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 scenario. This interesting relationship makes it possible to establish distributed kernel PCA for feature-distributed cases from ideas in distributed PCA in sample-distributed scenario. In 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.
翻译:本信建议对分布特性的内核五氯苯甲醚进行一次性算法。 我们的算法受样本分布式和特性分布式两种情况之间的双重关系的启发。 这种有趣的关系使得有可能建立分布式内核五氯苯甲醚,用于根据分布式五氯苯甲醚在分布式分布式分布式设想情景中的想法来分配特性分布式案例。 在理论部分,我们分析了线性和RBF内核的近似误差。 结果表明,当源值快速衰减时, 提议的算法会以较低的通信成本带来高质量的结果。 这个结果也通过数字实验得到验证, 显示了我们算法的实际效果。