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Principal Component Analysis with Contaminated Data：The High Dimensional Case
Statistical Learning Dimension Reduction Principal Component Analysis Robustness Outlier
2010/3/10
We consider the dimensionality-reduction problem (finding a subspace approximation of observed data) for
contaminated data in the high dimensional regime, where the number of observations is of the s...
A note on sensitivity of principal component subspaces and the efficient detection of influential observations in high dimensions
distance between subspaces influential observations perturbation principal component analysis
2009/9/16
In this paper we introduce an influence measure based on second order expansion of the RV and GCD measures for the comparison between unperturbed and perturbed eigenvectors of a symmetric matrix estim...
Theoretical Justification of Decision Rules for the Number of Factors: Principal Component Analysis as a Substitute for Factor Analysis in One-Factor Cases
cubic equation greater-than-one rule number of factors principal component analysis representation of a polynomial in terms of a remainder sequence scree test
2009/3/5
Applying principal component analysis as a substitute for factor analysis, we often adopt the following greater-than-one rule to decide the number of factors, k: Take the number of eigenvalues of the ...
Finite sample approximation results for principal component analysis：a matrix perturbation approach
Principal component analysis spiked covariance model randommatrix theory matrix perturbation phase transition
2010/3/17
Principal component analysis (PCA) is a standard tool for dimensional
reduction of a set of n observations (samples), each with
p variables. In this paper, using a matrix perturbation approach, we
...
Decomposable Principal Component Analysis
Principal Component Analysis Gaussian graphical models
2010/4/30
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 ...
Local functional principal component analysis
Local functional principal component analysis random functions Covariance operators
2010/4/26
Covariance operators of random functions are crucial tools to study
the way random elements concentrate over their support. The principal
component analysis of a random function X is well-known from...