A Survey on Multi-View Clustering

With advances in information acquisition technologies, multi-view data become ubiquitous. Multi-view learning has thus become more and more popular in machine learning and data mining fields. Multi-view unsupervised or semi-supervised learning, such as co-training, co-regularization has gained considerable attention. Although recently, multi-view clustering (MVC) methods have been developed rapidly, there has not been a survey to summarize and analyze the current progress. Therefore, this paper reviews the common strategies for combining multiple views of data and based on this summary we propose a novel taxonomy of the MVC approaches. We further discuss the relationships between MVC and multi-view representation, ensemble clustering, multi-task clustering, multi-view supervised and semi-supervised learning. Several representative real-world applications are elaborated. To promote future development of MVC, we envision several open problems that may require further investigation and thorough examination.Comment: 17 pages, 4 figure

Feature Concatenation Multi-view Subspace Clustering

Multi-view clustering aims to achieve more promising clustering results than single-view clustering by exploring the multi-view information. Since statistic properties of different views are diverse, even incompatible, few approaches implement multi-view clustering based on the concatenated features directly. However, feature concatenation is a natural way to combine multiple views. To this end, this paper proposes a novel multi-view subspace clustering approach dubbed Feature Concatenation Multi-view Subspace Clustering (FCMSC). Specifically, by exploring the consensus information, multi-view data are concatenated into a joint representation firstly, then, $l_{2,1}$-norm is integrated into the objective function to deal with the sample-specific and cluster-specific corruptions of multiple views for benefiting the clustering performance. Furthermore, by introducing graph Laplacians of multiple views, a graph regularized FCMSC is also introduced to explore both the consensus information and complementary information for clustering. It is noteworthy that the obtained coefficient matrix is not derived by directly applying the Low-Rank Representation (LRR) to the joint view representation simply. Finally, an effective algorithm based on the Augmented Lagrangian Multiplier (ALM) is designed to optimized the objective functions. Comprehensive experiments on six real world datasets illustrate the superiority of the proposed methods over several state-of-the-art approaches for multi-view clustering

Low-rank Kernel Learning for Graph-based Clustering

Constructing the adjacency graph is fundamental to graph-based clustering. Graph learning in kernel space has shown impressive performance on a number of benchmark data sets. However, its performance is largely determined by the chosen kernel matrix. To address this issue, the previous multiple kernel learning algorithm has been applied to learn an optimal kernel from a group of predefined kernels. This approach might be sensitive to noise and limits the representation ability of the consensus kernel. In contrast to existing methods, we propose to learn a low-rank kernel matrix which exploits the similarity nature of the kernel matrix and seeks an optimal kernel from the neighborhood of candidate kernels. By formulating graph construction and kernel learning in a unified framework, the graph and consensus kernel can be iteratively enhanced by each other. Extensive experimental results validate the efficacy of the proposed method

Clustering with Similarity Preserving

Graph-based clustering has shown promising performance in many tasks. A key step of graph-based approach is the similarity graph construction. In general, learning graph in kernel space can enhance clustering accuracy due to the incorporation of nonlinearity. However, most existing kernel-based graph learning mechanisms is not similarity-preserving, hence leads to sub-optimal performance. To overcome this drawback, we propose a more discriminative graph learning method which can preserve the pairwise similarities between samples in an adaptive manner for the first time. Specifically, we require the learned graph be close to a kernel matrix, which serves as a measure of similarity in raw data. Moreover, the structure is adaptively tuned so that the number of connected components of the graph is exactly equal to the number of clusters. Finally, our method unifies clustering and graph learning which can directly obtain cluster indicators from the graph itself without performing further clustering step. The effectiveness of this approach is examined on both single and multiple kernel learning scenarios in several datasets

Spectral and matrix factorization methods for consistent community detection in multi-layer networks

We consider the problem of estimating a consensus community structure by combining information from multiple layers of a multi-layer network using methods based on the spectral clustering or a low-rank matrix factorization. As a general theme, these "intermediate fusion" methods involve obtaining a low column rank matrix by optimizing an objective function and then using the columns of the matrix for clustering. However, the theoretical properties of these methods remain largely unexplored. In the absence of statistical guarantees on the objective functions, it is difficult to determine if the algorithms optimizing the objectives will return good community structures. We investigate the consistency properties of the global optimizer of some of these objective functions under the multi-layer stochastic blockmodel. For this purpose, we derive several new asymptotic results showing consistency of the intermediate fusion techniques along with the spectral clustering of mean adjacency matrix under a high dimensional setup, where the number of nodes, the number of layers and the number of communities of the multi-layer graph grow. Our numerical study shows that the intermediate fusion techniques outperform late fusion methods, namely spectral clustering on aggregate spectral kernel and module allegiance matrix in sparse networks, while they outperform the spectral clustering of mean adjacency matrix in multi-layer networks that contain layers with both homophilic and heterophilic communities

