Gaussian mixture model decomposition of multivariate signals

Abstract We propose a greedy variational method for decomposing non-negative multivariate signal as weighted sum of Gaussians, which, borrowing the terminology from statistics, we refer to Gaussian mixture model. Notably, our has following features: (1) It accepts signals, i.e., sampled functions, histograms, time series, images, etc., input. (2) The can handle general (i.e., ellipsoidal) Gaussians. (3) No prior assumption on number components is needed. To best knowledge, no previous model decomposition simultaneously enjoys all these features. also prove an upper bound, which cannot be improved by global constant, distance any mode set corresponding means. For mixtures spherical Gaussians with common variance $$\sigma ^2$$ ? 2 , bound takes simple form $$\sqrt{n}\sigma $$ n . evaluate one- and two-dimensional signals. Finally, discuss relation between clustering decomposition, compare baseline expectation maximization algorithm.