A Decentralized Framework for Kernel PCA With Projection Consensus Constraints

This paper studies kernel PCA in a decentralized setting, where data are distributively observed with full features in local nodes, and a fusion center is prohibited. Compared with linear PCA, the use of kernel brings challenges to the design of decentralized consensus optimization: the local projection directions are data-dependent. As a result, the consensus constraint in distributed linear PCA is no longer valid. To overcome this problem, we propose a projection consensus constraint and obtain an effective decentralized consensus framework, where local solutions are expected to be the projection of the global solution on the column space of the local dataset. We also derive a fully non-parametric, fast, and convergent algorithm based on the alternative direction method of multiplier, of which each iteration is analytic and communication-efficient. Experiments on a truly parallel architecture are conducted on real-world data, showing that the proposed decentralized algorithm is effective in utilizing information from other nodes and takes great advantages in running time over the central kernel PCA.