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Article overview
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Distributed Estimation of Principal Eigenspaces | | Jianqing Fan
; Dong Wang
; Kaizheng Wang
; Ziwei Zhu
; | | Date: |
21 Feb 2017 | | Abstract: | Principal component analysis (PCA) is fundamental to statistical machine
learning. It extracts latent principal factors that contribute to the most
variation of the data. When data are stored across multiple machines, however,
communication cost can prohibit the computation of PCA in a central location
and distributed algorithms for PCA are thus needed. This paper proposes and
studies a distributed PCA algorithm: each node machine computes the top $K$
eigenvectors and transmits them to the central server; the central server then
aggregates the information from all the node machines and conducts a PCA based
on the aggregated information. We investigate the bias and variance for the
resulting distributed estimator of the top $K$ eigenvectors. In particular, we
show that for distributions with symmetric innovation, the distributed PCA is
"unbiased". We derive the rate of convergence for distributed PCA estimators,
which depends explicitly on the effective rank of covariance, eigen-gap, and
the number of machines. We show that when the number of machines is not
unreasonably large, the distributed PCA performs as well as the whole sample
PCA, even without full access of whole data. The theoretical results are
verified by an extensive simulation study. We also extend our analysis to the
heterogeneous case where the population covariance matrices are different
across local machines but share similar top eigen-structures. | | Source: | arXiv, 1702.6488 | | Services: | Forum | Review | PDF | Favorites | |
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