Decomposable Principal Component Analysis

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

Reduced-Dimension Linear Transform Coding of Correlated Signals in Networks

A model, called the linear transform network (LTN), is proposed to analyze the compression and estimation of correlated signals transmitted over directed acyclic graphs (DAGs). An LTN is a DAG network with multiple source and receiver nodes. Source nodes transmit subspace projections of random correlated signals by applying reduced-dimension linear transforms. The subspace projections are linearly processed by multiple relays and routed to intended receivers. Each receiver applies a linear estimator to approximate a subset of the sources with minimum mean squared error (MSE) distortion. The model is extended to include noisy networks with power constraints on transmitters. A key task is to compute all local compression matrices and linear estimators in the network to minimize end-to-end distortion. The non-convex problem is solved iteratively within an optimization framework using constrained quadratic programs (QPs). The proposed algorithm recovers as special cases the regular and distributed Karhunen-Loeve transforms (KLTs). Cut-set lower bounds on the distortion region of multi-source, multi-receiver networks are given for linear coding based on convex relaxations. Cut-set lower bounds are also given for any coding strategy based on information theory. The distortion region and compression-estimation tradeoffs are illustrated for different communication demands (e.g. multiple unicast), and graph structures.Comment: 33 pages, 7 figures, To appear in IEEE Transactions on Signal Processin

Multivariate Generalized Gaussian Distribution: Convexity and Graphical Models

We consider covariance estimation in the multivariate generalized Gaussian distribution (MGGD) and elliptically symmetric (ES) distribution. The maximum likelihood optimization associated with this problem is non-convex, yet it has been proved that its global solution can be often computed via simple fixed point iterations. Our first contribution is a new analysis of this likelihood based on geodesic convexity that requires weaker assumptions. Our second contribution is a generalized framework for structured covariance estimation under sparsity constraints. We show that the optimizations can be formulated as convex minimization as long the MGGD shape parameter is larger than half and the sparsity pattern is chordal. These include, for example, maximum likelihood estimation of banded inverse covariances in multivariate Laplace distributions, which are associated with time varying autoregressive processes

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

USO DE ANÁLISE DE COMPONENTES PRINCIPAIS NA SELEÇÃO DE VARIÁVEIS PARA CLASSIFICAÇÃO EM BASES DE DADOS CONTAMINADAS POR RUÍDO BRANCO

Técnicas de indução de modelos podem ser usadas na tentativa de descobrir conhecimento em bases de dados, contudo, o requerimento relativo à complexidade da amostra pode inviabilizar a obtenção de resultados confiáveis. Uma forma de reduzir as exigências da complexidade da amostra é selecionar um subconjunto de variáveis. Este trabalho avalia como asserções de independência sobre as variáveis do domínio de aplicação afetam o desempenho dos métodos B2 e B4, baseados na Análise de Componentes Principais, na seleção de variáveis para indução de Redes Neurais Artificiais. A diferença no desempenho dos classificadores dada a presença ou ausência de informações de independências foi determinada em experimentos realizados sobre bases dados sintéticas e agrícolas

USO DE ANÁLISE DE COMPONENTES PRINCIPAIS NA SELEÇÃO DE VARIÁVEIS PARA CLASSIFICAÇÃO EM BASES DE DADOS CONTAMINADAS POR RUÍDO BRANCO

Técnicas de indução de modelos podem ser usadas na tentativa de descobrir conhecimento em bases de dados, contudo, o requerimento relativo à complexidade da amostra pode inviabilizar a obtenção de resultados confiáveis. Uma forma de reduzir as exigências da complexidade da amostra é selecionar um subconjunto de variáveis. Este trabalho avalia como asserções de independência sobre as variáveis do domínio de aplicação afetam o desempenho dos métodos B2 e B4, baseados na Análise de Componentes Principais, na seleção de variáveis para indução de Redes Neurais Artificiais. A diferença no desempenho dos classificadores dada a presença ou ausência de informações de independências foi determinada em experimentos realizados sobre bases dados sintéticas e agrícolas