Multi-view subspace clustering has attracted intensive attention to effectively fuse multi-view information by exploring appropriate graph structures. Although existing works have made impressive progress in clustering performance, most of them suffer from the cubic time complexity which could prevent them from being efficiently applied into large-scale applications. To improve the efficiency, anchor sampling mechanism has been proposed to select vital landmarks to represent the whole data. However, existing anchor selecting usually follows the heuristic sampling strategy, e.g. $k$ -means or uniform sampling. As a result, the procedures of anchor selecting and subsequent subspace graph construction are separated from each other which may adversely affect clustering performance. Moreover, the involved hyper-parameters further limit the application of traditional algorithms. To address these issues, we propose a novel subspace clustering method termed Fast Parameter-free Multi-view Subspace Clustering with Consensus Anchor Guidance (FPMVS-CAG). Firstly, we jointly conduct anchor selection and subspace graph construction into a unified optimization formulation. By this way, the two processes can be negotiated with each other to promote clustering quality. Moreover, our proposed FPMVS-CAG is proved to have linear time complexity with respect to the sample number. In addition, FPMVS-CAG can automatically learn an optimal anchor subspace graph without any extra hyper-parameters. Extensive experimental results on various benchmark datasets demonstrate the effectiveness and efficiency of the proposed method against the existing state-of-the-art multi-view subspace clustering competitors. These merits make FPMVS-CAG more suitable for large-scale subspace clustering. The code of FPMVS-CAG is publicly available at https://github.com/wangsiwei2010/FPMVS-CAG .

Incomplete multi-view clustering optimally integrates a group of pre-specified incomplete views to improve clustering performance. Among various excellent solutions, multiple kernel $k$ -means with incomplete kernels forms a benchmark, which redefines the incomplete multi-view clustering as a joint optimization problem where the imputation and clustering are alternately performed until convergence. However, the comparatively intensive computational and storage complexities preclude it from practical applications. To address these issues, we propose Late Fusion Incomplete Multi-view Clustering (LF-IMVC) which effectively and efficiently integrates the incomplete clustering matrices generated by incomplete views. Specifically, our algorithm jointly learns a consensus clustering matrix, imputes each incomplete base matrix, and optimizes the corresponding permutation matrices. We develop a three-step iterative algorithm to solve the resultant optimization problem with linear computational complexity and theoretically prove its convergence. Further, we conduct comprehensive experiments to study the proposed LF-IMVC in terms of clustering accuracy, running time, advantages of late fusion multi-view clustering, evolution of the learned consensus clustering matrix, parameter sensitivity and convergence. As indicated, our algorithm significantly and consistently outperforms some state-of-the-art algorithms with much less running time and memory.

Existing MKC algorithms cannot efficiently address the situation where some rows and columns of base kernel matrices are absent. This paper proposes two simple yet effective algorithms to address this issue. Different from existing approaches where incomplete kernel matrices are firstly imputed and a standard MKC algorithm is applied to the imputed kernel matrices, our first algorithm integrates imputation and clustering into a unified learning procedure. Specifically, we perform multiple kernel clustering directly with the presence of incomplete kernel matrices, which are treated as auxiliary variables to be jointly optimized. Also, it adaptively imputes incomplete kernel matrices and combines them to best serve clustering. Moreover, we further improve this algorithm by encouraging these incomplete kernel matrices to mutually complete each other. The three-step iterative algorithm is designed to solve the resultant optimization problems. After that, we theoretically study the generalization bound of the proposed algorithms. Extensive experiments are conducted on 13 benchmark data sets to compare the proposed algorithms with existing imputation-based methods. Our algorithms consistently achieve superior performance and the improvement becomes more significant with increasing missing ratio, verifying the effectiveness and advantages of the proposed joint imputation and clustering.

Deep clustering gains superior performance than conventional clustering by jointly performing feature learning and cluster assignment. Although numerous deep clustering algorithms have emerged in various applications, most of them fail to learn robust cluster-oriented features which in turn hurts the final clustering performance. To solve this problem, we propose a two-stage deep clustering algorithm by incorporating data augmentation and self-paced learning. Specifically, in the first stage, we learn robust features by training an autoencoder with examples that are augmented by random shifting and rotating the given clean examples. Then in the second stage, we encourage the learned features to be cluster-oriented by alternatively finetuning the encoder with the augmented examples and updating the cluster assignments of the clean examples. During finetuning the encoder, the target of each augmented example in the loss function is the center of the cluster to which the clean example is assigned. The targets may be computed incorrectly, and the examples with incorrect targets could mislead the encoder network. To stabilize the network training, we select most confident examples in each iteration by utilizing the adaptive self-paced learning. Extensive experiments validate that our algorithm outperforms the state of the arts on four image datasets.

In this paper, we propose to integrate feature selection and feature extration into a unified framework and design an unsupervised linear feature selective projection (FSP) for feature extraction with low-rank embedding and dual Laplacian regularization to exploit the intrinsic relationship among data and suppress the impact of noise. Specifically, a projection matrix with an $\ell_{2,1}$ -norm regularization is introduced to project original high dimensional data points into a new subspace with lower dimension, where the $\ell_{2,1}$ -norm regularization can endow the projection with good interpretability. We deploy a coefficient matrix with low rank constraint to reconstruct data points and the $\ell_{2,1}$ -norm is imposed to regularize the data reconstruction errors in the low-dimensional subspace and make FSP robust to noise. Furthermore, a dual graph Laplacian regularization term is imposed on the low dimensional data and data reconstruction matrix for preserving the local manifold geometrical structure of data. Finally, an alternatively iterative algorithm is carefully designed for solving the proposed optimization model. Theoretical convergence and computational complexity analysis of the algorithm are also provided. Comprehensive experiments on various benchmark datasets have been carried out to evaluate the performance of the proposed FSP. As indicated, our algorithm significantly outperforms other state-of-the-art methods for feature extraction