Gaussian mixture model decomposition of multivariate signals
This work addresses signal decomposition for applications like image and time series analysis, but it appears incremental as it builds on existing Gaussian mixture model techniques with specific enhancements.
The authors tackled the problem of decomposing non-negative multivariate signals into Gaussian mixture models without prior assumptions on component count, proposing a greedy variational method that handles ellipsoidal Gaussians and proving an upper bound of √nσ for spherical Gaussian mixtures. They evaluated the method on one- and two-dimensional signals and compared it to expectation maximization.
We propose a greedy variational method for decomposing a non-negative multivariate signal as a weighted sum of Gaussians, which, borrowing the terminology from statistics, we refer to as a Gaussian mixture model. Notably, our method has the following features: (1) It accepts multivariate signals, i.e. sampled multivariate functions, histograms, time series, images, etc. as input. (2) The method can handle general (i.e. ellipsoidal) Gaussians. (3) No prior assumption on the number of mixture components is needed. To the best of our knowledge, no previous method for Gaussian mixture model decomposition simultaneously enjoys all these features. We also prove an upper bound, which cannot be improved by a global constant, for the distance from any mode of a Gaussian mixture model to the set of corresponding means. For mixtures of spherical Gaussians with common variance $σ^2$, the bound takes the simple form $\sqrt{n}σ$. We evaluate our method on one- and two-dimensional signals. Finally, we discuss the relation between clustering and signal decomposition, and compare our method to the baseline expectation maximization algorithm.