Anisotropic k-Nearest Neighbor Search Using Covariance Quadtree
Abstract
We present a variant of the hyper-quadtree that divides a multidimensional space according to the hyperplanes associated to the principal components of the data in each hyperquadrant. Each of the hyper-quadrants is a data partition in a -dimension subspace, whose intrinsic dimensionality is reduced from the root dimensionality by the principal components analysis, which discards the irrelevant eigenvalues of the local covariance matrix. In the present method a component is irrelevant if its length is smaller than, or comparable to, the local inter-data spacing. Thus, the covariance hyper-quadtree is fully adaptive to the local dimensionality. The proposed data-structure is used to compute the anisotropic K nearest neighbors (kNN), supported by the Mahalanobis metric. As an application, we used the present k nearest neighbors method to perform density estimation over a noisy data distribution. Such estimation method can be further incorporated to the smoothed particle hydrodynamics, allowing computer simulations of anisotropic fluid flows.
Cite
@article{arxiv.1108.6304,
title = {Anisotropic k-Nearest Neighbor Search Using Covariance Quadtree},
author = {Eraldo Pereira Marinho and Carmen Maria Andreazza},
journal= {arXiv preprint arXiv:1108.6304},
year = {2014}
}
Comments
Work presented at the Minisymposia of Computational Geometry in the joint events IX Argentinian Congress on Computational Mechanics, XXXI Iberian-Latin-American Congress on Computational Methods in Engineering, II South American Congress on Computational Mechanics, held in Buenos Aires in 15-18 November 2010; Mec\'anica Computacional (Computational Mechanics) Vol. XXIX, 2010, ISSN 1666-6070