A New Matrix-Free Algorithm for the Large-Scale Trust-Region Subproblem
SIAM Journal on Optimization
Estimation of entropy and mutual information
Neural Computation
Introducing a weighted non-negative matrix factorization for image classification
Pattern Recognition Letters
Nonnegative matrix factorization with quadratic programming
Neurocomputing
Document clustering using nonnegative matrix factorization
Information Processing and Management: an International Journal
Multiplicative Update for Projective Nonnegative Matrix Factorization with Bregman Divergence
ISIP '10 Proceedings of the 2010 Third International Symposium on Information Processing
Csiszár’s divergences for non-negative matrix factorization: family of new algorithms
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Non-negative matrix factorization with quasi-newton optimization
ICAISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Soft Computing
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Recently, Nonnegative Matrix Factorization (NMF) is a developed method for dimension reduction, feature extraction and data mining, etc. In this paper, we propose an interior point trust region (IPTR) method, which can find a better solution in global region for NMF with general cost functions. First, to control the growth in the size of the solution with noise and regularize the solution in iterations, two auxiliary constraints are added into NMF. Then we introduce the logarithmic barrier function to eliminate the nonnegative regularization, and obtain an equivalent quadratic trust region problem by some mathematical calculation. According to the necessary and sufficient conditions of the trust region problem, we obtain a solution of the original problem by solving a parameterized linear system. We apply this method into NMF with different cost functions, including @a-divergence, @b-divergence, KL-divergence, dual KL(DKL)-divergence, where different cost functions are imposed on different types of data. Numerical experiments demonstrate the high performance of the proposed method.