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
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).