Graph-based multi-view learning, which has hitherto been used to discover the intrinsic patterns of graph data giving the credit to its convenience of implementation and effectiveness. Note that even though these approaches have been increasingly adopted in multi-view clustering and have generated promising outcomes, they are still faced with the sub-optimal solution. For one thing, multi-view data can be corrupted in the raw feature space. For the other, most existing approaches normally utilize euclidean distance to obtain the similarity between two samples, which can not be the best option for all types of real-world data and leads to inferior results. Therefore, to overcome the aforementioned issues, we integrate multi-metric learning, graph filtering, and subspace learning into a collaborative learning framework for multi-view clustering. Particularly, we prefer to recover a smooth representation of data by graph filtering, which can reserve the geometric structure of the original multi-view data and discard the corruptions simultaneously. Furthermore, instead of using euclidean distance as a Swiss army knife, multiple metrics are utilized to fully exploit the correlation of data based on the smooth representation, hence finally facilitating the downstream clustering task. Extensive experiments on multi-view clustering tasks validate our theoretical findings of ours and prove the improvement of our method over the SOTA approaches.

Graph-based methods have hitherto been used to pursue the coherent patterns of data due to its ease of implementation and efficiency. These methods have been increasingly applied in multi-view learning and achieved promising performance in various clustering tasks. However, despite their noticeable empirical success, existing graph-based multi-view clustering methods may still suffer the suboptimal solution considering that multi-view data can be very complicated in raw feature space. Moreover, existing methods usually adopt the similarity metric by an ad hoc approach, which largely simplifies the relationship among real-world data and results in an inaccurate output. To address these issues, we propose to seamlessly integrates metric learning and graph learning for multi-view clustering. Specifically, we employ a useful metric to depict the inherent structure with linearity-aware of affinity graph representation learned based on the self-expressiveness property. Furthermore, instead of directly utilizing the raw features, we prefer to recover a smooth representation such that the geometric structure of the original data can be retained. We model the above concerns into a unified learning framework, and hence complements each learning subtask in a mutual reinforcement manner. The empirical studies corroborate our theoretical findings, and demonstrate that the proposed method is able to boost the multi-view clustering performance.

Multi-view clustering has hitherto been studied due to their effectiveness in dealing with heterogeneous data. Despite the empirical success made by recent works, there still exists several severe challenges. Particularly, previous multi-view clustering algorithms seldom consider the topological structure in data, which is essential for clustering data on manifold. Moreover, existing methods cannot fully explore the consistency of local structures between different views as they uncover the clustering structure in a intra-view way instead of a inter-view manner. In this paper, we propose to exploit the implied data manifold by learning the topological structure of data. Besides, considering that the consistency of multiple views is manifested in the generally similar local structure while the inconsistent structures are the minority, we further explore the intersections of multiple views in the sample level such that the cross-view consistency can be better maintained. We model the above concerns in a unified framework and design an efficient algorithm to solve the corresponding optimization problem. Experimental results on various multi-view datasets certificate the effectiveness of the proposed method and verify its superiority over other SOTA approaches.

Subspace clustering, which recoveries the subspace representation in the form of an affinity graph, has drawn tons of attention due to its effectiveness in various clustering tasks. However, existing subspace clustering methods are usually fed with raw data, which may lead to a suboptimal result since it is difficult to directly and accurately depict the inherent relation between data points. In this paper, we propose a novel subspace clustering method by holistically utilizing the pairwise similarity and graph geometric structure. Our model first constructs an initial subspace representation by means of self-expression, which is able to depict the global structure of data. Then, we use an effective metric to recover an intrinsic matrix with pairwise similarity based on the obtained representation, which further preserves the local structure. Besides, we propose to facilitate the downstream subspace learning task by searching for a smooth representation of the original data, which is obtained by applying a low-pass filter to retain the graph geometric features. By leveraging the subtasks of learning the smooth representation, performing the subspace learning, and recovering the intrinsic similarity matrix in a unified learning framework, each subtask can be alternately boosted. Experiments on several benchmark data sets have been conducted to verify the proposed method.

In multi-view subspace clustering, it is significant to find a common latent space in which the multi-view datasets are located. A number of multi-view subspace clustering methods have been proposed to explore the common latent subspace and achieved promising performance. However, previous multi-view subspace clustering algorithms seldom consider the multi-view consistency and multi-view diversity, let alone take them into consideration simultaneously. In this paper, we propose a novel multi-view subspace clustering by joint measuring the consistency and diversity, which is able to exploit these two complementary criteria seamlessly into a holistic design of clustering algorithms. The proposed model first searches a pure graph for each view by detecting the intrinsic consistent and diverse parts. A consensus graph is then obtained by fusing the multiple pure graphs. Moreover, the consensus graph is structurized to contain exactly$c$connected components where$c$is the number of clusters. In this way, the final clustering result can be obtained directly since each connected component precisely corresponds to an individual cluster. Extensive experimental studies on various datasets manifest that our model achieves comparable performance than the other state-of-the-art methods.

Multi-view subspace clustering aims to exploit data correlation consensus among multiple views, which essentially can be treated as graph-based approach. However, existing methods usually suffer from suboptimal solution as the raw data might not be separable into subspaces. In this paper, we propose to achieve a smooth representation for each view and thus facilitate the downstream clustering task. It is based on a assumption that a graph signal is smooth if nearby nodes on the graph have similar features representations. Specifically, our mode is able to retain the graph geometric features by applying a low-pass filter to extract the smooth representations of multiple views. Besides, our method achieves the smooth representation learning as well as multi-view clustering interactively in a unified framework, hence it is an end-to-end single-stage learning problem. Substantial experiments on benchmark multi-view datasets are performed to validate the effectiveness of the proposed method, compared to the state-of-the-arts over the clustering performance.