Exploiting Correlation Consensus

IEEE Transactions on Image Processing, 2015

More often than not, a multimedia data described by multiple features, such as color and shape features, can be naturally decomposed of multi-views. Since multi-views provide complementary information to each other, great endeavors have been dedicated by leveraging multiple views instead of a single view to achieve the better clustering performance. To effectively exploit data correlation consensus among multi-views, in this paper we study subspace clustering for multi-view data while keeping individual views well encapsulated. For characterizing data correlations, we generate a similarity matrix in a way that high affinity values are assigned to data objects within the same subspace across views, while the correlations among data objects from distinct subspaces are minimized. Before generating this matrix, however, we should consider that multi-view data in practice might be corrupted by noise. The corrupted data will significantly downgrade clustering results. We firstly present a novel objective function coupled with an angular based regularizer. By minimizing this function, multiple sparse vectors are obtained for each data object as its multiple representations. In fact, these sparse vectors result from reaching data correlation consensus on all views. For tackling noise corruption, we present a sparsity based approach that refines the angular based data correlation. By using this approach, a more ideal data similarity matrix is generated for multi-view data. Spectral clustering is then applied to the similarity matrix to obtain the final subspace clustering. Extensive experiments have been conducted to validate the effectiveness of our proposed approach.

Pattern Recognition

Most existing approaches address multi-view subspace clustering problem by constructing the affinity matrix on each view separately and afterwards propose how to extend spectral clustering algorithm to handle multi-view data. This paper presents an approach to multi-view subspace clustering that learns a joint subspace representation by constructing affinity matrix shared among all views. Relying on the importance of both low-rank and sparsity constraints in the construction of the affinity matrix, we introduce the objective that balances between the agreement across different views, while at the same time encourages sparsity and low-rankness of the solution. Related low-rank and sparsity constrained optimization problem is for each view solved using the alternating direction method of multipliers. Furthermore, we extend our approach to cluster data drawn from nonlinear subspaces by solving the corresponding problem in a reproducing kernel Hilbert space. The proposed algorithm outperforms state-of-the-art multi-view subspace clustering algorithms on one synthetic and four real-world datasets.

IEEE Transactions on Cybernetics, 2021

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 paper, 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, i.e., 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.

2018

For many clustering applications, Multi-view data sets are very common. Multi-view clustering aims to exploit information across views instead of individual views, which is promising to improve clustering performance. Note that a high-dimensional data set usually distributes on certain low-dimensional subspace. Thus, many multi-view subspace clustering algorithms have been developed. However, existing multi-view subspace clustering methods rarely perform clustering on the subspace representation of each view simultaneously as well as keep the indicator consistency among the representations, i.e., the same data point in different views should be assigned to the same cluster. In this paper, we propose a novel multi-view subspace clustering method. In our method, we use the indicator matrix to ensure that we perform clustering on the subspace representation of each view simultaneously. And at the same time, a co-regularized term is added to guarantee the consistency of the indicator matrices. Experiments on several real-world multi-view datasets demonstrate the effectiveness and superiority of our proposed method.

IEEE transactions on neural networks and learning systems, 2016

Subspace clustering groups a set of samples from a union of several linear subspaces into clusters, so that the samples in the same cluster are drawn from the same linear subspace. In the majority of the existing work on subspace clustering, clusters are built based on feature information, while sample correlations in their original spatial structure are simply ignored. Besides, original high-dimensional feature vector contains noisy/redundant information, and the time complexity grows exponentially with the number of dimensions. To address these issues, we propose a tensor low-rank representation (TLRR) and sparse coding-based (TLRRSC) subspace clustering method by simultaneously considering feature information and spatial structures. TLRR seeks the lowest rank representation over original spatial structures along all spatial directions. Sparse coding learns a dictionary along feature spaces, so that each sample can be represented by a few atoms of the learned dictionary. The affin...

