Treffer: One-shot Distributed Algorithm for Generalized Eigenvalue Problem

Title:
One-shot Distributed Algorithm for Generalized Eigenvalue Problem
Authors:
Lv, Kexin, He, Fan, Huang, Xiaolin, Yang, Jie, Chen, Liming
Source:
Proceedings of the 8th International Conference on Computing and Artificial Intelligence. :104-109
Publication Status:
Preprint
Publisher Information:
ACM, 2022.
Publication Year:
2022
Subject Terms:
FOS: Computer and information sciences, Computer Science - Machine Learning, 0202 electrical engineering, electronic engineering, information engineering, 02 engineering and technology, Machine Learning (cs.LG)
Document Type:
Fachzeitschrift Article
DOI:
10.1145/3532213.3532229
DOI:
10.48550/arxiv.2010.11625
Access URL:
http://arxiv.org/abs/2010.11625
Rights:
arXiv Non-Exclusive Distribution
URL: https://www.acm.org/publications/policies/copyright_policy#Background
Accession Number:
edsair.doi.dedup.....35a8da1e7b5921ea29f254b2d5ccdaaf
Database:
OpenAIRE

Weitere Informationen

Nowadays, more and more datasets are stored in a distributed way for the sake of memory storage or data privacy. The generalized eigenvalue problem (GEP) plays a vital role in a large family of high-dimensional statistical models. However, the existing distributed method for eigenvalue decomposition cannot be applied in GEP for the divergence of the empirical covariance matrix. Here we propose a general distributed GEP framework with one-shot communication for GEP. If the symmetric data covariance has repeated eigenvalues, e.g., in canonical component analysis, we further modify the method for better convergence. The theoretical analysis on approximation error is conducted and the relation to the divergence of the data covariance, the eigenvalues of the empirical data covariance, and the number of local servers is analyzed. Numerical experiments also show the effectiveness of the proposed algorithms.
The derivation of the bound in the proof of Theorem 1 contains some errors. And it cannot be resolved at this time.