Fast, Warped Graph Embedding: Unifying Framework and One-Click Algorithm

TL;DR

This paper introduces GEM-D, a unifying framework for graph embedding algorithms, and proposes UltimateWalk, a scalable, parameter-free method that outperforms existing algorithms like DeepWalk and node2vec.

Contribution

The paper unifies existing graph embedding methods under GEM-D, introduces a novel warping function, and presents UltimateWalk, a one-click, scalable algorithm with superior performance.

Findings

GEM-D effectively unifies past graph embedding algorithms.

The exponential warping function empirically yields the best embeddings.

UltimateWalk outperforms DeepWalk and node2vec in experiments.

Abstract

What is the best way to describe a user in a social network with just a few numbers? Mathematically, this is equivalent to assigning a vector representation to each node in a graph, a process called graph embedding. We propose a novel framework, GEM-D that unifies most of the past algorithms such as LapEigs, DeepWalk and node2vec. GEM-D achieves its goal by decomposing any graph embedding algorithm into three building blocks: node proximity function, warping function and loss function. Based on thorough analysis of GEM-D, we propose a novel algorithm, called UltimateWalk, which outperforms the most-recently proposed state-of-the-art DeepWalk and node2vec. The contributions of this work are: (1) The proposed framework, GEM-D unifies the past graph embedding algorithms and provides a general recipe of how to design a graph embedding; (2) the nonlinearlity in the warping function contributes significantly to the quality of embedding and the exponential function is empirically optimal; (3) the proposed algorithm, UltimateWalk is one-click (no user-defined parameters), scalable and has a closed-form solution.