Decomposable Principal Component Analysis

In this paper, we consider principal component analysis (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 a...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2009-11, Vol.57 (11), p.4369-4377
Main Authors: Wiesel, A., Hero, A.O.
Format: Article
Language:English
Subjects:
Ambient intelligence
Anomaly detection
Applied sciences
Approximation
Computation
Computer networks
Decomposition
Detection, estimation, filtering, equalization, prediction
Distributed computing
Eigenvalues
Eigenvalues and eigenfunctions
Exact sciences and technology
Graphical models
Inference algorithms
Information, signal and communications theory
Inverse
Mathematical models
Miscellaneous
Network topology
Networks
Principal component analysis
Signal and communications theory
Signal processing
Signal processing algorithms
Signal, noise
Spine
Telecommunications and information theory
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Summary:In this paper, we consider principal component analysis (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 address 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 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.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2009.2025806