion strategy effectively exploits the correlations among multiple modalities, where a Mixed Fusion Block (MFB) is proposed to adaptively weight different fusion strategies. Extensive experiments demonstrate the proposed model outperforms other state-of-the-art medical image synthesis methods.