Anchor graph learning has become a widely used technique for significantly reducing the computational complexity in existing multi-view clustering methods. However, most existing approaches select anchors independently for each view and then generate the consensus graph by directly fusing all anchor graphs. This process overlooks the correspondence between anchor sets across different views, i.e., the column order correspondence of the anchor graphs. To address this limitation, we propose a novel anchor-based tensor multi-rank constraint multi-view clustering method (TMC). Specifically, TMC captures the high-order structural information of the original data by constructing an anchor graph tensor and enforcing a multi-rank constraint to induce a block-diagonal structure. Additionally, to enhance anchor consistency across all view, we construct the anchor graph of each view into an anchor tensor and impose a low-rank constraint on it. In this way, the block-diagonal structure of each anchor graph maintains an approximate alignment between anchors. Furthermore, we provide theoretical proof that the generated anchor graphs inherently exhibit a block-diagonal structure. Extensive experimental results on six multi-view datasets demonstrate that TMC outperforms existing state-of-the-art methods, highlighting its effectiveness in multi-view clustering task.

Graph-based multi-view clustering methods have demonstrated satisfying performance by effectively capturing relationships among data samples. However, most existing methods primarily emphasize direct pairwise relationships, neglecting the exploration of high-order correlations present within each view. To this end, a novel approach, called multiview clustering via high-order bipartite graph learning and tensor low-rank representation (HBGTLRR), is proposed. Specifically, we first construct high-order bipartite graphs to capture latent relationships and concatenate them into a tensor. By applying tensor nuclear norm (TNN) minimization, we obtain a low-rank representation that reduces noise and preserves high-order consistency. Subsequently, a consensus graph is constructed by adaptively fusing the high-order bipartite graphs with corresponding weights, and then a Laplacian low-rank constraint is imposed on it to effectively capture the intrinsic data structure. Finally, extensive experimental results show that HBGTLRR significantly outperforms existing methods, thereby validating the effectiveness of our proposed method.

Multiple kernel clustering (MKC) enhances clustering performance by deriving a consensus partition or graph from a predefined set of kernels. Despite many advanced MKC methods proposed in recent years, the prevalent approaches involve incorporating all kernels by default to capture diverse information within the data. However, learning from all kernels may not be better than one of a few kernels, particularly since some kernels exhibit a higher proportion of noise than semantic content. Additionally, existing MKC methods, whether based on early-fusion or late-fusion approaches, predominantly rely on pairwise relationships among samples or cluster structures, neglecting potential correlations between these two aspects. To this end, we propose a multiple kernel clustering with an adaptive multi-scale partition selection method (MPS), which exploits multiple-dimensional representations and the pairwise cluster structure for clustering. By the proposed kernel selection framework, potentially harmful kernels are dynamically excluded during the kernel fusion process, and then the multi-scale partitions and similarity graphs derived from the retained kernels are utilized to facilitate the improved consensus partition generation. Finally, extensive experiments are conducted to demonstrate the effectiveness of MPS on eight benchmark datasets.

Multiple Kernel Clustering (MKC) has emerged as a prominent research domain in recent decades due to its capacity to exploit diverse information from multiple views by learning an optimal kernel. Despite the successes achieved by various MKC methods, a significant challenge lies in the computational complexity associated with generating a consensus partition from the optimal kernel matrix, typically of size$n \times n$, where$n$represents the number of samples. This computational bottleneck restricts the practical applicability of these methods when confronted with large-scale datasets. Furthermore, certain existing MKC algorithms derive the consensus partition matrix by fusing all base partitions. However, this fusion process may inadvertently overlook critical information embedded in individual base kernels, potentially leading to inferior clustering performance. In light of these challenges, we introduce an innovative and efficient multiple kernel$k$-means approach, denoted as FAMKKM. Notably, FAMKKM incorporates two approximated partition matrices instead of the original individual partition matric for each base kernel. This strategic substitution significantly reduces computational complexity. Additionally, FAMKKM leverages the original kernel information to guide the fusion of all base partitions, thereby enhancing the quality of the resulting consensus partition matrix. Finally, we substantiate the efficacy and efficiency of the proposed FAMKKM through extensive experiments conducted on six benchmark datasets. Our results demonstrate its superiority over state-of-the-art methods. The demo code of this work is publicly available athttps://github.com/WangJun2023/FAMKKM

Multi-view spectral clustering, which exploits the complementary information among graphs of diverse views to obtain superior clustering results, has attracted intensive attention recently. However, most existing multi-view spectral clustering methods obtain the clustering partitions in a two-step scheme, i.e., spectral embedding and subsequent$k$-means. This two-step scheme inevitably seeks sub-optimal clustering results due to the information loss during the two-steps processes. Besides, existing multi-view spectral clustering methods do not jointly utilize the information of graphs and embedding matrices, which also degrades final clustering results. To solve these issues, we propose a unified one-step multi-view spectral clustering method, which integrates the spectral embedding and$k$-means into a unified framework to obtain discrete clustering labels with a one-step strategy. Under the observation that the inner product of the embedding matrix is a low-rank approximation of the graph, we combine graphs and embedding matrices of different views to obtain a unified graph. Then, we directly capture the discrete clustering indicator matrix from the unified graph. Furthermore, we design an effective optimization algorithm to solve the resultant problem. Finally, a set of experiments on various datasets are conducted to verify the effectiveness of the proposed method. The demo code of this work is publicly available atrgb]0,0,1https://github.com/guanyuezhen/UOMvSC.