Soft Clustering Based on Non-negative Matrix Factorization for Longitudinal Data

Abstract

In this paper, we consider a matrix consisting of longitudinal data as a frequency table for each individual at each observation time point, and apply a topic model based on Non-negative Matrix Factorization (NMF).Thus, it is possible for us to apply the soft clustering based on NMF and grasp the similar time-trend of longitudinal data.NMF also has an aspect of a regression model in which the observed data of each individual is approximated by a linear combination of several basis vectors.Two cases are illustrated, 1) the case where the number of observation time points is smaller than the number of individuals, 2) the case where the number of observation time points is larger than the number of individuals, which makes regression analysis difficult.From the results of the examples, varying coefficients were considered on the coefficient matrix of NMF.As a result, it is possible to predict the longitudinal data using the location information not included in the observation matrix.