Title: Clustering using low rank matrix estimation
Authors: Stephane Chretien - NPL (United Kingdom) [presenting]
Abstract: The problem of unsupervised clustering of high dimensional data, e.g.images, time series, gene expression data, etc. is considered. Such problems have attracted much interest in mathematical learning research, because of its wide applicability, from image segmentation, automatic medical diagnosis, marketing, data quality assessment, outlier detection, etc. We show how clustering can be addressed using a very simple low rank nonnegative matrix estimation problem, which can be solved efficiently using Burer-Monteiro type factorisation techniques. We then apply this clustering technique cluster-based reduced-order modelling (CROM), a recent technique generalising the Ulam-Galerkin method classically used for non-linear dynamical system analysis in order to determine a finite-rank approximation of the Perron-Frobenius operator.