Constrained Multi-View Video Face Clustering

Segmentation and Completion of Human Motion Sequence via Temporal Learning of Subspace Variety Model

Subspace-based models have been extensively employed in unsupervised segmentation and completion of human motion sequence (HMS). However, existing approaches often neglect the incorporation of temporal priors embedded in HMS, resulting in suboptimal results. This paper presents a subspace variety model for HMS, along with an innovative Temporal Learning of Subspace Variety Model (TL-SVM) method for enhanced segmentation and completion in HMS. The key idea is to segment incomplete HMS into motion clusters and extracting the subspace features of each motion through the temporal learning of the subspace variety model. Subsequently, the HMS is completed based on the extracted subspace features. Thus, the main challenge is to learn the subspace variety model with temporal priors when confronted with missing entries. To tackle this, the paper develops a spatio-temporal assignment consistency (STAC) constraint for the subspace variety model, leveraging temporal priors embedded in HMS. In addition, a subspace clustering approach under the STAC constraint is proposed to learn the subspace variety model by extracting subspace features from HMS and segmenting HMS into motion clusters alternatively. The proposed subspace clustering model can also handle missing entries with theoretical guarantees. Furthermore, the missing entries of HMS are completed by minimizing the distance between each human motion frame and its corresponding subspace. Extensive experimental results, along with comparisons to state-of-the-art methods on four benchmark datasets, underscore the advantages of the proposed method.

Multiview Clustering With Propagating Information Bottleneck

In many practical applications, massive data are observed from multiple sources, each of which contains multiple cohesive views, called hierarchical multiview (HMV) data, such as image-text objects with different types of visual and textual features. Naturally, the inclusion of source and view relationships offers a comprehensive view of the input HMV data and achieves an informative and correct clustering result. However, most existing multiview clustering (MVC) methods can only process single-source data with multiple views or multisource data with single type of feature, failing to consider all the views across multiple sources. Observing the rich closely related multivariate (i.e., source and view) information and the potential dynamic information flow interacting among them, in this article, a general hierarchical information propagation model is first built to address the above challenging problem. It describes the process from optimal feature subspace learning (OFSL) of each source to final clustering structure learning (CSL). Then, a novel self-guided method named propagating information bottleneck (PIB) is proposed to realize the model. It works in a circulating propagation fashion, so that the resulting clustering structure obtained from the last iteration can "self-guide" the OFSL of each source, and the learned subspaces are in turn used to conduct the subsequent CSL. We theoretically analyze the relationship between the cluster structures learned in the CSL phase and the preservation of relevant information propagated from the OFSL phase. Finally, a two-step alternating optimization method is carefully designed for optimization. Experimental results on various datasets show the superiority of the proposed PIB method over several state-of-the-art methods.

Self-Supervised Video-Centralised Transformer for Video Face Clustering

This article presents a novel method for face clustering in videos using a video-centralised transformer. Previous works often employed contrastive learning to learn frame-level representation and used average pooling to aggregate the features along the temporal dimension. This approach may not fully capture the complicated video dynamics. In addition, despite the recent progress in video-based contrastive learning, few have attempted to learn a self-supervised clustering-friendly face representation that benefits the video face clustering task. To overcome these limitations, our method employs a transformer to directly learn video-level representations that can better reflect the temporally-varying property of faces in videos, while we also propose a video-centralised self-supervised framework to train the transformer model. We also investigate face clustering in egocentric videos, a fast-emerging field that has not been studied yet in works related to face clustering. To this end, we present and release the first large-scale egocentric video face clustering dataset named EasyCom-Clustering. We evaluate our proposed method on both the widely used Big Bang Theory (BBT) dataset and the new EasyCom-Clustering dataset. Results show the performance of our video-centralised transformer has surpassed all previous state-of-the-art methods on both benchmarks, exhibiting a self-attentive understanding of face videos.

