Linlin Zong

Multi-view clustering via multi-manifold regularized non-negative matrix factorization

Non-negative matrix factorization based multi-view clustering algorithms have shown their competitiveness among different multi-view clustering algorithms. However, non-negative matrix factorization fails to preserve the locally geometrical structure of the data space. In this paper, we propose a multi-manifold regularized non-negative matrix factorization framework (MMNMF) which can preserve the locally geometrical structure of the manifolds for multi-view clustering. MMNMF incorporates consensus manifold and consensus coefficient matrix with multi-manifold regularization to preserve the locally geometrical structure of the multi-view data space. We use two methods to construct the consensus manifold and two methods to find the consensus coefficient matrix, which leads to four instances of the framework. Experimental results show that the proposed algorithms outperform existing non-negative matrix factorization based algorithms for multi-view clustering.

Constrained Clustering With Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) and symmetric NMF (SymNMF) have been shown to be effective for clustering linearly separable data and nonlinearly separable data, respectively. Nevertheless, many practical applications demand constrained algorithms in which a small number of constraints in the form of must-link and cannot-link are available. In this paper, we propose an NMF-based constrained clustering framework in which the similarity between two points on a must-link is enforced to approximate 1 and the similarity between two points on a cannot-link is enforced to approximate 0. We then formulate the framework using NMF and SymNMF to deal with clustering of linearly separable data and nonlinearly separable data, respectively. Furthermore, we present multiplicative update rules to solve them and show the correctness and convergence. Experimental results on various text data sets, University of California, Irvine (UCI) data sets, and gene expression data sets demonstrate the superiority of our algorithms over existing constrained clustering algorithms.

Local linear neighbor reconstruction for multi-view data

We propose to learn a unified similarity matrix by using multi-view information.The unified similarity matrix interacts with multi-view original local data.The learned similarity matrix enhances both spectral clustering and label propagation.Results on several datasets show the effectiveness of the learned similarity matrix. Graph based multi-view data analysis has become a hot topic in the past decade, and multi-view similarity matrix is fundamental for such tasks. Existing multi-view similarity matrix construction methods cannot learn local geometrical information in the original data space from multiple views simultaneously. Considering the fact that an appropriate similarity matrix is block-wise with intra-class similarity, it is more reasonable to learn a similarity matrix by using local geometrical information in multiple original data space. In this paper, we propose to construct a unified similarity matrix by using local linear neighbors in multiple views. In each view, the similarity matrix can be reconstructed with the weights of the neighbors of each data point in the original space. In multiple views, we seek for a unified similarity matrix which consists of the similarity matrix in each view. The unified similarity matrix can be used for spectral clustering, label propagation and other graph based learning algorithms. Experimental results show that spectral clustering and label propagation algorithms using the unified similarity matrix outperform those using other multi-view similarity matrices, they also outperform typical multi-view spectral clustering algorithms and typical multi-view label propagation algorithms.

Multi-view clustering via graph regularized symmetric nonnegative matrix factorization

Multi-view clustering has become a hot topic since the past decade and nonnegative matrix factorization (NMF) based multi-view clustering algorithms have shown their superiorities. Nevertheless, two drawbacks prevent NMF based multi-view algorithms from being a better algorithm: (1) The solution of NMF based multi-view algorithms is not unique. (2) Standard orthogonal basis matrix is not obtained for each view. Orthogonality is utilized to settle these above problems in our framework and high computational complexity caused by orthogonality is avoided. Moreover, to preserve the locally geometrical structure between views, graph regularization is utilized. Finally, we offer an update rule for the parameter of the graph regularization to balance the reconstruct error and regularization and make the objective function converge faster. Experimental results and theoretical proof show the validity and efficiency of our algorithm.

Multi-view clustering on unmapped data via constrained non-negative matrix factorization

Existing multi-view clustering algorithms require that the data is completely or partially mapped between each pair of views. However, this requirement could not be satisfied in many practical settings. In this paper, we tackle the problem of multi-view clustering on unmapped data in the framework of NMF based clustering. With the help of inter-view constraints, we define the disagreement between each pair of views by the fact that the indicator vectors of two samples from two different views should be similar if they belong to the same cluster and dissimilar otherwise. The overall objective of our algorithm is to minimize the loss function of NMF in each view as well as the disagreement between each pair of views. Furthermore, we provide an active inter-view constraints selection strategy which tries to query the relationships between samples that are the most influential and samples that are the farthest from the existing constraint set. Experimental results show that, with a small number of (either randomly selected or actively selected) constraints, the proposed algorithm performs well on unmapped data, and outperforms the baseline algorithms on partially mapped data and completely mapped data.

Heterogeneous Information Networks Bi-clustering with Similarity Regularization

Clustering analysis of multi-typed objects in heterogeneous information network HINs is an important and challenging problem. Nonnegative Matrix Tri-Factorization NMTF is a popular bi-clustering algorithm on document data and relational data. However, few algorithms utilize this method for clustering in HINs. In this paper, we propose a novel bi-clustering algorithm, BMFClus, for HIN based on NMTF. BMFClus not only simultaneously generates clusters for two types of objects but also takes rich heterogeneous information into account by using a similarity regularization. Experiments on both synthetic and real-world datasets demonstrate that BMFClus outperforms the state-of-the-art methods.

Active Semi-supervised Spectral Clustering

Spectral clustering is widely used in these years. Recently, methods that connect spectral clustering and semi-supervised clustering become popular. These methods improve the result through using constraint information in spectral clustering. Generally, there are two ways to select constrained information, one is random selection method and the other is active learning method. Here we focus on active learning methods. In this paper, we propose an active learning process, which considers the local and global information of dataset, and decide which constraint to choose by studying the change of eigenvectors.