On Error Probability of Search in High-Dimensional Binary Space with Scalar Neural Network Tree

Vladimir Kryzhanovsky, Magomed Malsagov, Juan Antonio Clares Tomas, Irina Zhelavskaya

2014

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).

References

  1. Friedman, J.H., Bentley, J.L. and Finkel, R.A., 1977.An algorithm for finding best matches in logarithmic expected time. ACM Transactions on Mathematical Software. vol. 3. pp. 209-226.
  2. Ting Liu, Andrew W. Moore, Alexander Gray and Ke Yang., 2004. An Investigation of Practical Approximate Nearest Neighbor Algorithms. Proceeding of Conference. Neural Information Processing Systems.
  3. Indyk, P. and Motwani, R., 1998. Approximate nearest neighbors: Towards removing the curse of dimensionality. In Proc. 30th STOC. pp. 604-613.
  4. Beis, J.S. and Lowe, D.G., 1997. Shape Indexing Using Approximate Nearest-Neighbor Search in HighDimensional Spaces. Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition. pp. 1000-1006.
  5. Kryzhanovsky B., Kryzhanovskiy V., Litinskii. L., 2010. Machine Learning in Vector Models of Neural Networks. // Advances in Machine Learning II. Dedicated to the memory of Professor Ryszard S. Michalski. Koronacki, J., Ras, Z.W., Wierzchon, S.T. (et al.) (Eds.), Series “Studies in Computational Intelligence”. Springer. SCI 263, pp. 427-443.
  6. Kryzhanovsky V., Malsagov M., Tomas J.A.C., 2013. Hierarchical Classifier: Based on Neural Networks Searching Tree with Iterative Traversal and Stop Criterion. Optical Memory and Neural Networks (Information Optics). vol. 22. No. 4. pp. 217-223.
  7. Kryzhanovsky V., Malsagov M., Zelavskaya I., Tomas J.A.C., 2014. High-Dimensional Binary Pattern Classification by Scalar Neural Network Tree. Proceedings of International Conference on Artificial Neural Networks. (in print).
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Paper Citation


in Harvard Style

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


in Bibtex Style

@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},
}


in EndNote Style

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