Cholesky decomposition rectification for non-negative matrix factorization

Authors:
Tetsuya Yoshida
Affiliations:
Graduate School of Information Science and Technology, Hokkaido University, Sapporo, Japan
Venue:
ISMIS'11 Proceedings of the 19th international conference on Foundations of intelligent systems
Year:
2011

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Abstract

We propose a method based on Cholesky decomposition for Non-negative Matrix Factorization (NMF). NMF enables to learn local representation due to its non-negative constraint. However, when utilizing NMF as a representation leaning method, the issues due to the non-orthogonality of the learned representation has not been dealt with. Since NMF learns both feature vectors and data vectors in the feature space, the proposed method 1) estimates the metric in the feature space based on the learned feature vectors, 2) applies Cholesky decomposition on the metric and identifies the upper triangular matrix, 3) and utilizes the upper triangular matrix as a linear mapping for the data vectors. The proposed approach is evaluated over several real world datasets. The results indicate that it is effective and improves performance.