Tri-regularized nonnegative matrix tri-factorization for co-clustering

Abstract 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.