Graph Quantization

TL;DR

This paper extends vector quantization to attributed graphs, providing theoretical foundations, optimality conditions, and statistical justification for clustering algorithms in graph domains.

Contribution

It introduces a theoretical framework for graph quantization, including Lloyd-Max conditions and consistency results, linking structural and statistical pattern recognition.

Findings

Lloyd-Max optimality conditions for graph quantizers

Consistency results for empirical graph quantization

Statistical justification for existing graph clustering algorithms

Abstract

Vector quantization(VQ) is a lossy data compression technique from signal processing, which is restricted to feature vectors and therefore inapplicable for combinatorial structures. This contribution presents a theoretical foundation of graph quantization (GQ) that extends VQ to the domain of attributed graphs. We present the necessary Lloyd-Max conditions for optimality of a graph quantizer and consistency results for optimal GQ design based on empirical distortion measures and stochastic optimization. These results statistically justify existing clustering algorithms in the domain of graphs. The proposed approach provides a template of how to link structural pattern recognition methods other than GQ to statistical pattern recognition.