Principal component analysis in decomposable Gaussian graphical models

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 (concen-tration) domain and solve the global eigenvalue problem using a se-quence of local eigenvalue problems in each of the cliques of the de-composable graph. We demonstrate the application of our methodol-ogy in the context of decentralized anomaly detection in the Abilene backbone network. Based on the topology of the network, we pro-pose an approximate statistical graphical model and distribute the computation of PCA. Index Terms — Principal component analysis, graphical mod-els, distributed data mining. 1