Noise Fuzzy Clustering-Based Robust Non-negative Matrix Factorization with I-divergence Criterion

Abstract

AbstractNon-negative Matrix Factorization (NMF) is a technique for factorizing a non-negative matrix into the products of non-negative component matrices and has been used in such applications as air pollution analysis. In order to make NMF robust against noise, noise clustering-based approach was proposed with least square criterion, where NMF model estimation was performed in conjunction with noise rejection under the iterative optimization principle. In this paper, another robust NMF model was proposed supported by I-divergence criterion, which considers asymmetric distance measures rather than symmetric ones in the least square model. The updating formula of fuzzy memberships for non-noise degrees of objects are also constructed based on I-divergence criterion. The characteristic features of the proposed method are compared with the conventional one through numerical experiments using an artificial dataset.KeywordsNon-negative matrix factorizationNoise fuzzy clusteringI-divergence