One-Shot Distributed Algorithm for PCA With RBF Kernels

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.