Formula omitted]-divergence NMF with biorthogonal regularization for data representation

Abstract

Non-Negative Matrix Factorization (NMF) has become a commonly used method for data representation. Orthogonal NMF improves the clustering performance by adding orthogonal constraints to the decomposed matrices. The existing orthogonal NMF methods typically use Euclidean distance to measure the difference between before and after factorization for convenience and simplicity. However, limitations of the Euclidean distance can lead to inflexibilities. In addition, failure to consider orthogonality of the decomposed features and sparsity of the data representation can also lead to degraded performance of the algorithm. In order to overcome the above shortcomings, we propose a novel β-divergence-based NMF with biorthogonal regularization (BO-βNMF). Our BO-βNMF method uses generalized β-divergence instead of Euclidean distance to measure the similarity between matrices, and selects an appropriate β for each type of data to obtain a more flexible way of measuring similarity. In addition, we also incorporate biorthogonal constraints into the minimized objective function, which ensures both orthogonality of the decomposed features and sparsity of the data representation. Furthermore, we use trace rather than Euclidean distance to measure the orthogonality of the decomposed matrices, which reduces execution time. Finally, clustering experiments on image datasets show that the overall clustering effect of BO-βNMF is better than state-of-the-art methods.