Multi-View Clustering via Semi-non-negative Tensor Factorization

Multi-view clustering (MVC) based on non-negative matrix factorization (NMF) and its variants have received a huge amount of attention in recent years due to their advantages in clustering interpretability. However, existing NMF-based multi-view clustering methods perform NMF on each view data respectively and ignore the impact of between-view. Thus, they can't well exploit the within-view spatial structure and between-view complementary information. To resolve this issue, we present semi-non-negative tensor factorization (Semi-NTF) and develop a novel multi-view clustering based on Semi-NTF with one-side orthogonal constraint. Our model directly performs Semi-NTF on the 3rd-order tensor which is composed of anchor graphs of views. Thus, our model directly considers the between-view relationship. Moreover, we use the tensor Schatten p-norm regularization as a rank approximation of the 3rd-order tensor which characterizes the cluster structure of multi-view data and exploits the between-view complementary information. In addition, we provide an optimization algorithm for the proposed method and prove mathematically that the algorithm always converges to the stationary KKT point. Extensive experiments on various benchmark datasets indicate that our proposed method is able to achieve satisfactory clustering performance

Nonconvex Nonsmooth Low-Rank Minimization via Iteratively Reweighted Nuclear Norm

The nuclear norm is widely used as a convex surrogate of the rank function in compressive sensing for low rank matrix recovery with its applications in image recovery and signal processing. However, solving the nuclear norm based relaxed convex problem usually leads to a suboptimal solution of the original rank minimization problem. In this paper, we propose to perform a family of nonconvex surrogates of $L_0$-norm on the singular values of a matrix to approximate the rank function. This leads to a nonconvex nonsmooth minimization problem. Then we propose to solve the problem by Iteratively Reweighted Nuclear Norm (IRNN) algorithm. IRNN iteratively solves a Weighted Singular Value Thresholding (WSVT) problem, which has a closed form solution due to the special properties of the nonconvex surrogate functions. We also extend IRNN to solve the nonconvex problem with two or more blocks of variables. In theory, we prove that IRNN decreases the objective function value monotonically, and any limit point is a stationary point. Extensive experiments on both synthesized data and real images demonstrate that IRNN enhances the low-rank matrix recovery compared with state-of-the-art convex algorithms

Bi-nuclear tensor Schatten-p norm minimization for multi-view subspace clustering

Multi-view subspace clustering aims to integrate the complementary information contained in different views to facilitate data representation. Currently, low-rank representation (LRR) serves as a benchmark method. However, we observe that these LRR-based methods would suffer from two issues: limited clustering performance and high computational cost since (1) they usually adopt the nuclear norm with biased estimation to explore the low-rank structures; (2) the singular value decomposition of large-scale matrices is inevitably involved. Moreover, LRR may not achieve low-rank properties in both intra-views and interviews simultaneously. To address the above issues, this paper proposes the Bi-nuclear tensor Schatten-p norm minimization for multi-view subspace clustering (BTMSC). Specifically, BTMSC constructs a third-order tensor from the view dimension to explore the high-order correlation and the subspace structures of multi-view features. The Bi-Nuclear Quasi-Norm (BiN) factorization form of the Schatten-p norm is utilized to factorize the third-order tensor as the product of two small-scale thirdorder tensors, which not only captures the low-rank property of the third-order tensor but also improves the computational efficiency. Finally, an efficient alternating optimization algorithm is designed to solve the BTMSC model. Extensive experiments with ten datasets of texts and images illustrate the performance superiority of the proposed BTMSC method over state-of-the-art methods

Multi-view Fuzzy Representation Learning with Rules based Model

Unsupervised multi-view representation learning has been extensively studied for mining multi-view data. However, some critical challenges remain. On the one hand, the existing methods cannot explore multi-view data comprehensively since they usually learn a common representation between views, given that multi-view data contains both the common information between views and the specific information within each view. On the other hand, to mine the nonlinear relationship between data, kernel or neural network methods are commonly used for multi-view representation learning. However, these methods are lacking in interpretability. To this end, this paper proposes a new multi-view fuzzy representation learning method based on the interpretable Takagi-Sugeno-Kang (TSK) fuzzy system (MVRL_FS). The method realizes multi-view representation learning from two aspects. First, multi-view data are transformed into a high-dimensional fuzzy feature space, while the common information between views and specific information of each view are explored simultaneously. Second, a new regularization method based on L_(2,1)-norm regression is proposed to mine the consistency information between views, while the geometric structure of the data is preserved through the Laplacian graph. Finally, extensive experiments on many benchmark multi-view datasets are conducted to validate the superiority of the proposed method.Comment: This work has been accepted by IEEE Transactions on Knowledge and Data Engineerin