In this paper, we address the multi-view subspace clustering problem. Our method utilizes the circulant algebra for tensor, which is constructed by stacking the subspace representation matrices of different views and then rotating, to capture the low rank tensor subspace so that the refinement of the view-specific subspaces can be achieved, as well as the high order correlations underlying multi-view data can be explored. By introducing a recently proposed tensor factorization, namely tensor-Singular Value Decomposition (t-SVD) kilmer13 , we can impose a new type of low-rank tensor constraint on the rotated tensor to capture the complementary information from multiple views. Different from traditional unfolding based tensor norm, this low-rank tensor constraint has optimality properties similar to that of matrix rank derived from SVD, so the complementary information among views can be explored more efficiently and thoroughly. The established model, called t-SVD based Multi-view Subspace Clustering (t-SVD-MSC), falls into the applicable scope of augmented Lagrangian method, and its minimization problem can be efficiently solved with theoretical convergence guarantee and relatively low computational complexity. Extensive experimental testing on eight challenging image dataset shows that the proposed method has achieved highly competent objective performance compared to several state-of-the-art multi-view clustering methods.
The first stream is the graph-based approaches @cite_3 @cite_8 @cite_32 @cite_42 @cite_33 which exploit the relationship among different views by using multiple graph fusion strategy. @cite_3 constructed a bipartite graph underlying the minimizing-disagreement criterion to connect the two-view feature, and then solved standard spectral clustering problem on the bipartite graph. The method @cite_42 proposed to learn a latent graph transition probability matrix via low-rank and sparse decomposition to handle the noise from different views. Given graphs constructed separately from single view data, @cite_33 built cross-view tensor product graphs to explore higher order information. Moreover, graph based algorithms is closely related to Multiple Kernel Learning (MKL) technique, in which views are considered as given kernel matrices. The aim is to learn the weighted combination of these kernel and the partitioning simultaneously @cite_48 .
@cite_33 @cite_8 @cite_48 @cite_42 @cite_32 @cite_3
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Multi-view clustering takes diversity of multiple views (representations) into consideration. Multiple views may be obtained from various sources or dierent feature subsets and often provide complementary information to each other. In this paper, we propose a novel graph-based approach to integrate multiple representations to improve clustering performance. While original graphs have been widely used in many existing multi-view clustering approaches, the key idea of our approach is to integrate multiple views by exploring higher order information. In particular, given graphs constructed separately from single view data, we build cross-view tensor product graphs (TPGs), each of which is a Kronecker product of a pair of single-view graphs. Since each cross-view TPG captures higher order relationships of data under two dierent views, it is no surprise that we obtain more reliable similarities. We linearly combine multiple cross-view TPGs to integrate higher order information. Ecient graph diusion process on the fusion TPG helps to reveal the underlying cluster structure and boosts the clustering performance. Empirical study shows that the proposed approach outperforms state-of-the-art methods on benchmark datasets. We consider spectral clustering and transductive inference for data with multiple views. A typical example is the web, which can be described by either the hyperlinks between web pages or the words occurring in web pages. When each view is represented as a graph, one may convexly combine the weight matrices or the discrete Laplacians for each graph, and then proceed with existing clustering or classification techniques. Such a solution might sound natural, but its underlying principle is not clear. Unlike this kind of methodology, we develop multiview spectral clustering via generalizing the normalized cut from a single view to multiple views. We further build multiview transductive inference on the basis of multiview spectral clustering. Our framework leads to a mixture of Markov chains defined on every graph. The experimental evaluation on real-world web classification demonstrates promising results that validate our method. Exploiting multiple representations, or views, for the same set of instances within a clustering framework is a popular practice for boosting clustering accuracy. However, some of the available sources may be misleading (due to noise, errors in measurement etc.) in revealing the true structure of the data, thus, their inclusion in the clustering process may have negative influence. This aspect seems to be overlooked in the multi-view literature where all representations are equally considered. In this work, views are expressed in terms of given kernel matrices and a weighted combination of the kernels is learned in parallel to the partitioning. Weights assigned to kernels are indicative of the quality of the corresponding views' information. Additionally, the combination scheme incorporates a parameter that controls the admissible sparsity of the weights to avoid extremes and tailor them to the data. Two efficient iterative algorithms are proposed that alternate between updating the view weights and recomputing the clusters to optimize the intra-cluster variance from different perspectives. The conducted experiments reveal the effectiveness of our methodology compared to other multi-view methods. Multi-view clustering, which seeks a partition of the data in multiple views that often provide complementary information to each other, has received considerable attention in recent years. In real life clustering problems, the data in each view may have considerable noise. However, existing clustering methods blindly combine the information from multi-view data with possibly considerable noise, which often degrades their performance. In this paper, we propose a novel Markov chain method for Robust Multi-view Spectral Clustering (RMSC). Our method has a flavor of lowrank and sparse decomposition, where we firstly construct a transition probability matrix from each single view, and then use these matrices to recover a shared low-rank transition probability matrix as a crucial input to the standard Markov chain method for clustering. The optimization problem of RMSC has a low-rank constraint on the transition probability matrix, and simultaneously a probabilistic simplex constraint on each of its rows. To solve this challenging optimization problem, we propose an optimization procedure based on the Augmented Lagrangian Multiplier scheme. Experimental results on various real world datasets show that the proposed method has superior performance over several state-of-the-art methods for multi-view clustering. In graph-based learning models, entities are often represented as vertices in an undirected graph with weighted edges describing the relationships between entities. In many real-world applications, however, entities are often associated with relations of different types and or from different sources, which can be well captured by multiple undirected graphs over the same set of vertices. How to exploit such multiple sources of information to make better inferences on entities remains an interesting open problem. In this paper, we focus on the problem of clustering the vertices based on multiple graphs in both unsupervised and semi-supervised settings. As one of our contributions, we propose Linked Matrix Factorization (LMF) as a novel way of fusing information from multiple graph sources. In LMF, each graph is approximated by matrix factorization with a graph-specific factor and a factor common to all graphs, where the common factor provides features for all vertices. Experiments on SIAM journal data show that (1) we can improve the clustering accuracy through fusing multiple sources of information with several models, and (2) LMF yields superior or competitive results compared to other graph-based clustering methods.