2007/10/09 by N. Paul, Nicolas Paul, Michel Terré +6
Chemistry · Computer Science · Mathematics · Physics and Astronomy · #Advanced Statistical Methods and Models #Bayesian Methods and Mixture Models #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectroscopy and Chemometric Analyses #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.0710.1760
arxiv created 2007/10/09 · openalex publication_date 2007/10/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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