Multiview Clustering by Consensus Spectral Rotation Fusion

Multiview clustering (MVC) aims to partition data into different groups by taking full advantage of the complementary information from multiple views. Most existing MVC methods fuse information of multiple views at the raw data level. They may suffer from performance degradation due to the redundant information contained in the raw data. Graph learning-based methods often heavily depend on one specific graph construction, which limits their practical applications. Moreover, they often require a computational complexity of O(n3 ) because of matrix inversion or eigenvalue decomposition for each iterative computation. In this paper, we propose a consensus spectral rotation fusion (CSRF) method to learn a fused affinity matrix for MVC at the spectral embedding feature level. Specifically, we first introduce a CSRF model to learn a consensus low-dimensional embedding, which explores the complementary and consistent information across multiple views. We develop an alternating iterative optimization algorithm to solve the CSRF optimization problem, where a computational complexity of O(n2 ) is required during each iterative computation. Then, the sparsity policy is introduced to design two different graph construction schemes, which are effectively integrated with the CSRF model. Finally, a multiview fused affinity matrix is constructed from the consensus low-dimensional embedding in spectral embedding space. We analyze the convergence of the alternating iterative optimization algorithm and provide an extension of CSRF for incomplete MVC. Extensive experiments on multiview datasets demonstrate the effectiveness and efficiency of the proposed CSRF method.

Adaptive Feature Projection With Distribution Alignment for Deep Incomplete Multi-View Clustering

Incomplete multi-view clustering (IMVC) analysis, where some views of multi-view data usually have missing data, has attracted increasing attention. However, existing IMVC methods still have two issues: 1) they pay much attention to imputing or recovering the missing data, without considering the fact that the imputed values might be inaccurate due to the unknown label information, 2) the common features of multiple views are always learned from the complete data, while ignoring the feature distribution discrepancy between the complete and incomplete data. To address these issues, we propose an imputation-free deep IMVC method and consider distribution alignment in feature learning. Concretely, the proposed method learns the features for each view by autoencoders and utilizes an adaptive feature projection to avoid the imputation for missing data. All available data are projected into a common feature space, where the common cluster information is explored by maximizing mutual information and the distribution alignment is achieved by minimizing mean discrepancy. Additionally, we design a new mean discrepancy loss for incomplete multi-view learning and make it applicable in mini-batch optimization. Extensive experiments demonstrate that our method achieves the comparable or superior performance compared with state-of-the-art methods.

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 Clustering: A Scalable and Parameter-Free Bipartite Graph Fusion Method

Multiview clustering partitions data into different groups according to their heterogeneous features. Most existing methods degenerate the applicability of models due to their intractable hyper-parameters triggered by various regularization terms. Moreover, traditional spectral based methods always encounter the expensive time overheads and fail in exploring the explicit clusters from graphs. In this paper, we present a scalable and parameter-free graph fusion framework for multiview clustering, seeking for a joint graph compatible across multiple views in a self-supervised weighting manner. Our formulation coalesces multiple view-wise graphs straightforward and learns the weights as well as the joint graph interactively, which could actively release the model from any weight-related hyper-parameters. Meanwhile, we manipulate the joint graph by a connectivity constraint such that the connected components indicate clusters directly. The designed algorithm is initialization-independent and time-economical which obtains the stable performance and scales well with the data size. Substantial experiments on toy data as well as real datasets are conducted that verify the superiority of the proposed method compared to the state-of-the-arts over the clustering performance and time expenditure.

Multi‐view intrinsic low‐rank representation for robust face recognition and clustering

In the last years, subspace‐based multi‐view face recognition has attracted increasing attention and many related methods have been proposed. However, the most existing methods ignore the specific local structure of different views. This drawback can cause these methods' discriminating ability to degrade when many noisy samples exist in data. To tackle this problem, a multi‐view low‐rank representation method is proposed, which exploits both intrinsic relationships and specific local structures of different views simultaneously. It is achieved by hierarchical Bayesian methods that constrain the low‐rank representation of each view so that it matches a linear combination of an intrinsic representation matrix and a specific representation matrix to obtain common and specific characteristics of different views. The intrinsic representation matrix holds the consensus information between views, and the specific representation matrices indicate the diversity among views. Furthermore, the model injects a clustering structure into the low‐rank representation. This approach allows for adaptive adjustment of the clustering structure while pursuing the optimization of the low‐rank representation. Hence, the model can well capture both the relationship between data and the clustering structure explicitly. Extensive experiments on several datasets demonstrated the effectiveness of the proposed method compared to similar state‐of‐the‐art methods in classification and clustering.

View-Wise Versus Cluster-Wise Weight: Which Is Better for Multi-View Clustering?

