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Kernel-based classification using quantum mechanics (2007)
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BibTeX
@MISC{Nasios07kernel-basedclassification,
author = {Nikolaos Nasios and Adrian G. Bors},
title = { Kernel-based classification using quantum mechanics},
year = {2007}
}
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Abstract
This paper introduces a new nonparametric estimation approach inspired from quantum mechanics. Kernel density estimation associates a function to each data sample. In classical kernel estimation theory the probability density function is calculated by summing up all the kernels. The proposed approach assumes that each data sample is associated with a quantum physics particle that has a radial activation field around it. Schrödinger differential equation is used in quantum mechanics to define locations of particles given their observed energy level. In our approach, we consider the known location of each data sample and we model their corresponding probability density function using the analogy with the quantum potential function. The kernel scale is estimated from distributions of K-nearest neighbours statistics. In order to apply the proposed algorithm to pattern classification we use the local Hessian for detecting the modes in the quantum potential hypersurface. Each mode is assimilated with a nonparametric class which is defined by means of a region growing algorithm. We apply the proposed algorithm on artificial data and for the topography segmentation from radar images of terrain.
Keyphrases
quantum mechanic kernel-based classification data sample radial activation field radar image new nonparametric estimation approach classical kernel estimation quantum physic particle probability density function k-nearest neighbour statistic schr dinger differential equation local hessian kernel density estimation corresponding probability density function kernel scale quantum potential hypersurface observed energy level nonparametric class quantum potential function topography segmentation artificial data
