Principal component analysis in decomposable Gaussian graphical models

Authors:
Ami Wiesel;Alfred O. Hero
Affiliations:
Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, 48109, USA;Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, 48109, USA
Venue:
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
Year:
2009

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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.