Dual self-paced multi-view clustering

Towards a unified framework for graph-based multi-view clustering

Recently, clustering data collected from various sources has become a hot topic in real-world applications. The most common methods for multi-view clustering can be divided into several categories: Spectral clustering algorithms, subspace multi-view clustering algorithms, matrix factorization approaches, and kernel methods. Despite the high performance of these methods, they directly fuse all similarity matrices of all views and separate the affinity learning process from the multiview clustering process. The performance of these algorithms can be affected by noisy affinity matrices. To overcome this drawback, this paper presents a novel method called One Step Multi-view Clustering via Consensus Graph Learning and Nonnegative Embedding (OSMGNE). Instead of directly merging the similarity matrices of different views, which may contain noise, a step of learning a consensus similarity matrix is performed. This step forces the similarity matrices of different views to be too similar, which eliminates the problem of noisy data. Moreover, the use of the nonnegative embedding matrix (soft cluster assignment matrix makes it possible to directly obtain the final clustering result without any extra step. The proposed method can solve five subtasks simultaneously. It jointly estimates the similarity matrix of all views, the similarity matrix of each view, the corresponding spectral projection matrix, the unified clustering indicator matrix, and automatically gives the weight of each view without the use of hyper-parameters. In addition, another version of our method is also studied in this paper. This method differs from the first one by using a consensus spectral projection matrix and a consensus Laplacian matrix over all views. An iterative algorithm is proposed to solve the optimization problem of these two methods. The two proposed methods are tested on several real datasets, which prove their superiority.

Adaptive-weighted deep multi-view clustering with uniform scale representation

Multi-view clustering has attracted growing attention owing to its powerful capacity of multi-source information integration. Although numerous advanced methods have been proposed in past decades, most of them generally fail to distinguish the unequal importance of multiple views to the clustering task and overlook the scale uniformity of learned latent representation among different views, resulting in blurry physical meaning and suboptimal model performance. To address these issues, in this paper, we propose a joint learning framework, termed Adaptive-weighted deep Multi-view Clustering with Uniform scale representation (AMCU). Specifically, to achieve more reasonable multi-view fusion, we introduce an adaptive weighting strategy, which imposes simplex constraints on heterogeneous views for measuring their varying degrees of contribution to consensus prediction. Such a simple yet effective strategy shows its clear physical meaning for the multi-view clustering task. Furthermore, a novel regularizer is incorporated to learn multiple latent representations sharing approximately the same scale, so that the objective for calculating clustering loss cannot be sensitive to the views and thus the entire model training process can be guaranteed to be more stable as well. Through comprehensive experiments on eight popular real-world datasets, we demonstrate that our proposal performs better than several state-of-the-art single-view and multi-view competitors.

Low-rank discrete multi-view spectral clustering

Spectral clustering has attracted intensive attention in multimedia applications due to its good performance on arbitrary shaped clusters and well-defined mathematical framework. However, most existing multi-view spectral clustering methods still have the following demerits: (1) They ignore useful complementary information embedded in indicator matrices of different views. (2) The conventional post-processing methods based on the relax and discrete strategy inevitably result in the sub-optimal discrete solution. To tackle the aforementioned drawbacks, we propose a low-rank discrete multi-view spectral clustering model. Drawing inspiration from the fact that the difference between indicator matrices of different views provides useful complementary information for clustering, our model exploits the complementary information embedded in indicator matrices with tensor Schatten p-norm constraint. Further, we integrate low-rank tensor learning and discrete label recovering into a uniform framework, which avoids the uncertainty of the relaxed and discrete strategy. Extensive experiments on benchmark datasets have demonstrated the effectiveness and superiority of the proposed method.

Enhanced tensor low-rank representation learning for multi-view clustering

Multi-view subspace clustering (MSC), assuming the multi-view data are generated from a latent subspace, has attracted considerable attention in multi-view clustering. To recover the underlying subspace structure, a successful approach adopted recently is subspace clustering based on tensor nuclear norm (TNN). But there are some limitations to this approach that the existing TNN-based methods usually fail to exploit the intrinsic cluster structure and high-order correlations well, which leads to limited clustering performance. To address this problem, the main purpose of this paper is to propose a novel tensor low-rank representation (TLRR) learning method to perform multi-view clustering. First, we construct a 3rd-order tensor by organizing the features from all views, and then use the t-product in the tensor space to obtain the self-representation tensor of the tensorial data. Second, we use the ℓ_1,2 norm to constrain the self-representation tensor to make it capture the class-specificity distribution, that is important for depicting the intrinsic cluster structure. And simultaneously, we rotate the self-representation tensor, and use the tensor singular value decomposition-based weighted TNN as a tighter tensor rank approximation to constrain the rotated tensor. For the challenged mathematical optimization problem, we present an effective optimization algorithm with a theoretical convergence guarantee and relatively low computation complexity. The constructed convergent sequence to the Karush-Kuhn-Tucker (KKT) critical point solution is mathematically validated in detail. We perform extensive experiments on four datasets and demonstrate that TLRR outperforms state-of-the-art multi-view subspace clustering methods.

Single Cell Self-Paced Clustering with Transcriptome Sequencing Data

Single cell RNA sequencing (scRNA-seq) allows researchers to explore tissue heterogeneity, distinguish unusual cell identities, and find novel cellular subtypes by providing transcriptome profiling for individual cells. Clustering analysis is usually used to predict cell class assignments and infer cell identities. However, the performance of existing single-cell clustering methods is extremely sensitive to the presence of noise data and outliers. Existing clustering algorithms can easily fall into local optimal solutions. There is still no consensus on the best performing method. To address this issue, we introduce a single cell self-paced clustering (scSPaC) method with F-norm based nonnegative matrix factorization (NMF) for scRNA-seq data and a sparse single cell self-paced clustering (sscSPaC) method with l21-norm based nonnegative matrix factorization for scRNA-seq data. We gradually add single cells from simple to complex to our model until all cells are selected. In this way, the influences of noisy data and outliers can be significantly reduced. The proposed method achieved the best performance on both simulation data and real scRNA-seq data. A case study about human clara cells and ependymal cells scRNA-seq data clustering shows that scSPaC is more advantageous near the clustering dividing line.

Efficient correntropy-based multi-view clustering with anchor graph embedding

Although multi-view clustering has received widespread attention due to its far superior performance to single-view clustering, it still faces the following issues: (1) high computational cost, considering the introduction of multi-view information, reduces the clustering efficiency greatly; (2) complex noises and outliers, existed in real-world data, pose a huge challenge to the robustness of clustering algorithms. Currently, how to increase the efficiency and robustness has become two important issues of multi-view clustering. To cope with the above issues, an efficient correntropy-based multi-view clustering algorithm (ECMC) is proposed in this paper, which can not only improve clustering efficiency by constructing embedded anchor graph and utilizing nonnegative matrix factorization (NMF), but also enhance the robustness by exploring correntropy to suppress various noises and outliers. To further improve clustering efficiency, one of the factors of NMF is constrained to be an indicator matrix instead of a traditional non-negative matrix, so that the categories of samples can be obtained directly without any extra operation. Subsequently, a novel half-quadratic-based strategy is proposed to optimize the non-convex objective function of ECMC. Finally, extensive experiments on eight real-world datasets and eighteen noisy datasets show that ECMC can guarantee faster speed and better robustness than other state-of-the-art multi-view clustering algorithms.