Streaming Kernel PCA with $\tilde{O}(\sqrt{n})$ Random Features

Part of Advances in Neural Information Processing Systems 31 (NeurIPS 2018)

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Enayat Ullah, Poorya Mianjy, Teodor Vanislavov Marinov, Raman Arora


We study the statistical and computational aspects of kernel principal component analysis using random Fourier features and show that under mild assumptions, $O(\sqrt{n} \log n)$ features suffices to achieve $O(1/\epsilon^2)$ sample complexity. Furthermore, we give a memory efficient streaming algorithm based on classical Oja's algorithm that achieves this rate