Learning Optimal Graph Filters for Clustering of Attributed Graphs

TL;DR

This paper introduces a novel graph signal processing approach that learns optimal FIR and ARMA graph filters specifically designed for clustering attributed graphs, improving cluster separation.

Contribution

It proposes a two-step iterative optimization method to learn interpretable graph filters tailored for clustering attributed graphs, addressing limitations of existing lowpass filtering methods.

Findings

Outperforms state-of-the-art clustering methods on attributed networks.

Learned filters effectively enhance cluster separation.

Method provides interpretable filter parameters.

Abstract

Many real-world systems can be represented as graphs where the different entities in the system are presented by nodes and their interactions by edges. An important task in studying large datasets with graphical structure is graph clustering. While there has been a lot of work on graph clustering using the connectivity between the nodes, many real-world networks also have node attributes. Clustering attributed graphs requires joint modeling of graph structure and node attributes. Recent work has focused on combining these two complementary sources of information through graph convolutional networks and graph filtering. However, these methods are mostly limited to lowpass filtering and do not explicitly learn the filter parameters for the clustering task. In this paper, we introduce a graph signal processing based approach, where we learn the parameters of Finite Impulse Response (FIR) and Autoregressive Moving Average (ARMA) graph filters optimized for clustering. The proposed approach is formulated as a two-step iterative optimization problem, focusing on learning interpretable graph filters that are optimal for the given data and that maximize the separation between different clusters. The proposed approach is evaluated on attributed networks and compared to the state-of-the-art methods.