Graph Laplacian mixture model

TL;DR

This paper introduces a novel generative model for jointly clustering data and learning multiple underlying graphs, addressing the challenge of mixed data that resides on different graph structures.

Contribution

It proposes a new graph Laplacian mixture model that can infer multiple graphs and cluster data simultaneously, handling high-dimensional and mixed datasets.

Findings

Effective in clustering and graph inference on weather and traffic data

Demonstrates interpretability and robustness in high-dimensional settings

Shows promising results in digit classification

Abstract

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.