Mixture Density Function Estimation in Shape Clustering

Abstract

Recent developments in measurement tools have made it easier to obtain shape data, a collection of point coordinates in vector space that are meaningful when some of them are gathered together. As a result, clustering of shape data becomes increasingly important. However, few studies still perform applicable clustering in various cases because some studies rely on their specific shape representations. Thus, we apply a simple and widely recognized representation and generative model to shape. A configuration matrix of the point coordinates is used for the representation, and it is the simplest and most well-accepted representation in conventional shape analysis. As a generative model, we consider the mixture density function, a well-known model in statistics for expressing a population density function, which is a linear combination of subpopulation density functions. The aim of this article is to present a mixture density-based model that will be useful for clustering shape data. The clustering of shapes involves estimating the parameters of the model, and this estimation is derived using an EM algorithm based on the model. As examples of promising shape-data applications, the computational analyses of ape skulls, American football formations, and baseball pitches were performed. In addition, we evaluated the performance of the EM algorithm by comparing it with other typical clustering methods. The theoretical results not only contribute to statistical estimation for shape data but also extend the clustering of nonvector shape data. The experimental results show that the derived EM algorithm performs well in shape clustering.