A Spectral Analysis Approach for Gaussian Mixture Estimation

TL;DR

This paper introduces a spectral analysis method for estimating the means of components in a one-dimensional Gaussian mixture, leveraging characteristic functions and Toeplitz matrices, and demonstrates superior performance over EM in simulations.

Contribution

The paper presents a novel spectral approach using Toeplitz matrices for Gaussian mixture expectation estimation, outperforming traditional EM algorithms.

Findings

Method outperforms EM in simulations

Effective for known number of components

Applicable to various Gaussian mixture configurations

Abstract

This paper deals with the estimation of one-dimensional Gaussian mixture. Given a set of observations of a K-component Gaussian mixture, we focus on the estimation of the component expectations. The number of components is supposed to be known. Our method is based on a spectral analysis of the estimated first characteristic function. We construct a Toeplitz matrix RM with 2M-1 estimated samples of the first characteristic function and show that the mixture component expectations can be derived from the eigenvector decomposition of RM. Simulations illustrate the performance of our algorithm on several configurations of a six-component Gaussian mixture. In the investigated scenarios the proposed method outperforms the Expectation-Maximization algorithm