Network Embedding Using Sparse Approximations of Random Walks

TL;DR

This paper introduces a novel, efficient network embedding method based on sparse approximations of diffusion processes, improving clustering and classification performance.

Contribution

It presents a new numerical approach using sparse diffusion wavelets for network embedding, combining theoretical justification with practical efficiency.

Findings

Effective for data clustering and multi-label classification

Outperforms existing methods in efficiency and accuracy

Theoretically justified scheme

Abstract

In this paper, we propose an efficient numerical implementation of Network Embedding based on commute times, using sparse approximation of a diffusion process on the network obtained by a modified version of the diffusion wavelet algorithm. The node embeddings are computed by optimizing the cross entropy loss via the stochastic gradient descent method with sampling of low-dimensional representations of green functions. We demonstrate the efficacy of this method for data clustering and multi-label classification through several examples, and compare its performance over existing methods in terms of efficiency and accuracy. Theoretical issues justifying the scheme are also discussed.