Uncoupled Nonnegative Matrix Factorization with Pairwise Comparison Data

Masahiro Kohjima

Abstract: In this paper, we propose a new method called uncoupled nonnegative matrix factorization (UNMF). UNMF enables us to analyze data that cannot be represented by a matrix, due to the lack of correspondence between the index and values of the matrix elements caused by e.g., data collection under the constraint of privacy protection. We derive the multiplicative update rules for parameter estimation and confirm the effectiveness of UNMF by numerical experiments.