Decomposable Principal Component Analysis

TL;DR

This paper introduces a distributed PCA method tailored for decomposable Gaussian graphical models, enabling efficient eigenvalue computation and anomaly detection in large-scale networks by leveraging local clique structures.

Contribution

It presents a novel approach to perform PCA in decomposable graphical models by reformulating in the sparse inverse covariance domain and distributing the computation across network cliques.

Findings

Effective distributed PCA algorithm demonstrated on network anomaly detection.

Reduces computational complexity by leveraging graph decomposability.

Applicable to large-scale decentralized systems.

Abstract

We consider principal component analysis (PCA) in decomposable Gaussian graphical models. We exploit the prior information in these models in order to distribute its computation. For this purpose, we reformulate the problem in the sparse inverse covariance (concentration) domain and solve the global eigenvalue problem using a sequence of local eigenvalue problems in each of the cliques of the decomposable graph. We demonstrate the application of our methodology in the context of decentralized anomaly detection in the Abilene backbone network. Based on the topology of the network, we propose an approximate statistical graphical model and distribute the computation of PCA.