Decomposable principal components analysis

Abstract—In this paper, we consider principal component anal-ysis (PCA) in decomposable Gaussian graphical models. We exploit the prior information in these models in order to distribute PCA computation. For this purpose, we reformulate the PCA problem in the sparse inverse covariance (concentration) domain and ad-dress the global eigenvalue problem by solving a sequence of local eigenvalue problems in each of the cliques of the decomposable graph. We illustrate our methodology in the context of decentral-ized 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. Index Terms—Anomaly detection, graphical models, principal component analysis. I