# EFFICIENT COMPUTATION OF VORONOI NEIGHBORS BASED ON POLYTOPE SEARCH IN PATTERN RECOGNITION

### Juan Mendez, Javier Lorenzo

#### Abstract

Some algorithms in Pattern Recognition and Machine Learning as neighborhood-based classification and dataset condensation can be improved with the use of Voronoi tessellation. The paper shows the weakness of some existing algorithms of tessellation to deal with high dimensional datasets. The use of linear programming can improve the tessellation procedures by focusing in Voronoi adjacency. It will be shown that the adjacency test based on linear programming is a version of the polytope search. However, the polytope search procedure provides more information than a simple Boolean test. The paper proposes a strategy to use the additional information contained in the basis of the linear programming algorithm to obtain other tests. The theoretical results are applied to tessellate several random datasets, and also for much-used datasets in Machine Learning repositories.

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#### Paper Citation

#### in Harvard Style

Mendez J. and Lorenzo J. (2012). **EFFICIENT COMPUTATION OF VORONOI NEIGHBORS BASED ON POLYTOPE SEARCH IN PATTERN RECOGNITION** . In *Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods - Volume 2: ICPRAM,* ISBN 978-989-8425-99-7, pages 357-364. DOI: 10.5220/0003755703570364

#### in Bibtex Style

@conference{icpram12,

author={Juan Mendez and Javier Lorenzo},

title={EFFICIENT COMPUTATION OF VORONOI NEIGHBORS BASED ON POLYTOPE SEARCH IN PATTERN RECOGNITION},

booktitle={Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods - Volume 2: ICPRAM,},

year={2012},

pages={357-364},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003755703570364},

isbn={978-989-8425-99-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods - Volume 2: ICPRAM,

TI - EFFICIENT COMPUTATION OF VORONOI NEIGHBORS BASED ON POLYTOPE SEARCH IN PATTERN RECOGNITION

SN - 978-989-8425-99-7

AU - Mendez J.

AU - Lorenzo J.

PY - 2012

SP - 357

EP - 364

DO - 10.5220/0003755703570364