Abstract
The permutation based algorithm has been proved unbeatable in high dimensional spaces, requiring O(|ℙ|) distance evaluations when solving similarity queries (where ℙ is the set of permutants); but needs n evaluations of the permutant distance to compute the order to review the metric dataset, requires O(n|ℙ|) space, and does not take much benefit from low dimensionality. There have been several proposals to avoid the n computations of the permutant distance, however all of them lost precision. Inspired in the list of cluster, in this paper we group the permutations and establish a criterion to discard whole clusters according the permutation of their centers. As a consequence of our proposal, we now reduce not only the space of the index and the number of distance evaluations but also the cpu time required when comparing the permutations themselves. Also, we can use the permutations in low dimensions.
This work is partially funded by National Council of Science and Technology (CONACyT) of México, Universidad Michoacana de San Nicolás de Hidalgo, México, and Fondecyt grant 1131044, Chile.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Böhm, C., Berchtold, S., Keim, D.A.: Searching in high-dimensional spaces: Index structures for improving the performance of multimedia databases. ACM Computing Surveys 33(3), 322–373 (2001)
Bolettieri, P., Esuli, A., Falchi, F., Lucchese, C., Perego, R., Piccioli, T., Rabitti, F.: CoPhIR: A test collection for content-based image retrieval. CoRR abs/0905.4627v2 (2009), http://cophir.isti.cnr.it
Chávez, E., Figueroa, K., Navarro, G.: Proximity searching in high dimensional spaces with a proximity preserving order. In: Gelbukh, A., de Albornoz, Á., Terashima-Marín, H. (eds.) MICAI 2005. LNCS(LNAI), vol. 3789, pp. 405–414. Springer, Heidelberg (2005)
Chávez, E., Navarro, G.: Probabilistic proximity search: Fighting the curse of dimensionality in metric spaces. Information Processing Letters 85(1), 39–46 (2003)
Chávez, E., Navarro, G.: A compact space decomposition for effective metric indexing. Pattern Recognition Letters 26(9), 1363–1376 (2005)
Chávez, E., Navarro, G., Baeza-Yates, R., Marroquín, J.: Proximity searching in metric spaces. ACM Computing Surveys 33(3), 273–321 (2001)
Esuli, A.: Mipai: using the pp-index to build an efficient and scalable similarity search system. In: Proc. 2nd Intl. Workshop on Similary Searching and Applications (SISAP 2009), pp. 146–148. IEEE Computer Society (2009)
Fagin, R., Kumar, R., Sivakumar, D.: Comparing top k lists. SIAM J. Discrete Math. 17(1), 134–160 (2003)
Figueroa, K., Chávez, E., Navarro, G., Paredes, R.: Speeding up spatial approximation search in metric spaces. ACM Journal of Experimental Algorithmics (JEA) 14, article 3.6, 21 pages (2009), doi: http://doi.acm.org/10.1145/1498698.1564506
Figueroa Mora, K., Paredes, R., Rangel, R.: Efficient group of permutants for proximity searching. In: Martínez-Trinidad, J.F., Carrasco-Ochoa, J.A., Ben-Youssef Brants, C., Hancock, E.R. (eds.) MCPR 2011. LNCS, vol. 6718, pp. 42–49. Springer, Heidelberg (2011)
Figueroa, K., Frediksson, K.: Speeding up permutation based indexing with indexing. In: Proceedings of the 2009 Second International Workshop on Similarity Search and Applications, SISAP 2009, pp. 107–114. IEEE Computer Society, Washington, DC (2009), http://dx.doi.org/10.1109/SISAP.2009.12
Patella, M., Ciaccia, P.: Approximate similarity search: A multi-faceted problem. Journal of Discrete Algorithms 7(1), 36–48 (2009)
Skala, M.: Counting distance permutations. J. of Discrete Algorithms 7(1), 49–61 (2009), http://dx.doi.org/10.1016/j.jda.2008.09.011
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Figueroa, K., Paredes, R. (2013). List of Clustered Permutations for Proximity Searching. In: Brisaboa, N., Pedreira, O., Zezula, P. (eds) Similarity Search and Applications. SISAP 2013. Lecture Notes in Computer Science, vol 8199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41062-8_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-41062-8_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-41061-1
Online ISBN: 978-3-642-41062-8
eBook Packages: Computer ScienceComputer Science (R0)