Multi-view Metric Learning for Multi-view Video Summarization

Traditional methods on video summarization are designed to generate summaries for single-view video records; and thus they cannot fully exploit the redundancy in multi-view video records. In this paper, we present a multi-view metric learning framework for multi-view video summarization that combines the advantages of maximum margin clustering with the disagreement minimization criterion. The learning framework thus has the ability to find a metric that best separates the data, and meanwhile to force the learned metric to maintain original intrinsic information between data points, for example geometric information. Facilitated by such a framework, a systematic solution to the multi-view video summarization problem is developed. To the best of our knowledge, it is the first time to address multi-view video summarization from the viewpoint of metric learning. The effectiveness of the proposed method is demonstrated by experiments

Guided Co-training for Large-Scale Multi-View Spectral Clustering

In many real-world applications, we have access to multiple views of the data, each of which characterizes the data from a distinct aspect. Several previous algorithms have demonstrated that one can achieve better clustering accuracy by integrating information from all views appropriately than using only an individual view. Owing to the effectiveness of spectral clustering, many multi-view clustering methods are based on it. Unfortunately, they have limited applicability to large-scale data due to the high computational complexity of spectral clustering. In this work, we propose a novel multi-view spectral clustering method for large-scale data. Our approach is structured under the guided co-training scheme to fuse distinct views, and uses the sampling technique to accelerate spectral clustering. More specifically, we first select $p$ ($\ll n$) landmark points and then approximate the eigen-decomposition accordingly. The augmented view, which is essential to guided co-training process, can then be quickly determined by our method. The proposed algorithm scales linearly with the number of given data. Extensive experiments have been performed and the results support the advantage of our method for handling the large-scale multi-view situation

Multi-view Unsupervised Feature Selection by Cross-diffused Matrix Alignment

Multi-view high-dimensional data become increasingly popular in the big data era. Feature selection is a useful technique for alleviating the curse of dimensionality in multi-view learning. In this paper, we study unsupervised feature selection for multi-view data, as class labels are usually expensive to obtain. Traditional feature selection methods are mostly designed for single-view data and cannot fully exploit the rich information from multi-view data. Existing multi-view feature selection methods are usually based on noisy cluster labels which might not preserve sufficient information from multi-view data. To better utilize multi-view information, we propose a method, CDMA-FS, to select features for each view by performing alignment on a cross diffused matrix. We formulate it as a constrained optimization problem and solve it using Quasi-Newton based method. Experiments results on four real-world datasets show that the proposed method is more effective than the state-of-the-art methods in multi-view setting.Comment: 8 page

Multi-view Low-rank Sparse Subspace Clustering

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

Robust Kernelized Multi-View Self-Representations for Clustering by Tensor Multi-Rank Minimization

Most recently, tensor-SVD is implemented on multi-view self-representation clustering and has achieved the promising results in many real-world applications such as face clustering, scene clustering and generic object clustering. However, tensor-SVD based multi-view self-representation clustering is proposed originally to solve the clustering problem in the multiple linear subspaces, leading to unsatisfactory results when dealing with the case of non-linear subspaces. To handle data clustering from the non-linear subspaces, a kernelization method is designed by mapping the data from the original input space to a new feature space in which the transformed data can be clustered by a multiple linear clustering method. In this paper, we make an optimization model for the kernelized multi-view self-representation clustering problem. We also develop a new efficient algorithm based on the alternation direction method and infer a closed-form solution. Since all the subproblems can be solved exactly, the proposed optimization algorithm is guaranteed to obtain the optimal solution. In particular, the original tensor-based multi-view self-representation clustering problem is a special case of our approach and can be solved by our algorithm. Experimental results on several popular real-world clustering datasets demonstrate that our approach achieves the state-of-the-art performance.Comment: 8 pages, 5 figures, AAAI2018 submitte