Decomposable Principal Component Analysis

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.

References in corpus (2)

• Model Selection Through Sparse Maximum Likelihood Estimation
• Sparse inverse covariance estimation with the lasso

Cited by in corpus (6)

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• Covariance estimation in decomposable Gaussian graphical models
• Reduced-Dimension Linear Transform Coding of Correlated Signals in Networks
• Testing the Structure of a Gaussian Graphical Model with Reduced Transmissions in a Distributed Setting
• A New Approach to Dimensionality Reduction for Anomaly Detection in Data Traffic
• Decentralized Eigenvalue Algorithms for Distributed Signal Detection in Cognitive Networks