MS-IMAP -- A Multi-Scale Graph Embedding Approach for Interpretable Manifold Learning

TL;DR

This paper presents a multi-scale graph embedding framework using spectral graph wavelets and contrastive learning, enabling interpretable representations and feature importance derivation for complex high-dimensional data.

Contribution

Introduces a novel multi-scale graph embedding method based on spectral graph wavelets with theoretical insights and interpretability features.

Findings

Effective in clustering tasks across multiple datasets

Provides feature importance insights from embeddings

Outperforms baseline methods in representation quality

Abstract

Deriving meaningful representations from complex, high-dimensional data in unsupervised settings is crucial across diverse machine learning applications. This paper introduces a framework for multi-scale graph network embedding based on spectral graph wavelets that employs a contrastive learning approach. We theoretically show that in Paley-Wiener spaces on combinatorial graphs, the spectral graph wavelets operator provides greater flexibility and control over smoothness compared to the Laplacian operator, motivating our approach. A key advantage of the proposed embedding is its ability to establish a correspondence between the embedding and input feature spaces, enabling the derivation of feature importance. We validate the effectiveness of our graph embedding framework on multiple public datasets across various downstream tasks, including clustering and unsupervised feature importance.