Weighted multi-view clustering (MVC) aims to combine the complementary information of multi-view data (such as image data with different types of features) in a weighted manner to obtain a consistent clustering result. However, when the cluster-wise weights across views are vastly different, most existing weighted MVC methods may fail to fully utilize the complementary information, because they are based on view-wise weight learning and can not learn the fine-grained cluster-wise weights. Additionally, extra parameters are needed for most of them to control the weight distribution sparsity or smoothness, which are hard to tune without prior knowledge. To address these issues, in this paper we propose a novel and effective Cluster-weighted mUlti-view infoRmation bottlEneck (CURE) clustering algorithm, which can automatically learn the cluster-wise weights to discover the discriminative clusters across multiple views and thus can enhance the clustering performance by properly exploiting the cluster-level complementary information. To learn the cluster-wise weights, we design a new weight learning scheme by exploring the relation between the mutual information of the joint distribution of a specific cluster (containing a group of data samples) and the weight of this cluster. Finally, a novel draw-and-merge method is presented to solve the optimization problem. Experimental results on various multi-view datasets show the superiority and effectiveness of our cluster-wise weighted CURE over several state-of-the-art methods.

Constrained Clustering With Dissimilarity Propagation-Guided Graph-Laplacian PCA

In this article, we propose a novel model for constrained clustering, namely, the dissimilarity propagation-guided graph-Laplacian principal component analysis (DP-GLPCA). By fully utilizing a limited number of weakly supervisory information in the form of pairwise constraints, the proposed DP-GLPCA is capable of capturing both the local and global structures of input samples to exploit their characteristics for excellent clustering. More specifically, we first formulate a convex semisupervised low-dimensional embedding model by incorporating a new dissimilarity regularizer into GLPCA (i.e., an unsupervised dimensionality reduction model), in which both the similarity and dissimilarity between low-dimensional representations are enforced with the constraints to improve their discriminability. An efficient iterative algorithm based on the inexact augmented Lagrange multiplier is designed to solve it with the global convergence guaranteed. Furthermore, we innovatively propose to propagate the cannot-link constraints (i.e., dissimilarity) to refine the dissimilarity regularizer to be more informative. The resulting DP model is iteratively solved, and we also prove that it can converge to a Karush-Kuhn-Tucker point. Extensive experimental results over nine commonly used benchmark data sets show that the proposed DP-GLPCA can produce much higher clustering accuracy than state-of-the-art constrained clustering methods. Besides, the effectiveness and advantage of the proposed DP model are experimentally verified. To the best of our knowledge, it is the first time to investigate DP, which is contrast to existing pairwise constraint propagation that propagates similarity. The code is publicly available at https://github.com/jyh-learning/DP-GLPCA.

Pseudo-Supervised Deep Subspace Clustering

Auto-Encoder (AE)-based deep subspace clustering (DSC) methods have achieved impressive performance due to the powerful representation extracted using deep neural networks while prioritizing categorical separability. However, self-reconstruction loss of an AE ignores rich useful relation information and might lead to indiscriminative representation, which inevitably degrades the clustering performance. It is also challenging to learn high-level similarity without feeding semantic labels. Another unsolved problem facing DSC is the huge memory cost due to n×n similarity matrix, which is incurred by the self-expression layer between an encoder and decoder. To tackle these problems, we use pairwise similarity to weigh the reconstruction loss to capture local structure information, while a similarity is learned by the self-expression layer. Pseudo-graphs and pseudo-labels, which allow benefiting from uncertain knowledge acquired during network training, are further employed to supervise similarity learning. Joint learning and iterative training facilitate to obtain an overall optimal solution. Extensive experiments on benchmark datasets demonstrate the superiority of our approach. By combining with the k -nearest neighbors algorithm, we further show that our method can address the large-scale and out-of-sample problems. The source code of our method is available: https://github.com/sckangz/SelfsupervisedSC.

Fast Multi-View Clustering via Nonnegative and Orthogonal Factorization

The rapid growth of the number of data brings great challenges to clustering, especially the introduction of multi-view data, which collected from multiple sources or represented by multiple features, makes these challenges more arduous. How to clustering large-scale data efficiently has become the hottest topic of current large-scale clustering tasks. Although several accelerated multi-view methods have been proposed to improve the efficiency of clustering large-scale data, they still cannot be applied to some scenarios that require high efficiency because of the high computational complexity. To cope with the issue of high computational complexity of existing multi-view methods when dealing with large-scale data, a fast multi-view clustering model via nonnegative and orthogonal factorization (FMCNOF) is proposed in this paper. Instead of constraining the factor matrices to be nonnegative as traditional nonnegative and orthogonal factorization (NOF), we constrain a factor matrix of this model to be cluster indicator matrix which can assign cluster labels to data directly without extra post-processing step to extract cluster structures from the factor matrix. Meanwhile, the F-norm instead of the L2-norm is utilized on the FMCNOF model, which makes the model very easy to optimize. Furthermore, an efficient optimization algorithm is proposed to solve the FMCNOF model. Different from the traditional NOF optimization algorithm requiring dense matrix multiplications, our algorithm can divide the optimization problem into three decoupled small size subproblems that can be solved by much less matrix multiplications. Combined with the FMCNOF model and the corresponding fast optimization method, the efficiency of the clustering process can be significantly improved, and the computational complexity is nearly O(n) . Extensive experiments on various benchmark data sets validate our approach can greatly improve the efficiency when achieve acceptable performance.

