Modal Clustering Using Semiparametric Mixtures and Mode Flattening

Abstract

Modal clustering has a clear population goal, where density estimation plays a critical role. In this paper, we study how to provide better density estimation so as to serve the objective of modal clustering. In particular, we use semiparametric mixtures for density estimation, aided with a novel mode-flattening technique. The use of semiparametric mixtures helps to produce better density estimates, especially in the multivariate situation, and the mode-flattening technique is intended to identify and smooth out spurious and minor modes. With mode flattening, the number of clusters can be sequentially reduced until there is only one mode left. In addition, we adopt the likelihood function in a coherent manner to measure the relative importance of a mode and let the current least important mode disappear in each step. For both simulated and real-world data sets, the proposed method performs very well, as compared with some well-known clustering methods in the literature, and can successfully solve some fairly difficult clustering problems.