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Distributed estimation of principal eigenspaces.

Jianqing Fan1, Dong Wang1, Kaizheng Wang1

  • 1Department of Operations Research and Financial Engineering Princeton University.

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|November 9, 2019
PubMed
Summary
This summary is machine-generated.

This study introduces a distributed Principal Component Analysis (PCA) algorithm for large datasets. The proposed method efficiently computes top eigenvectors across multiple machines, achieving results comparable to centralized PCA without full data access.

Keywords:
Communication EfficiencyDistributed LearningHeterogeneityOne-shot ApproachPCAUnbiasedness of Empirical Eigenspaces

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Area of Science:

  • Machine Learning
  • Statistical Analysis
  • Data Science

Background:

  • Principal Component Analysis (PCA) is crucial for identifying key data variations.
  • Centralized PCA is often infeasible for large, distributed datasets due to communication costs.

Purpose of the Study:

  • To develop and analyze a distributed PCA algorithm for large-scale data.
  • To investigate the performance and accuracy of distributed PCA estimators.

Main Methods:

  • A novel distributed PCA algorithm where nodes compute top K eigenvectors and transmit them to a central server.
  • Theoretical analysis of bias and variance for the distributed estimator.
  • Derivation of convergence rates based on data properties and network size.

Main Results:

  • The distributed PCA estimator is unbiased for distributions with symmetric innovation.
  • Convergence rates depend on effective rank, eigen-gap, and the number of machines.
  • Performance closely matches whole-sample PCA when the number of machines is reasonable.

Conclusions:

  • The proposed distributed PCA algorithm is efficient and accurate for large datasets.
  • The method maintains high performance even without access to the complete dataset.
  • The analysis extends to heterogeneous data with similar underlying eigen-structures.