  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distributed linear PCA is no longer valid.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.
