On q-Gaussian kernel and its Reproducing Kernel Hilbert Space

Details On q-Gaussian kernel and its Reproducing Kernel Hilbert Space On q-Gaussian kernel and its Reproducing Kernel Hilbert Space

2012-04-09

arxiv.org/abs/1204.1800v1

Computer Science

Learning

7 pages, 3 figures, 4 tables

Scientific paper

The role of kernels is central to machine learning. Motivated by the importance of power law distributions in modeling, simulation and learning, in this paper, we propose a power-law generalization of the Gaussian kernel. This generalization is based on q-Gaussian distribution, which is a power-law distribution studied in context of nonextensive statistical mechanics. We prove that the proposed kernel is positive definite, and provide some insights regarding the corresponding Reproducing Kernel Hilbert Space (RKHS). We also study practical significance of q-Gaussian kernels in classification, regression and clustering, and present some simulation results.

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