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One-Shot Distributed Algorithm for PCA With RBF Kernels
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DOI：10.1109/LSP.2021.3095017.png)
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Abstract
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This letter proposes a one-shot algorithm for feature-distributed kernel PCA. Our algorithm is inspired by the dual relationship between sample-distributed and feature-distributed scenarios. This interesting relationship makes it possible to establish distributed kernel PCA for feature-distributed cases from ideas of distributed PCA in the sample-distributed scenario. In the theoretical part, we analyze the approximation error for both linear and RBF kernels. The result suggests that when eigenvalues decay fast, the proposed algorithm gives high-quality results with low communication cost. This result is also verified by numerical experiments, showing the effectiveness of our algorithm in practice.
Keywords:
Kernel
Principal component analysis
Signal processing algorithms
Partitioning algorithms
Covariance matrices
Eigenvalues and eigenfunctions
Distributed databases
Distributed data
distributed learning
principal component analysis
one-shot algorithm
RBF kernels
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9.6
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