Robust Kernelized Multiview Self-Representation for Subspace Clustering

In this article, we propose a multiview self-representation model for nonlinear subspaces clustering. By assuming that the heterogeneous features lie within the union of multiple linear subspaces, the recent multiview subspace learning methods aim to capture the complementary and consensus from multiple views to boost the performance. However, in real-world applications, data feature usually resides in multiple nonlinear subspaces, leading to undesirable results. To this end, we propose a kernelized version of tensor-based multiview subspace clustering, which is referred to as Kt-SVD-MSC, to jointly learn self-representation coefficients in mapped high-dimensional spaces and multiple views correlation in unified tensor space. In view-specific feature space, a kernel-induced mapping is introduced for each view to ensure the separability of self-representation coefficients. In unified tensor space, a new kind of tensor low-rank regularizer is employed on the rotated self-representation coefficient tensor to preserve the global consistency across different views. We also derive an algorithm to efficiently solve the optimization problem with all the subproblems having closed-form solutions. Furthermore, by incorporating the nonnegative and sparsity constraints, the proposed method can be easily extended to a useful variant, meaning that several useful variants can be easily constructed in a similar way. Extensive experiments of the proposed method are tested on eight challenging data sets, in which a significant (even a breakthrough) advance over state-of-the-art multiview clustering is achieved.

Hyper-Laplacian Regularized Multilinear Multiview Self-Representations for Clustering and Semisupervised Learning

In this paper, we address the multiview nonlinear subspace representation problem. Traditional multiview subspace learning methods assume that the heterogeneous features of the data usually lie within the union of multiple linear subspaces. However, instead of linear subspaces, the data feature actually resides in multiple nonlinear subspaces in many real-world applications, resulting in unsatisfactory clustering performance. To overcome this, we propose a hyper-Laplacian regularized multilinear multiview self-representation model, which is referred to as HLR-M²VS, to jointly learn multiple views correlation and a local geometrical structure in a unified tensor space and view-specific self-representation feature spaces, respectively. In unified tensor space, a well-founded tensor low-rank regularization is adopted to impose on the self-representation coefficient tensor to ensure global consensus among different views. In view-specific feature space, hypergraph-induced hyper-Laplacian regularization is utilized to preserve the local geometrical structure embedded in a high-dimensional ambient space. An efficient algorithm is then derived to solve the optimization problem of the established model with theoretical convergence guarantee. Furthermore, the proposed model can be extended to semisupervised classification without introducing any additional parameters. An extensive experiment of our method is conducted on many challenging datasets, where a clear advance over state-of-the-art multiview clustering and multiview semisupervised classification approaches is achieved.

Effective and Generalizable Graph-Based Clustering for Faces in the Wild

Face clustering is the task of grouping unlabeled face images according to individual identities. Several applications require this type of clustering, for instance, social media, law enforcement, and surveillance applications. In this paper, we propose an effective graph-based method for clustering faces in the wild. The proposed algorithm does not require prior knowledge of the data. This fact increases the pertinence of the proposed method near to market solutions. The experiments conducted on four well-known datasets showed that our proposal achieves state-of-the-art results, regarding the clustering performance, also showing stability for different values of the input parameter. Moreover, in these experiments, it is shown that our proposal discovers a number of identities closer to the real number existing in the data.

