Multi-view anchor graph clustering selects representative anchors to avoid full pair-wise similarities and therefore reduce the complexity of graph methods. Although widely applied in large-scale applications, existing approaches do not pay sufficient attention to establishing correct correspondences between the anchor sets across views. To be specific, anchor graphs obtained from different views are not aligned column-wisely. Such an Anchor-Unaligned Problem (AUP) would cause inaccurate graph fusion and degrade the clustering performance. Under multi-view scenarios, generating correct correspondences could be extremely difficult since anchors are not consistent in feature dimensions.

Multi-view unsupervised feature selection (MUFS) has recently emerged as an effective dimensionality reduction method for unlabeled multi-view data. However, most existing methods mainly use first-order similarity graphs to preserve local structure, often overlooking the global structure that can be captured by second-order similarity. In addition, a few MUFS methods leverage predefined second-order similarity graphs, making them vulnerable to noise and outliers and resulting in suboptimal feature selection performance. In this paper, we propose a novel MUFS method, termed Structure-aware Hybrid-order sImilarity learNing for multi-viEw unsupervised Feature Selection (SHINE-FS), to address the aforementioned problem. SHINE-FS first learns consensus anchors and the corresponding anchor graph to capture the cross-view relationships between the anchors and the samples. Based on the acquired cross-view consensus information, it generates low-dimensional representations of the samples, which facilitate the reconstruction of multi-view data by identifying discriminative features. Subsequently, it employs the anchor-sample relationships to learn a second-order similarity graph. Furthermore, by jointly learning first-order and second-order similarity graphs, SHINE-FS constructs a hybrid-order similarity graph that captures both local and global structures, thereby revealing the intrinsic data structure to enhance feature selection. Comprehensive experimental results on real multi-view datasets show that SHINE-FS outperforms the state-of-the-art methods.

Incomplete multi-view clustering aims to learn complete correlations among samples by leveraging complementary information across multiple views for clustering.

Incomplete multi-view clustering aims to learn complete correlations among samples by leveraging complementary information across multiple views for clustering.

Although widely applied in large-scale applications, existing approaches do not pay sufficient attention to establishing correct correspondences between the anchor sets across views.

Abstract--In light of their capability to capture structural information while reducing computing complexity, anchor graph-based multi-view clustering (AGMC) methods have attracted considerable attention in large-scale clustering problems. Nevertheless, existing AGMC methods still face the following two issues: 1) They directly embedded diverse anchor graphs into a consensus anchor graph (CAG), and hence ignore redundant information and numerous noises contained in these anchor graphs, leading to a decrease in clustering effectiveness; 2) They drop effectiveness and efficiency due to independent post-processing to acquire clustering indicators. T o overcome the aforementioned issues, we deliver a novel one-step multi-view clustering method with adaptive low-rank anchor-graph learning (OMCAL). T o construct a high-quality CAG, OMCAL provides a nuclear norm-based adaptive CAG learning model against information redundancy and noise interference. Then, to boost clustering effectiveness and efficiency substantially, we incorporate category indicator acquisition and CAG learning into a unified framework. Numerous studies conducted on ordinary and large-scale datasets indicate that OMCAL outperforms existing state-of-the-art methods in terms of clustering effectiveness and efficiency. Index T erms--Multi-view clustering, low-rank graph, anchor graph, matrix decomposition. HE rapid development of multimedia technology and information technology has led to the explosive growth of multi-view data. In the realm of multi-view clustering [1], [2], graph-based multi-view clustering (GMC) [3], [4], [5], [6] methods have garnered significant attention for their capacity to capture rich structural information within the given data. Zhiping Lin is with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore.

Deep multi-view clustering incorporating graph learning has presented tremendous potential. Most methods encounter costly square time consumption w.r.t. data size. Theoretically, anchor-based graph learning can alleviate this limitation, but related deep models mainly rely on manual discretization approaches to select anchors, which indicates that 1) the anchors are fixed during model training and 2) they may deviate from the true cluster distribution. Consequently, the unreliable anchors may corrupt clustering results. In this paper, we propose the Deep Multi-view Anchor Clustering (DMAC) model that performs clustering in linear time. Concretely, the initial anchors are intervened by the positive-incentive noise sampled from Gaussian distribution, such that they can be optimized with a newly designed anchor learning loss, which promotes a clear relationship between samples and anchors. Afterwards, anchor graph convolution is devised to model the cluster structure formed by the anchors, and the mutual information maximization loss is built to provide cross-view clustering guidance. In this way, the learned anchors can better represent clusters. With the optimal anchors, the full sample graph is calculated to derive a discriminative embedding for clustering. Extensive experiments on several datasets demonstrate the superior performance and efficiency of DMAC compared to state-of-the-art competitors.