Gaussian Mixture Models Implementation to Enhance Spectral Clustering

Abstract

Nature variability has been studied for many years due to its importance in research areas such as Biology or Medicine. In order to characterize such variability, different methods have been used. Since the shape is one of the most important features of human perception, it is natural to assess the variation using shape models. Moreover, one of the most important activities in data analysis is clustering, meaning the task of grouping a set of objects in such a way that objects in the same group are more similar than objects in different groups. This paper presents a modification to the spectral clustering methodology, introduced by Valdes-Amaro and Bhalerao in 2009, using the Gaussian Mixture Models as a replacement for K-Means. In addition, a new shape descriptor is proposed to use it in the aforementioned methodology, called angular magnitude. Results are presented over different sets of shapes from natural and artificial objects, along with two different measurements to evaluate them quantitatively.