Adaptive Sample-level Graph Combination for Partial Multiview Clustering

Multiview clustering explores complementary information among distinct views to enhance clustering performance under the assumption that all samples have complete information in all available views. However, this assumption does not hold in many real applications, where the information of some samples in one or more views may be missing, leading to partial multiview clustering problems. In this case, significant performance degeneration is usually observed. A collection of partial multiview clustering algorithms has been proposed to address this issue and most treat all different views equally during clustering. In fact, because different views provide features collected from different angles/feature spaces, they might play different roles in the clustering process. With the diversity of different views considered, in this study, a novel adaptive method is proposed for partial multiview clustering by automatically adjusting the contributions of different views. The samples are divided into complete and incomplete sets, while a joint learning mechanism is established to facilitate the connection between them and thereby improve clustering performance. More specifically, the method is characterized by a joint optimization model comprising two terms. The first term mines the underlying cluster structure from both complete and incomplete samples by adaptively updating their importance in all available views. The second term is designed to group all data with the aid of the cluster structure modeled in the first term. These two terms seamlessly integrate the complementary information among multiple views and enhance the performance of partial multiview clustering. Experimental results on real-world datasets illustrate the effectiveness and efficiency of our proposed method.

Simultaneous Subspace Clustering and Cluster Number Estimating Based on Triplet Relationship

In this paper, we propose a unified framework to discover the number of clusters and group the data points into different clusters using subspace clustering simultaneously. Real data distributed in a high-dimensional space can be disentangled into a union of low-dimensional subspaces, which can benefit various applications. To explore such intrinsic structure, state-of-the-art subspace clustering approaches often optimize a self-representation problem among all samples, to construct a pairwise affinity graph for spectral clustering. However, a graph with pairwise similarities lacks robustness for segmentation, especially for samples which lie on the intersection of two subspaces. To address this problem, we design a hyper-correlation-based data structure termed as the triplet relationship, which reveals high relevance and local compactness among three samples. The triplet relationship can be derived from the self-representation matrix, and be utilized to iteratively assign the data points to clusters. Based on the triplet relationship, we propose a unified optimizing scheme to automatically calculate clustering assignments. Specifically, we optimize a model selection reward and a fusion reward by simultaneously maximizing the similarity of triplets from different clusters while minimizing the correlation of triplets from the same cluster. The proposed algorithm also automatically reveals the number of clusters and fuses groups to avoid over-segmentation. Extensive experimental results on both synthetic and real-world datasets validate the effectiveness and robustness of the proposed method.

Discrete Multi-Graph Clustering

Spectral clustering plays a significant role in applications that rely on multi-view data due to its well-defined mathematical framework and excellent performance on arbitrarily-shaped clusters. Unfortunately, directly optimizing the spectral clustering inevitably results in an NP-hard problem due to the discrete constraints on the clustering labels. Hence, conventional approaches intuitively include a relax-and-discretize strategy to approximate the original solution. However, there are no principles in this strategy that prevent the possibility of information loss between each stage of the process. This uncertainty is aggravated when a procedure of heterogeneous features fusion has to be included in multi-view spectral clustering. In this paper, we avoid an NP-hard optimization problem and develop a general framework for multi-view discrete graph clustering by directly learning a consensus partition across multiple views, instead of using the relax-and-discretize strategy. An effective re-weighting optimization algorithm is exploited to solve the proposed challenging problem. Further, we provide a theoretical analysis of the model's convergence properties and computational complexity for the proposed algorithm. Extensive experiments on several benchmark datasets verify the effectiveness and superiority of the proposed algorithm on clustering and image segmentation tasks.

Variational Textured Dirichlet Process Mixture Model with Pairwise Constraint for Unsupervised Classification of Polarimetric SAR Images

This paper proposes an unsupervised classification method for multilook polarimetric synthetic aperture radar (Pol-SAR) data. The proposed method simultaneously deals with the heterogeneity and incorporates the local correlation in PolSAR images. Specifically, within the probabilistic framework of the Dirichlet process mixture model (DPMM), an observed PolSAR data point is described by the multiplication of a Wishartdistributed component and a class-dependent random variable (i.e., the textual variable). This modeling scheme leads to the proposed textured DPMM (tDPMM), which possesses more flexibility in characterizing PolSAR data in heterogeneous areas and from high-resolution images due to the introduction of the classdependent texture variable. The proposed tDPMM is learned by solving an optimization problem to achieve its Bayesian inference. With the knowledge of this optimization-based learning, the local correlation is incorporated through the pairwise constraint, which integrates an appropriate penalty term into the objective function so as to encourage the neighboring pixels to fall into the same category and to alleviate the "salt-and-pepper" classification appearance.We develop the learning algorithm with all the closed-form updates. The performance of the proposed method is evaluated with both low-resolution and high-resolution PolSAR images, which involve homogeneous, heterogeneous, and extremely heterogeneous areas. The experimental results reveal that the class-dependent texture variable is beneficial to PolSAR image classification and the pairwise constraint can effectively incorporate the local correlation in PolSAR images.

