Graph Laplacian mixture model

Graph learning methods have recently been receiving increasing interest as means to infer structure in datasets. Most of the recent approaches focus on different relationships between a graph and data sample distributions, mostly in settings where all available relate to the same graph. This is, however, not always the case, as data is often available in mixed form, yielding the need for methods that are able to cope with mixture data and learn multiple graphs. We propose a novel generative model that explains a collection of distinct data naturally living on different graphs. We assume the mapping of data to graphs is not known and investigate the problem of jointly clustering a set of data and learning a graph for each of the clusters. Experiments in both synthetic and real-world datasets demonstrate promising performance both in terms of data clustering, as well as multiple graph inference from mixture data.