MIXANDMIX: numerical techniques for the computation of empirical spectral distributions of population mixtures The MIXANDMIX (mixtures by Anderson mixing) tool for the computation of the empirical spectral distribution of random matrices generated by mixtures of populations is described. Within the population mixture model the mapping between the population distributions and the limiting spectral distribution can be obtained by solving a set of systems of nonlinear equations, for which an efficient implementation is provided. The contributions include a method for accelerated fixed point convergence, a homotopy continuation strategy to prevent convergence to nonadmissible solutions, a blind nonuniform grid construction for effective distribution support detection and approximation, and a parallel computing architecture. Comparisons are performed with available packages for the single population case and with results obtained by simulation for the more general model implemented here. Results show competitive performance and improved flexibility.

Segmentation of multivariate mixed data via lossy coding and compression In this paper, based on ideas from lossy data coding and compression, we present a simple but surprisingly effective technique for segmenting multivariate mixed data that are drawn from a mixture of Gaussian distributions or linear subspaces. The goal is to find the optimal segmentation that minimizes the overall coding length of the segmented data, subject to a given distortion. We show that deterministic segmentation minimizes an upper bound on the (asymptotically) optimal solution. The proposed algorithm does not require any prior knowledge of the number or dimension of the groups, nor does it involve any parameter estimation. Simulation results reveal intriguing phasetransition behaviors of the number of segments when changing the level of distortion or the amount of outliers. Finally, we demonstrate how this technique can be readily applied to segment real imagery and bioinformatic data.