Hanson-Wright inequality in Hilbert spaces with application to $K$-means clustering for non-Euclidean data

Xiaohui Chen; Yun Yang

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arXiv · 1810.11180

Hanson-Wright inequality in Hilbert spaces with application to $K$-means clustering for non-Euclidean data

Xiaohui Chen·Yun Yang

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Abstract

We derive a dimension-free Hanson-Wright inequality for quadratic forms of independent sub-gaussian random variables in a separable Hilbert space. Our inequality is an infinite-dimensional generalization of the classical Hanson-Wright inequality for finite-dimensional Euclidean random vectors. We illustrate an application to the generalized $K$-means clustering problem for non-Euclidean data. Specifically, we establish the exponential rate of convergence for a semidefinite relaxation of the generalized $K$-means, which together with a simple rounding algorithm imply the exact recovery of the true clustering structure.

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BibTeX RIS

Xiaohui Chen, Yun Yang. 2018-10-26. Hanson-Wright inequality in Hilbert spaces with application to $K$-means clustering for non-Euclidean data. https://arxiv.org/abs/1810.11180

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