Multi-view clustering aims at simultaneously obtaining a consensus underlying subspace across multiple views and conducting clustering on the learned consensus subspace, which has gained a variety of interest in image processing. In this paper, we propose the Semi-supervised Structured Subspace Learning algorithm for clustering data points from Multiple sources (SSSL-M). We explicitly extend the traditional multi-view clustering with a semi-supervised manner and then build an anti-block-diagonal indicator matrix with small amount of supervisory information to pursue the block-diagonal structure of the shared affinity matrix. SSSL-M regularizes multiple view-specific affinity matrices into a shared affinity matrix based on reconstruction through a unified framework consisting of backward encoding networks and the self-expressive mapping. The shared affinity matrix is comprehensive and can flexibly encode complementary information from multiple view-specific affinity matrices. An enhanced structural consistency of affinity matrices from different views can be achieved and the intrinsic relationships among affinity matrices from multiple views can be effectively reflected in this manner. Technically, we formulate the proposed model as an optimization problem, which can be solved by an alternating optimization scheme. Experimental results over seven different benchmark datasets demonstrate that better clustering results can be obtained by our method compared with the state-of-the-art approaches.

Multi-view subspace clustering aims to cluster the data lying in a union of subspaces with low dimensions. The commonly used spectral clustering performs the final clustering based on an n×n affinity graph, which suffers from relative high time and space complexity. Some existing works have chosen key anchors with uniform sampling strategy or K -means for dealing with large-scale datasets. However, few of them pay attention to the physical meaning of cluster representation in the column of the dataset for learning informative anchors, which is independent from the instance representation. In this paper, we propose efficient dual multi-view clustering (EDMC) with relative low complexity. To be specific, EDMC makes full use of cluster representation space in the column of the dataset to help produce informative anchors, which has a clear physical meaning and is independent of instance representation in the row. It simultaneously explores the cluster and instance subspace representations to learn anchors for large-scale datasets. We perform anchor learning and efficient multi-view clustering in a unified framework and then adopt an alternative optimization strategy for solving the formulated problem. Extensive experiments performed on different datasets in terms of several metrics validate the superiority of the proposed method.

Multi-view clustering usually attempts to improve the final performance by integrating graph structure information from different views and methods based on anchor are presented to reduce the computation cost for datasets with large scales. Despite significant progress, these methods pay few attentions to ensuring that the cluster structure correspondence between anchor graph and partition is built on multi-view datasets. Besides, they ignore to discover the anchor graph depicting the shared cluster assignment across views under the orthogonal constraint on actual bases in factorization. In this paper, we propose a novel Dual consensus Anchor Learning for Fast multi-view clustering (DALF) method, where the cluster structure correspondence between anchor graph and partition is guaranteed on multi-view datasets with large scales. It jointly learns anchors, constructs anchor graph and performs partition under a unified framework with the rank constraint imposed on the built Laplacian graph and the orthogonal constraint on the centroid representation. DALF simultaneously focuses on the cluster structure in the anchor graph and partition. The final cluster structure is simultaneously shown in the anchor graph and partition. We introduce the orthogonal constraint on the centroid representation in anchor graph factorization and the cluster assignment is directly constructed, where the cluster structure is shown in the partition. We present an iterative algorithm for solving the formulated problem. Extensive experiments demonstrate the effectiveness and efficiency of DALF on different multi-view datasets compared with other methods.

Multiview clustering has received great attention and numerous subspace clustering algorithms for multiview data have been presented. However, most of these algorithms do not effectively handle high-dimensional data and fail to exploit consistency for the number of the connected components in similarity matrices for different views. In this article, we propose a novel consistency-induced multiview subspace clustering (CiMSC) to tackle these issues, which is mainly composed of structural consistency (SC) and sample assignment consistency (SAC). To be specific, SC aims to learn a similarity matrix for each single view wherein the number of connected components equals to the cluster number of the dataset. SAC aims to minimize the discrepancy for the number of connected components in similarity matrices from different views based on the SAC assumption, that is, different views should produce the same number of connected components in similarity matrices. CiMSC also formulates cluster indicator matrices for different views, and shared similarity matrices simultaneously in an optimization framework. Since each column of similarity matrix can be used as a new representation of the data point, CiMSC can learn an effective subspace representation for the high-dimensional data, which is encoded into the latent representation by reconstruction in a nonlinear manner. We employ an alternating optimization scheme to solve the optimization problem. Experiments validate the advantage of CiMSC over 12 state-of-the-art multiview clustering approaches, for example, the accuracy of CiMSC is 98.06% on the BBCSport dataset.

Data in real world are usually characterized in multiple views, including different types of features or different modalities. Multi-view learning has been popular in the past decades and achieved significant improvements. In this paper, we investigate three challenging problems in the field of incomplete multi-view representation learning, namely, i) how to reduce the influences produced by missing views in multi-view dataset, ii) how to learn a consistent and informative representation among different views and iii) how to alleviate the impacts of the inherent noise in multi-view data caused by high-dimensional features or varied quality for different data points. To address these challenges, we integrate these three tasks into a problem and propose a novel framework termed Noise-aware Incomplete Multi-view Learning Networks (NIM-Nets). NIM-Nets fully utilize incomplete data from different views to produce a multi-view shared representation which is consistent, informative and robust to noise. We model the inherent noise in data by defining the distribution $\Gamma $ and assuming that each observation in the incomplete dataset is sampled from the distribution $\Gamma $ . To the best of our knowledge, this is the first work to unify learning the consistent and informative representation, alleviating the impacts of noise in data and handling the view-missing patterns in multi-view learning into a framework. We also first give a definition of robustness and completeness for incomplete multi-view representation learning. Based on NIM-Nets, we present joint optimization models for classification and clustering, respectively. Extensive experiments on different datasets demonstrate the effectiveness of our method over the existing work based on classification and clustering tasks in terms of different metrics.

Multi-view clustering has gained great progress recently, which employs the representations from different views for improving the final performance. In this paper, we focus on the problem of multi-view clustering based on the Markov chain by considering low-rank constraints. Since most existing methods fail to simultaneously characterize the relations among different entries in a tensor from the global perspective and describe local structures of similarity matrices of a tensor, we propose a novel Flexible Tensor Learning for Multi-view Clustering with the Markov chain (FTLMCM) to solve this problem. We also construct transition probability matrices based on the Markov chain to fully utilize the connection between the Markov chain and spectral clustering. Specifically, the low-rank constraints of the tensor, the frontal slices and the lateral slices of the tensor are imposed on the objective function of the proposed method to achieve these goals. Besides, these three constraints can be optimized jointly to achieve mutual refinement. FTLMCM also uses the tensor rotation to better explore the relationships among different views. We formulate FTLMCM as a problem of low-rank tensor recovery and solve it with the augmented Lagrangian multiplier. Experiments on six different benchmark data sets under six metrics demonstrate that the proposed method is able to achieve better clustering performance.