This paper explores the problem of multi-view spectral clustering (MVSC) based on tensor low-rank modeling. Unlike the existing methods that all adopt an off-the-shelf tensor low-rank norm without considering the special characteristics of the tensor in MVSC, we design a novel structured tensor low-rank norm tailored to MVSC. Specifically, we explicitly impose a symmetric low-rank constraint and a structured sparse low-rank constraint on the frontal and horizontal slices of the tensor to characterize the intra-view and inter-view relationships, respectively. Moreover, the two constraints could be jointly optimized to achieve mutual refinement. On basis of the novel tensor low-rank norm, we formulate MVSC as a convex low-rank tensor recovery problem, which is then efficiently solved with an augmented Lagrange multiplier-based method iteratively. Extensive experimental results on seven commonly used benchmark datasets show that the proposed method outperforms state-of-the-art methods to a significant extent. Impressively, our method is able to produce perfect clustering. In addition, the parameters of our method can be easily tuned, and the proposed model is robust to different datasets, demonstrating its potential in practice. The code is available at https://github.com/jyh-learning/MVSC-TLRR .

As a variant of nonnegative matrix factorization (NMF), symmetric NMF (SNMF) has shown to be effective for capturing the cluster structure embedded in the graph representation. In contrast to the existing SNMF-based clustering methods that empirically construct the similarity matrix and rigidly introduce the supervisory information to the assignment matrix, in this paper, we propose a novel SNMF-based semisupervised clustering method, namely, pairwise constraint propagation-induced SNMF (PCPSNMF). By formulating a single-constrained optimization problem, PCPSNMF is capable of learning the similarity and assignment matrices adaptively and simultaneously, in which a small amount of supervisory information in the form of pairwise constraints is introduced in a flexible way to guide the construction of the similarity matrix, and the two matrices communicate with each other to achieve mutual refinement until convergence. In addition, we propose an efficient alternating iterative algorithm to solve the optimization problem, whose convergence is theoretically proven. Experimental results over several benchmark image data sets demonstrate that PCPSNMF is less sensitive to initialization and produces higher clustering performance, compared with the state-of-the-art methods.

As a variant of non-negative matrix factorization (NMF), symmetric NMF (SymNMF) can generate the clustering result without additional post-processing, by decomposing a similarity matrix into the product of a clustering indicator matrix and its transpose. However, the similarity matrix in the traditional SymNMF methods is usually predefined, resulting in limited clustering performance. Considering that the quality of the similarity graph is crucial to the final clustering performance, we propose a new semisupervised model, which is able to simultaneously learn the similarity matrix with supervisory information and generate the clustering results, such that the mutual enhancement effect of the two tasks can produce better clustering performance. Our model fully utilizes the supervisory information in the form of pairwise constraints to propagate it for obtaining an informative similarity matrix. The proposed model is finally formulated as a non-negativity-constrained optimization problem. Also, we propose an iterative method to solve it with the convergence theoretically proven. Extensive experiments validate the superiority of the proposed model when compared with nine state-of-the-art NMF models.

In this article, we propose a semi-supervised non-negative matrix factorization (NMF) model by means of elegantly modeling the label information. The proposed model is capable of generating discriminable low-dimensional representations to improve clustering performance. Specifically, a pair of complementary regularizers, i.e., similarity and dissimilarity regularizers, is incorporated into the conventional NMF to guide the factorization. And, they impose restrictions on both the similarity and dissimilarity of the low-dimensional representations of data samples with labels as well as a small number of unlabeled ones. The proposed model is formulated as a well-posed constrained optimization problem and further solved with an efficient alternating iterative algorithm. Moreover, we theoretically prove that the proposed algorithm can converge to a limiting point that meets the Karush-Kuhn-Tucker conditions. Extensive experiments as well as comprehensive analysis demonstrate that the proposed model outperforms the state-of-the-art NMF methods to a large extent over five benchmark data sets, i.e., the clustering accuracy increases to 82.2% from 57.0%.

Deep self-expressiveness-based subspace clustering methods have demonstrated effectiveness. However, existing works only consider the attribute information to conduct the self-expressiveness, limiting the clustering performance. In this paper, we propose a novel adaptive attribute and structure subspace clustering network (AASSC-Net) to simultaneously consider the attribute and structure information in an adaptive graph fusion manner. Specifically, we first exploit an auto-encoder to represent input data samples with latent features for the construction of an attribute matrix. We also construct a mixed signed and symmetric structure matrix to capture the local geometric structure underlying data samples. Then, we perform self-expressiveness on the constructed attribute and structure matrices to learn their affinity graphs separately. Finally, we design a novel attention-based fusion module to adaptively leverage these two affinity graphs to construct a more discriminative affinity graph. Extensive experimental results on commonly used benchmark datasets demonstrate that our AASSC-Net significantly outperforms state-of-the-art methods. In addition, we conduct comprehensive ablation studies to discuss the effectiveness of the designed modules. The code is publicly available at https://github.com/ZhihaoPENG-CityU/AASSC-Net .