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Authors: Vladimir Kryzhanovsky 1 ; Magomed Malsagov 1 ; Juan Antonio Clares Tomas 2 and Irina Zhelavskaya 3

Affiliations: 1 Russian Academy of Sciences, Russian Federation ; 2 Institute of secondary education: IES SANJE, Spain ; 3 Skolkovo Institute of Science and Technology, Russian Federation

ISBN: 978-989-758-054-3

Keyword(s): Nearest Neighbor Search, Perceptron, Search Tree, High-Dimensional Space, Error Probability.

Related Ontology Subjects/Areas/Topics: Artificial Intelligence ; Biomedical Engineering ; Biomedical Signal Processing ; Computational Intelligence ; Computational Neuroscience ; Health Engineering and Technology Applications ; Human-Computer Interaction ; Methodologies and Methods ; Neural Networks ; Neurocomputing ; Neuroinformatics and Bioinformatics ; Neurotechnology, Electronics and Informatics ; Pattern Recognition ; Physiological Computing Systems ; Sensor Networks ; Signal Processing ; Soft Computing ; Theory and Methods

Abstract: The paper investigates SNN-tree algorithm that extends the binary search tree algorithm so that it can deal with distorted input vectors. Unlike the SNN-tree algorithm, popular methods (LSH, k-d tree, BBF-tree, spill-tree) stop working as the dimensionality of the space grows (N > 1000). The proposed algorithm works much faster than exhaustive search (26 times faster at N=10000). However, some errors may occur during the search. In this paper we managed to obtain an estimate of the upper bound on the error probability for SNN-tree algorithm. In case when the dimensionality of input vectors is N≥500 bits, the probability of error is so small (P<10-15) that it can be neglected according to this estimate and experimental results. In fact, we can consider the proposed SNN-tree algorithm to be exact for high dimensionality (N ≥ 500).

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Paper citation in several formats:
Kryzhanovsky, V.; Malsagov, M.; Clares Tomas, J. and Zhelavskaya, I. (2014). On Error Probability of Search in High-Dimensional Binary Space with Scalar Neural Network Tree.In Proceedings of the International Conference on Neural Computation Theory and Applications - Volume 1: NCTA, (IJCCI 2014) ISBN 978-989-758-054-3, pages 300-305. DOI: 10.5220/0005152003000305

@conference{ncta14,
author={Vladimir Kryzhanovsky. and Magomed Malsagov. and Juan Antonio Clares Tomas. and Irina Zhelavskaya.},
title={On Error Probability of Search in High-Dimensional Binary Space with Scalar Neural Network Tree},
booktitle={Proceedings of the International Conference on Neural Computation Theory and Applications - Volume 1: NCTA, (IJCCI 2014)},
year={2014},
pages={300-305},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005152003000305},
isbn={978-989-758-054-3},
}

TY - CONF

JO - Proceedings of the International Conference on Neural Computation Theory and Applications - Volume 1: NCTA, (IJCCI 2014)
TI - On Error Probability of Search in High-Dimensional Binary Space with Scalar Neural Network Tree
SN - 978-989-758-054-3
AU - Kryzhanovsky, V.
AU - Malsagov, M.
AU - Clares Tomas, J.
AU - Zhelavskaya, I.
PY - 2014
SP - 300
EP - 305
DO - 10.5220/0005152003000305

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