—Many real-world problems deal with collections of high-dimensional data, such as images, videos, text and web documents, DNA microarray data, and more. Often, such high-dimensional data lie close to low-dimensional structures corresponding to several classes or categories to which the data belong. In this paper, we propose and study an algorithm, called Sparse Subspace Clustering (SSC), to cluster data points that lie in a union of low-dimensional subspaces. The key idea is that, among the infinitely many possible representations of a data point in terms of other points, a sparse representation corresponds to selecting a few points from the same subspace. This motivates solving a sparse optimization program whose solution is used in a spectral clustering framework to infer the clustering of the data into subspaces. Since solving the sparse optimization program is in general NP-hard, we consider a convex relaxation and show that, under appropriate conditions on the arrangement of the subspaces and the distribution of the data, the proposed minimization program succeeds in recovering the desired sparse representations. The proposed algorithm is efficient and can handle data points near the intersections of subspaces. Another key advantage of the proposed algorithm with respect to the state of the art is that it can deal directly with data nuisances, such as noise, sparse outlying entries, and missing entries, by incorporating the model of the data into the sparse optimization program. We demonstrate the effectiveness of the proposed algorithm through experiments on synthetic data as well as the two real-world problems of motion segmentation and face clustering.

2009

We propose a method based on sparse representation (SR) to cluster data drawn from multiple low-dimensional linear or affine subspaces embedded in a high-dimensional space. Our method is based on the fact that each point in a union of subspaces has a SR with respect to a dictionary formed by all other data points. In general, finding such a SR is NP hard. Our key contribution is to show that, under mild assumptions, the SR can be obtained 'exactly' by using 1 optimization. The segmentation of the data is obtained by applying spectral clustering to a similarity matrix built from this SR. Our method can handle noise, outliers as well as missing data. We apply our subspace clustering algorithm to the problem of segmenting multiple motions in video. Experiments on 167 video sequences show that our approach significantly outperforms state-of-the-art methods.

IEEE Access

Ongoing researches on multiple view data are showing competitive behavior in the machine learning field. Multi-view clustering has gained widespread acceptance for managing multi-view data and improves clustering efficiency. Large dimensionality in data from various views has recently drawn a lot of interest from researchers. How to efficiently learns the appropriate lower dimensional subspace which can manage the valuable information from the diverse views is challenging and considerable issue. To concentrate on the mentioned issue, we asserted a novel clustering approach for multiple view data through low-rank representation. We consider the importance of each view by assigning the weight control factor. We combine consensus representation with the degree of disagreement among lower rank matrices. The single objective function unifies all factors. Furthermore, we give the efficient solution to update the variable and to optimized the objective function through the Augmented Lagrange's Multiplier strategy. Real-world datasets are utilized in this study to exemplify the efficiency of the introduced technique, and it is contemplated to preceding algorithms to demonstrate its superiority. INDEX TERMS Low-rank representation, spectral clustering, weighted multi-view data, sparse constraints.

IEEE Transactions on Cybernetics

One of the major problems in cancer subtype discovery from multimodal omic data is that all the available modalities may not encode relevant and homogeneous information about the subtypes. Moreover, the high dimensional nature of the modalities makes sample clustering computationally expensive. In this regard, a novel algorithm is proposed to extract a lowrank joint subspace of the integrated data matrix. The proposed algorithm first evaluates the quality of subtype information provided by each of the modalities, and then judiciously selects only relevant ones to construct the joint subspace. The problem of incrementally updating the singular value decomposition of a data matrix is formulated for the multimodal data framework. The analytical formulation enables efficient construction of the joint subspace of integrated data from low-rank subspaces of the individual modalities. Construction of joint subspace by the proposed method is shown to be computationally more efficient as compared to performing principal component analysis (PCA) on the integrated data matrix. Some new quantitative indices are introduced to measure theoretically the accuracy of subspace construction by the proposed approach with respect to the principal subspace extracted by the PCA. The efficacy of clustering on the joint subspace constructed by the proposed algorithm is established over existing integrative clustering approaches on several real-life multimodal cancer data sets.

2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017

In this paper, we propose a novel Latent Multi-view Subspace Clustering (LMSC) method, which clusters data points with latent representation and simultaneously explores underlying complementary information from multiple views. Unlike most existing single view subspace clustering methods that reconstruct data points using original features, our method seeks the underlying latent representation and simultaneously performs data reconstruction based on the learned latent representation. With the complementarity of multiple views, the latent representation could depict data themselves more comprehensively than each single view individually, accordingly makes subspace representation more accurate and robust as well. The proposed method is intuitive and can be optimized efficiently by using the Augmented Lagrangian Multiplier with Alternating Direction Minimization (ALM-ADM) algorithm. Extensive experiments on benchmark datasets have validated the effectiveness of our proposed method.