Macrostate Mixture Models for Multiscale Spectral Clustering and Nonparametric Source Separation

Mixture modeling, cluster analysis, and graph partitioning methods are widely used in a variety of scientific and engineering disciplines. Accurately estimating the number of mixture components/clusters/partitions and their distributions is an active area of research. Macrostate theory describes the metastable states of physical systems and has an equivalent form to that of mixture models. Reformulating the original physical definition of macrostates in terms of mixture modeling problems encourages their use in data science and statistics applications outside of physics. Macrostate mixture models combine representation and inference into a single algorithm and also predict the appropriate number of mixture components directly from the spectrum of a data-dependent operator, unlike most other spectral clustering methods. Numerical examples on nonphysical mixture problems demonstrate the effectiveness and compare the advantages and disadvantages of this approach to other methods.