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Memory-efficient Kernel PCA via Partial Matrix Sampling and Nonconvex Optimization: a Model-free Analysis of Local Minima
Student-Run Research Seminar| Speaker: | Ji Chen, UC Davis |
| Related Webpage: | https://www.math.ucdavis.edu/~ljichen/ |
| Location: | 2112 MSB |
| Start time: | Thu, Feb 1 2018, 12:10PM |
Kernel PCA is a widely used nonlinear dimension reduction technique in machine learning, but storing the kernel matrix is notoriously challenging when the sample size is large. Inspired by Yi et al. (2016), where the idea of partial matrix sampling followed by nonconvex optimization is proposed for matrix completion and robust PCA, we apply a similar approach to memory-efficient Kernel PCA. In theory, with no assumptions on the kernel matrix in terms of eigenvalues or eigenvectors, we established a model-free theory for the low-rank approximation based on any local minimum of the proposed objective function. As interesting byproducts, when the underlying positive semidefinite matrix is assumed to be low-rank and highly structured, corollaries of our main theorem improve the state-of-the-art results of Ge et al. (2016, 2017) for nonconvex matrix completion with no spurious local minima.
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