Graph Wavelets via Sparse Cuts: Extended Version

TL;DR

This paper introduces a novel method for computing graph wavelet bases using sparse cuts, enabling efficient and accurate data encoding on large graphs by leveraging a regularized eigenvalue approach.

Contribution

It formulates the wavelet basis discovery as a relaxed vector optimization problem and proposes scalable algorithms for large graphs, improving data representation quality.

Findings

Effective encoding of graph structure and signals in diverse datasets

Outperforms baseline methods in compression and accuracy

Scalable algorithms for large graph datasets

Abstract

Modeling information that resides on vertices of large graphs is a key problem in several real-life applications, ranging from social networks to the Internet-of-things. Signal Processing on Graphs and, in particular, graph wavelets can exploit the intrinsic smoothness of these datasets in order to represent them in a both compact and accurate manner. However, how to discover wavelet bases that capture the geometry of the data with respect to the signal as well as the graph structure remains an open question. In this paper, we study the problem of computing graph wavelet bases via sparse cuts in order to produce low-dimensional encodings of data-driven bases. This problem is connected to known hard problems in graph theory (e.g. multiway cuts) and thus requires an efficient heuristic. We formulate the basis discovery task as a relaxation of a vector optimization problem, which leads to an elegant solution as a regularized eigenvalue computation. Moreover, we propose several strategies in order to scale our algorithm to large graphs. Experimental results show that the proposed algorithm can effectively encode both the graph structure and signal, producing compressed and accurate representations for vertex values in a wide range of datasets (e.g. sensor and gene networks) and significantly outperforming the best baseline.