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Semi-supervised multi-view clustering in the subspace has attracted sustained attention. The existing methods often project the samples with the same label into the same point in the low dimensional space. This hard constraint-based method magnifies the dimension reduction error, restricting the subsequent clustering performance. To relax the labeled data during projection, we propose a novel method called label relaxation-based semi-supervised non-negative matrix factorization (LRSNMF). In our method, we first employ the Spearman correlation coefficient to measure the similarity between samples. Based on this, we design a new relaxed non-negative label matrix for better subspace learning, instead of the binary matrix. Also, we derive an updated algorithm based on an alternative iteration rule to solve the proposed model. Finally, the experimental results on three real-world datasets (i.e., MSRC, ORL1, and ORL2) with six evaluation indexes (i.e., accuracy, NMI, purity, F-score, precision, and recall) show the advantages of our LRSNMF, with comparison to the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Incomplete multi-view clustering (IMC) has achieved widespread attention due to its advantage in fusing the multi-view information when the view samples are unobserved partly. Recently, it is shown that the clustering performance in the subspace can be improved by preserving the clustering structure of each view, but the problem of the inconsistent clustering structure caused by the incomplete graphs are seldom considered, restricting the clustering performance. Motivated by the clustering interpretation of the orthogonal non-negative matrix factorization, it is employed to unify the clustering structure of the data, and a new model called Incomplete Graph-regularized Orthogonal Non-negative Matrix Factorization (IGONMF) is proposed in this paper. In IGONMF, the reproduced representation is developed, based on which, a set of incomplete graphs are utilized to fully take advantage of the geometric structure of the data. And the orthogonality is further employed to alleviate the problem of the inconsistent clustering structure. Also, we design an effective iterative updating algorithm to solve the proposed model, along with its analysis on the convergence and the computational cost. Finally, experimental results on several real-world datasets indicate that our method is superior to the related state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Deep nonnegative matrix factorization (DMF) is a particularly useful technique for learning data representation in low-dimensional space. To further obtain the complex hidden information and keep the geometrical structures of the high-dimensional data, we propose a novel deep matrix factorization model with the graph regularization (called DGsnMF). For solving the model with multi-variables, we design a forward–backward splitting scheme. After that, the convergence analysis is attached to the proposed algorithm and it is proved to converge to a critical point. Empirical experiments on benchmark datasets show that the proposed method is superior to the compared methods. [ABSTRACT FROM AUTHOR]

Multiview data processing has attracted sustained attention as it can provide more information for clustering. To integrate this information, one often utilizes the non-negative matrix factorization (NMF) scheme which can reduce the data from different views into the subspace with the same dimension. Motivated by the clustering performance being affected by the distribution of the data in the learned subspace, a tri-factorization-based NMF model with an embedding matrix is proposed in this article. This model tends to generate decompositions with uniform distribution, such that the learned representations are more discriminative. As a result, the obtained consensus matrix can be a better representative of the multiview data in the subspace, leading to higher clustering performance. Also, a new lemma is proposed to provide the formulas about the partial derivation of the trace function with respect to an inner matrix, together with its theoretical proof. Based on this lemma, a gradient-based algorithm is developed to solve the proposed model, and its convergence and computational complexity are analyzed. Experiments on six real-world datasets are performed to show the advantages of the proposed algorithm, with comparison to the existing baseline methods. [ABSTRACT FROM AUTHOR]

Semi-supervised multi-view learning methods aim to boost the learning performance by conjunction with labeled data, because the label information can enhance the discriminant ability of the learned model. Recently, non-negative matrix factorization has received widespread attention in semi-supervised multi-view learning due to its powerful ability of feature extraction. However, the problem of very limited available labeled data is seldom considered. In this case, it is hard for existing approaches to obtain satisfied performance. Motivated by that the label propagation can classify a large number of unlabeled data with few labeled data, in this paper, we propose a novel semi-supervised multi-view learning approach to address the problem of sparse labeled data, called Label Propagation based Non-negative Matrix Factorization (LPNMF). In our model, the intrinsic manifold structure of data is constructed by the adaptive neighbors technology. Based on this intrinsic manifold structure, the label propagation is further employed to make full use of the limited labeled data. Besides, we design an efficient alternating algorithm for solving the optimization problem and provide theoretical analysis on its convergence properties and computational complexity. Finally, experiments on four real-world datasets demonstrate the advantage of our proposed methods, with comparison to the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Non-negative matrix factorization is widely used in multi-view clustering due to its ability of learning a common dimension-reduced factor. Recently, it is combined with the label information to improve the clustering, but the affection of the dimension-reduction to the classes of the labeled data is seldom considered. Motivated by that the graph constraint can keep the geometric structure of the data, it is employed to restrict the class variation of the data caused by the dimension reduction, and a semi-supervised method called Graph-regularized Partially Shared Non-negative Matrix Factorization (GPSNMF) is proposed for multi-view clustering in this paper. In our method, the affinity graph of each view is constructed to encode the geometric information, and the corresponding multiplication update algorithm based on alternative iteration rule is derived. In the experiments, two clustering approaches are tested based on the results of the proposed GPSNMF, and four real-world databases with different label proportions are performed to demonstrate the advantages of our method over the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Multi-view clustering (MVC) is an attractive clustering paradigm that can incorporate comprehensive information from multiple views. Among the MVC schemes, collective matrix factorization (CMF) has shown its great power in extracting shared information of multi-view data. Based on CMF, we propose a novel unified MVC framework, named Auto-weighted Collective Matrix Factorization with Graph Dual Regularization (ACMF-GDR). Specifically, we assign adaptive weights for each view and incorporate the smoothing cluster structure learning term to construct a unified auto-weighted CMF for MVC. Our ACMF-GDR model can obtain the cluster labels and common representations of the samples in a one-step manner. Furthermore, to make the common representations discriminative, graph dual regularization terms with orthogonality constraints are adopted on multiple views to preserve the geometrical structure of the decomposed factors simultaneously. Experimental results show the superior clustering performance of the proposed method. [ABSTRACT FROM AUTHOR]