Robust Subspace Segmentation Research Articles

Multiview Spectral Clustering via Robust Subspace Segmentation.

Multiview clustering refers to partition data according to its multiple views, where information from different perspectives can be jointly used in some certain complementary manner to produce more sensible clusters. It is believed that most of the existing multiview clustering methods technically suffer from possibly corrupted data, resulting in a dramatically decreased clustering performance. To overcome this challenge, we propose a multiview spectral clustering method based on robust subspace segmentation in this article. Our proposed algorithm is composed of three modules, that is: 1) the construction of multiple feature matrices from all views; 2) the formulation of a shared low-rank latent matrix by a low rank and sparse decomposition; and 3) the use of the Markov-chain-based spectral clustering method for producing the final clusters. To solve the optimization problem for a low rank and sparse decomposition, we develop an optimization procedure based on the scheme of the augmented Lagrangian method of multipliers. The experimental results on several benchmark datasets indicate that the proposed method outperforms favorably compared to several state-of-the-art multiview clustering techniques.

Feature extraction based on Low-rank affinity matrix for biological recognition

The low-rank representation (LRR) was presented recently and demonstrated its effectiveness for robust subspace segmentation. This paper presents a discriminative projection method based on Low-rank affinity matrix (LRA-DP) for robust feature extraction. The affinity matrix is designed to better preserve the underlying low-rank structure of data representation revealed by LRR. The experiments on the Yale, Extended Yale B, AR face image databases and the PolyU palmprint database showed LRA-DP is always better than or comparable to other state-of-the-art methods, which means underlying low-rank structure of data representation preserved by LRA-DP is helpful for classification problem.

Low-rank subspace learning based network community detection

Community structure is one of the most important inherent properties in complex networks. Generally, nodes in each community span a different subspace in the geometric space. However, the subspace based methods are not well studied, and the existing related algorithms are sensitive to the perturbations in networks, thus lack the ability to capture the robust subspace segmentation accurately. In this paper we propose a low-rank subspace learning based network community detection algorithm. The contribution of this paper is to find the lowest rank representation of all node vectors jointly in the geometric space using low-rank decomposition strategy. Then the final robust low-rank subspace based communities are obtained from the lowest rank representations. Low-rank decomposition is better at capturing global structure of networks, thus our algorithm is more robust to perturbations in networks and has a better performance on discriminating the community boundaries. Experimental results on both synthetic benchmarks and real-world networks demonstrate that the proposed algorithm outperforms the state-of-the-art community detection approaches and the results basically preserve the actual community structure, especially on networks with vague community structures.

Robust Subspace Segmentation by Self-Representation Constrained Low-Rank Representation

Low-rank representation (LRR) and its variants have been proved to be powerful tools for handling subspace segmentation problems. In this paper, we propose a new LRR-related algorithm, termed self-representation constrained low-rank presentation (SRLRR). SRLRR contains a self-representation constraint which is used to compel the obtained coefficient matrices can be reconstructed by themselves. An optimization algorithm for solving SRLRR problem is also proposed. Moreover, we present an alternative formulation of SRLRR so that SRLRR can be regarded as a kind of Laplacian regularized LRR. Consequently, the relationships and comparisons between SRLRR and some existing Laplacian regularized LRR-related algorithms have been discussed. Finally, subspace segmentation experiments conducted on both synthetic and real databases show that SRLRR dominates the related algorithms.

Non-Convex Sparse and Low-Rank Based Robust Subspace Segmentation for Data Mining.

Parsimony, including sparsity and low-rank, has shown great importance for data mining in social networks, particularly in tasks such as segmentation and recognition. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an objective function with convex l1-norm or nuclear norm constraints. However, the obtained results by convex optimization are usually suboptimal to solutions of original sparse or low-rank problems. In this paper, a novel robust subspace segmentation algorithm has been proposed by integrating lp-norm and Schatten p-norm constraints. Our so-obtained affinity graph can better capture local geometrical structure and the global information of the data. As a consequence, our algorithm is more generative, discriminative and robust. An efficient linearized alternating direction method is derived to realize our model. Extensive segmentation experiments are conducted on public datasets. The proposed algorithm is revealed to be more effective and robust compared to five existing algorithms.

