Tensor decomposition for learning Gaussian mixtures from moments. (November 2022)

• Record Type: Journal Article
• Authors: Khouja, Rima; Mattei, Pierre-Alexandre; Mourrain, Bernard
• Is Part Of: Journal of symbolic computation. Volume 113(2022)
• Page Start: 193
• Page End: 210
• Publication Date: 2022-11
• Subjects: Tensor decomposition -- Method of moments -- Gaussian mixture -- Symmetric tensor -- Clustering -- Simultaneous diagonalisation; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2022.04.002
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: In data processing and machine learning, an important challenge is to recover and exploit models that can represent accurately the data. We consider the problem of recovering Gaussian mixture models from datasets. We investigate symmetric tensor decomposition methods for tackling this problem, where the tensor is built from empirical moments of the data distribution. We consider identifiable tensors, which have a unique decomposition, showing that moment tensors built from spherical Gaussian mixtures have this property. We prove that symmetric tensors with interpolation degree strictly less than half their order are identifiable and we present an algorithm, based on simple linear algebra operations, to compute their decomposition. Illustrative experimentations show the impact of the tensor decomposition method for recovering Gaussian mixtures, in comparison with other state-of-the-art approaches.