Number of clusters, deconvolution and classical problem of moments

TL;DR

This paper explores the connection between cluster analysis, deconvolution, and the classical moment problem, providing methods to estimate the number of clusters in mixture models with known and unknown components.

Contribution

It introduces a novel approach linking deconvolution and moment problems to estimate the number of clusters in mixture distributions.

Findings

Methods for deconvolution with known and unknown distributions

Application to estimate the number of clusters in mixture models

Connections established between cluster analysis and classical moment problem

Abstract

In the paper there is given a connection between one special case of cluster analysis, deconvolution problem, and classical moment problem. Namely, the methods used there are applied to solve deconvolution problem for the case of one known distribution and another one concentrated in unknown finite number of points. These results can be applied to estimate a number of clusters for the case of scale or location mixture of identical distributions. keywords: number of clusters, deconvolution problem, classical moment problem, scale and location mixtures.