Adaptive Cluster Expansion (ACE): A Multilayer Network for Estimating Probability Density Functions

TL;DR

ACE is a hierarchical multilayer network method that adaptively estimates high-dimensional probability density functions, enabling detection of anomalous regions in images by producing probability images.

Contribution

This paper introduces the adaptive cluster expansion (ACE), a novel multilayer network approach for high-dimensional density estimation and anomaly detection in images.

Findings

Successfully estimates joint probability density functions of image pixels.

Identifies statistically anomalous regions in homogeneous images.

Produces probability images highlighting anomalies.

Abstract

We derive an adaptive hierarchical method of estimating high dimensional probability density functions. We call this method of density estimation the "adaptive cluster expansion" or ACE for short. We present an application of this approach, based on a multilayer topographic mapping network, that adaptively estimates the joint probability density function of the pixel values of an image, and presents this result as a "probability image". We apply this to the problem of identifying statistically anomalous regions in otherwise statistically homogeneous images.