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 data 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 represents a collection of distinct data which naturally live 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 demonstrate promising performance in data clustering and multiple graph inference, and show desirable properties in terms of interpretability and coping with high dimensionality on weather and traffic data, as well as digit classification.