
Robust Principal Component Analysis Using Statistical Estimators
Principal Component Analysis (PCA) finds a linear mapping and maximizes ...
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DiagonallyDominant Principal Component Analysis
We consider the problem of decomposing a large covariance matrix into th...
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Online Distributed Estimation of Principal Eigenspaces
Principal components analysis (PCA) is a widely used dimension reduction...
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On the asymptotics of Maronna's robust PCA
The eigenvalue decomposition (EVD) parameters of the second order statis...
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High dimensional PCA: a new model selection criterion
Given a random sample from a multivariate population, estimating the num...
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Quantifying the Estimation Error of Principal Components
Principal component analysis is an important pattern recognition and dim...
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Steerable ePCA
In photonlimited imaging, the pixel intensities are affected by photon ...
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Robust covariance estimation for distributed principal component analysis
Principal component analysis (PCA) is a wellknown tool for dimension reduction. It can summarise the data in fewer than the original number of dimensions without losing essential information. However, when data are dispersed across multiple servers, communication cost can't make PCA useful in this situation. Thus distributed algorithms for PCA are needed. Fan et al. [Annals of statistics 47(6) (2019) 30093031] proposed a distributed PCA algorithm to settle this problem. On each server, They computed the K leading eigenvectors V_K^(ℓ)=(v_1^(ℓ), …, v_K^(ℓ)) ∈ℝ^d × K of the sample covariance matrix Σ and sent V_K^(ℓ) to the data center. In this paper, we introduce robust covariance matrix estimators respectively proposed by Minsker [Annals of statistics 46(6A) (2018) 28712903] and Ke et al. [Statistical Science 34(3) (2019) 454471] into the distributed PCA algorithm and compute its top K eigenvectors on each server and transmit them to the central server. We investigate the statistical error of the resulting distributed estimator and derive the rate of convergence for distributed PCA estimators for symmetric innovation distribution and general distribution. By simulation study, the theoretical results are verified. Also, we extend our analysis to the heterogeneous case with weaker moments where samples on each server and across servers are independent and their population covariance matrices are different but share the same top K eigenvectors.
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