# Graph heat mixture model learning

## TL;DR

This paper introduces a generative model and an EM algorithm to learn multiple underlying graphs from mixed signals, enabling better data interpretation in complex scenarios.

## Contribution

It presents a novel heat diffusion-based generative model for mixed signals and an EM algorithm to infer multiple graphs and separate signals, addressing limitations of prior methods.

## Key findings

- Successfully separates signals into groups
- Infers multiple underlying graphs
- Demonstrates effectiveness on synthetic and real data

## Abstract

Graph inference methods have recently attracted a great interest from the scientific community, due to the large value they bring in data interpretation and analysis. However, most of the available state-of-the-art methods focus on scenarios where all available data can be explained through the same graph, or groups corresponding to each graph are known a priori. In this paper, we argue that this is not always realistic and we introduce a generative model for mixed signals following a heat diffusion process on multiple graphs. We propose an expectation-maximisation algorithm that can successfully separate signals into corresponding groups, and infer multiple graphs that govern their behaviour. We demonstrate the benefits of our method on both synthetic and real data.