Tensor LRR and Sparse Coding-Based Subspace Clustering.

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 affinity matrix used for spectral clustering is built from the joint similarities in both spatial and feature spaces. TLRRSC can well capture the global structure and inherent feature information of data and provide a robust subspace segmentation from corrupted data. Experimental results on both synthetic and real-world data sets show that TLRRSC outperforms several established stateof- the-art methods.

Latent space robust subspace segmentation based on low-rank and locality constraints

Low-rank representation (LRR) and its extensions have proven to be effective methods to handle different kinds of subspace segmentation applications. In this paper, we propose a new subspace segmentation algorithm, termed latent space robust subspace segmentation based on low-rank and locality constraints (LSRS2). Different from LRR, LSRS2 learns a low-dimensional space and a coefficient matrix for a data set simultaneously. In the obtained latent space, the coefficient matrix can faithfully reveal both the global and local structures for the data set. Furthermore, we build the connections between LSRS2 and robust coding methods, and show LSRS2 can be regarded as a kind of robust LRR method. Therefore, it can be guaranteed in theory that LSRS2 shows good performance. In addition, an efficient optimization method for solving LSRS2 is presented and its convergence is also proven. Extensive experiments show that the proposed algorithm outperforms the related subspace segmentation methods.

Semi-supervised classification via kernel low-rank representation graph

Sparse Representation based Graphs (SRGs) have attracted increasing interests in very recent years. However, for lacking global constraints on solutions to sparse representation, SRGs cannot accurately reveal data structure when data are grossly corrupted. In this paper, in order to achieve robust classification of wide range of datasets when only a small number of labeled samples are available, we advance a new semi-supervised kernel low-rank representation graph (SKLRG), by combining low-rank representation (LRR) with graphs and kernel trick. A kernel projection is first learned to find high-dimensional space where data have possible low-rank structure. Then a low-rank representation of the projected data is calculated from which we can derive a SKLRG matrix to evaluate data affinity and classify corrupted patterns. The proposed SKLRG can naturally reveal the relationship among data in the projected space, and can capture the global structure of complex data and implements more robust subspace segmentation. Moreover, connected weights of SKLRG are refined by pairwise constrains where label information is explored to further improve the classification results. Some experiments are taken on some benchmark datasets and Synthetic Aperture Radar (SAR) images that are corrupted by speckle noise. The results show that the proposed SKLRG can achieve better performance than its counterparts when there are only a small number of labeled samples.

Semi‐supervised low‐rank representation graph for pattern recognition

In this study, the authors propose a new semi-supervised low-rank representation graph for pattern recognition. A collection of samples is jointly coded by the recently developed low-rank representation (LRR), which better captures the global structure of data and implements more robust subspace segmentation from corrupted samples. By using the calculated LRR coefficients of both labelled and unlabelled samples as the graph weights, a low-rank representation graph is established in a parameter-free manner under the framework of semi-supervised learning. Some experiments are taken on the benchmark database to investigate the performance of the proposed method and the results show that it is superior to other related semi-supervised graphs.

Efficient Subspace Segmentation via Quadratic Programming

We explore in this paper efficient algorithmic solutions to robustsubspace segmentation. We propose the SSQP, namely SubspaceSegmentation via Quadratic Programming, to partition data drawnfrom multiple subspaces into multiple clusters. The basic idea ofSSQP is to express each datum as the linear combination of otherdata regularized by an overall term targeting zero reconstructioncoefficients over vectors from different subspaces. The derivedcoefficient matrix by solving a quadratic programming problem istaken as an affinity matrix, upon which spectral clustering isapplied to obtain the ultimate segmentation result. Similar tosparse subspace clustering (SCC) and low-rank representation (LRR),SSQP is robust to data noises as validated by experiments on toydata. Experiments on Hopkins 155 database show that SSQP can achievecompetitive accuracy as SCC and LRR in segmenting affine subspaces,while experimental results on the Extended Yale Face Database Bdemonstrate SSQP's superiority over SCC and LRR. Beyond segmentationaccuracy, all experiments show that SSQP is much faster than bothSSC and LRR in the practice of subspace segmentation.