A Decentralized Framework for Kernel PCA with Projection Consensus Constraints

TL;DR

This paper introduces a novel decentralized kernel PCA framework with projection consensus constraints, enabling efficient, communication-friendly computation across distributed data without a central fusion center.

Contribution

It proposes a new projection consensus constraint for decentralized kernel PCA and develops a fast, convergent algorithm based on ADMM that outperforms centralized methods.

Findings

Effective utilization of distributed data in kernel PCA

Significant reduction in running time compared to centralized approaches

Successful application on real-world parallel architecture

Abstract

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 As a result, the consensus constraint in distributed linear PCA is no longer valid.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 local dataset. We also derive a fully non-parametric, fast and convergent algorithm based on alternative direction method of multiplier, of which each iteration is analytic and communication-effcient. Experiments on a truly parallel architecture are conducted on real-world data, showing that the proposed decentralized algorithm is effective to utilize information of other nodes and takes great advantages in running time over the central kernel PCA.