Shuffled Graph Classification: Theory and Connectome Applications

TL;DR

This paper introduces a formal framework for classifying shuffled graphs with latent vertex labels, providing theoretical insights and practical algorithms that outperform existing methods in finite samples.

Contribution

It offers a novel formalism for shuffled graph classification, addressing key theoretical questions and developing state-of-the-art heuristic algorithms.

Findings

Shuffling vertices can degrade classification performance under certain conditions.

Existence of universally consistent graph classifiers is established.

Practical algorithms achieve state-of-the-art performance in finite samples.

Abstract

We develop a formalism to address statistical pattern recognition of graph valued data. Of particular interest is the case of all graphs having the same number of uniquely labeled vertices. When the vertex labels are latent, such graphs are called shuffled graphs. Our formalism provides insight to trivially answer a number of open statistical questions including: (i) under what conditions does shuffling the vertices degrade classification performance and (ii) do universally consistent graph classifiers exist? The answers to these questions lead to practical heuristic algorithms with state-of-the-art finite sample performance, in agreement with our theoretical asymptotics.