Robust Non-Negative Matrix Factorization Based on Noise Fuzzy Clustering Mechanism and Application to Environmental Observation Data Analysis

Non-negative Matrix Factorization (NMF) is a basic method for decomposing matrices composed of only nonnegative values and has been utilized in various fields including air pollution analysis. However, based on the least square principle, NMF is easily influenced by noise. This paper proposes a robust NMF model by introducing noise rejection mechanism of noise fuzzy clustering with the goal of eliminating the influence of noise observation. Robust estimation is realized by estimating the degree of belongingness of each observation unit to noise clusters, which contributes to reducing the influences of noise in matrix decomposition. The characteristics of the proposed method are demonstrated in a toy example with an artificial data set followed by a task of air pollutant measurement analysis.