Research Article
Error Probability for Scalar Neural Network Trees in High-Dimensional Binary Space
@INPROCEEDINGS{10.4108/icst.bict.2014.257924, author={Irina Zhelavskaya and Vladimir Kryzhanovsky and Magomed Malsagov}, title={Error Probability for Scalar Neural Network Trees in High-Dimensional Binary Space}, proceedings={8th International Conference on Bio-inspired Information and Communications Technologies (formerly BIONETICS)}, publisher={ICST}, proceedings_a={BICT}, year={2015}, month={2}, keywords={nearest neighbor search perceptron search tree hierarchical classifier multi-class classification}, doi={10.4108/icst.bict.2014.257924} }- Irina Zhelavskaya
Vladimir Kryzhanovsky
Magomed Malsagov
Year: 2015
Error Probability for Scalar Neural Network Trees in High-Dimensional Binary Space
BICT
ACM
DOI: 10.4108/icst.bict.2014.257924
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).