Multiview Consensus Graph Clustering

A graph is usually formed to reveal the relationship between data points and graph structure is encoded by the affinity matrix. Most graph-based multiview clustering methods use predefined affinity matrices and the clustering performance highly depends on the quality of graph. We learn a consensus graph with minimizing disagreement between different views and constraining the rank of the Laplacian matrix. Since diverse views admit the same underlying cluster structure across multiple views, we use a new disagreement cost function for regularizing graphs from different views toward a common consensus. Simultaneously, we impose a rank constraint on the Laplacian matrix to learn the consensus graph with exactly connected components where is the number of clusters, which is different from using fixed affinity matrices in most existing graph-based methods. With the learned consensus graph, we can directly obtain the cluster labels without performing any post-processing, such as -means clustering algorithm in spectral clustering-based methods. A multiview consensus clustering method is proposed to learn such a graph. An efficient iterative updating algorithm is derived to optimize the proposed challenging optimization problem. Experiments on several benchmark datasets have demonstrated the effectiveness of the proposed method in terms of seven metrics.

Rank-Constrained Spectral Clustering With Flexible Embedding

Spectral clustering (SC) has been proven to be effective in various applications. However, the learning scheme of SC is suboptimal in that it learns the cluster indicator from a fixed graph structure, which usually requires a rounding procedure to further partition the data. Also, the obtained cluster number cannot reflect the ground truth number of connected components in the graph. To alleviate these drawbacks, we propose a rank-constrained SC with flexible embedding framework. Specifically, an adaptive probabilistic neighborhood learning process is employed to recover the block-diagonal affinity matrix of an ideal graph. Meanwhile, a flexible embedding scheme is learned to unravel the intrinsic cluster structure in low-dimensional subspace, where the irrelevant information and noise in high-dimensional data have been effectively suppressed. The proposed method is superior to previous SC methods in that: 1) the block-diagonal affinity matrix learned simultaneously with the adaptive graph construction process, more explicitly induces the cluster membership without further discretization; 2) the number of clusters is guaranteed to converge to the ground truth via a rank constraint on the Laplacian matrix; and 3) the mismatch between the embedded feature and the projected feature allows more freedom for finding the proper cluster structure in the low-dimensional subspace as well as learning the corresponding projection matrix. Experimental results on both synthetic and real-world data sets demonstrate the promising performance of the proposed algorithm.

Graph Learning for Multiview Clustering

Most existing graph-based clustering methods need a predefined graph and their clustering performance highly depends on the quality of the graph. Aiming to improve the multiview clustering performance, a graph learning-based method is proposed to improve the quality of the graph. Initial graphs are learned from data points of different views, and the initial graphs are further optimized with a rank constraint on the Laplacian matrix. Then, these optimized graphs are integrated into a global graph with a well-designed optimization procedure. The global graph is learned by the optimization procedure with the same rank constraint on its Laplacian matrix. Because of the rank constraint, the cluster indicators are obtained directly by the global graph without performing any graph cut technique and the k-means clustering. Experiments are conducted on several benchmark datasets to verify the effectiveness and superiority of the proposed graph learning-based multiview clustering algorithm comparing to the state-of-the-art methods.

Constrained Low-Rank Representation for Robust Subspace Clustering

Subspace clustering aims to partition the data points drawn from a union of subspaces according to their underlying subspaces. For accurate semisupervised subspace clustering, all data that have a must-link constraint or the same label should be grouped into the same underlying subspace. However, this is not guaranteed in existing approaches. Moreover, these approaches require additional parameters for incorporating supervision information. In this paper, we propose a constrained low-rank representation (CLRR) for robust semisupervised subspace clustering, based on a novel constraint matrix constructed in this paper. While seeking the low-rank representation of data, CLRR explicitly incorporates supervision information as hard constraints for enhancing the discriminating power of optimal representation. This strategy can be further extended to other state-of-the-art methods, such as sparse subspace clustering. We theoretically prove that the optimal representation matrix has both a block-diagonal structure with clean data and a semisupervised grouping effect with noisy data. We have also developed an efficient optimization algorithm based on alternating the direction method of multipliers for CLRR. Our experimental results have demonstrated that CLRR outperforms existing methods.