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The goal of document co-clustering is to partition textual data sets into groups by utilizing the duality between documents (i.e., data points) and words (i.e., features). That is, the documents can be grouped based on their distribution on words, while words can be grouped based on their distribution on documents. However, traditional co-clustering methods are usually sensitive to the input affinity matrix since they partition the data based on the fixed data graph. To address this limitation, in this paper, based on nonnegative matrix tri-factorization, we propose a new framework of co-clustering with adaptive local structure learning. The proposed unified learning framework performs intrinsic structure learning and tri-factorization (i.e., 3-factor factorization) simultaneously. The intrinsic structure is adaptively learned from the results of tri-factorization, and the factors are reformulated to preserve the refined local structures of the textual data. In this way, the local structure learning and factorization can be mutually improved. Furthermore, considering the duality between documents and words, the proposed framework explores not only the adaptive local structure of the data space, but also the adaptive local structure of the feature space. In order to solve the optimization problem of our method, an efficient iterative updating algorithm is proposed with guaranteed convergence. Experiments on benchmark textual data sets demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The objective of co-clustering is to simultaneously identify blocks of similarity between the sample set and feature set. Co-clustering has become a widely used technique in data mining, machine learning, and other research areas. The nonnegative matrix tri-factorization (NMTF) algorithm, which aims to decompose an objective matrix into three low-dimensional matrices, is an important tool to achieve co-clustering. However, noise is usually introduced during objective matrix factorization, and the method of square loss is very sensitive to noise, which significantly reduces the performance of the model. To solve this issue, this paper proposes a tri-regularized NMTF (TRNMTF) model for co-clustering, which combines graph regularization, Frobenius norm, and l 1 norm to simultaneously optimize the objective function. TRNMTF can execute feature selection well, enhance the sparseness of the model, adjust the eigenvalues in the low-dimensional matrix, eliminate noise in the model, and obtain cleaner data matrices to approximate the objective matrix, which significantly improves the performance of the model and its generalization ability. Furthermore, to solve the iterative optimization schemes of TRNMTF, this study converts the objective function into elemental form to infer and provide detailed iterative update rules. Experimental results on 8 data sets show that the proposed model displays superior performance. [ABSTRACT FROM AUTHOR]

Nonnegative matrix factorization (NMF) has been a vital data representation technique, and has demonstrated significant potential in the field of machine learning and data mining. Nonnegative matrix tri-factorization (NMTF) is an extension of NMF, and provides more degrees of freedom than NMF. In this paper, we propose the correntropy based orthogonal nonnegative matrix tri-factorization (CNMTF) algorithm, which is robust to noisy data contaminated by non-Gaussian noise and outliers. Different from previous NMF algorithms, CNMTF firstly applies correntropy to NMTF to measure the similarity, and preserves double orthogonality conditions and dual graph regularization. We adopt the half-quadratic technique to solve the optimization problem of CNMTF, and derive the multiplicative update rules. The complexity issue of CNMTF is also presented. Furthermore, the robustness of the proposed algorithm is analyzed, and the relationships between CNMTF and several previous NMF based methods are discussed. Experimental results demonstrate that the proposed CNMTF method has better performance on real world image and text datasets for clustering tasks, compared with several state-of-the-art methods. • The correntropy based orthogonal nonnegative matrix tri-factorization (CNMTF) algorithm is proposed. • The robustness of CNMTF is analyzed by make a comparison with several robust NMF methods. • The relationships between CNMTF and several previous NMF methods are also discussed. [ABSTRACT FROM AUTHOR]