Abstract
Kernel based methods (such as k-nearest neighbors classifiers) for AI tasks translate the classification problem into a proximity search problem, in a space that is usually very high dimensional. Unfortunately, no proximity search algorithm does well in high dimensions. An alternative to overcome this problem is the use of approximate and probabilistic algorithms, which trade time for accuracy.
In this paper we present a new probabilistic proximity search algorithm. Its main idea is to order a set of samples based on their distance to each element. It turns out that the closeness between the order produced by an element and that produced by the query is an excellent predictor of the relevance of the element to answer the query.
The performance of our method is unparalleled. For example, for a full 128-dimensional dataset, it is enough to review 10% of the database to obtain 90% of the answers, and to review less than 1% to get 80% of the correct answers. The result is more impressive if we realize that a full 128-dimensional dataset may span thousands of dimensions of clustered data. Furthermore, the concept of proximity preserving order opens a totally new approach for both exact and approximated proximity searching.
Supported by CYTED VII.19 RIBIDI Project (all authors), CONACyT grant 36911A (first and second author) and Millennium Nucleus Center for Web Research, Grant P04-067-F, Mideplan, Chile (second and third author).
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References
Arya, S., Mount, D., Netanyahu, N., Silverman, R., Wu, A.: An optimal algorithm for approximate nearest neighbor searching in fixed dimension. In: Proc. 5th ACM-SIAM Symposium on Discrete Algorithms (SODA 1994), pp. 573–583 (1994)
Brin, S.: Near neighbor search in large metric spaces. In: Proc. 21st Conference on Very Large Databases (VLDB 1995), pp. 574–584 (1995)
Bustos, B., Navarro, G.: Probabilistic proximity search algorithms based on compact partitions. Journal of Discrete Algorithms (JDA) 2(1), 115–134 (2003)
Chávez, E., Figueroa, K.: Faster proximity searching in metric data. In: Proc. of the Mexican International Conference in Artificial Intelligence (MICAI). LNCS, pp. 222–231. Springer, Heidelberg (2004)
Chávez, E., Marroquin, J.L., Navarro, G.: Fixed queries array: A fast and economical data structure for proximity searching. Multimedia Tools and Applications (MTAP) 14(2), 113–135 (2001)
Chávez, E., Navarro, G.: Probabilistic proximity search: Fighting the curse of dimensionality in metric spaces. Inf. Process. Lett. 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., Marroquin, J.L.: Proximity searching in metric spaces. ACM Computing Surveys 33(3), 273–321 (2001)
Ciaccia, P., Patella, M.: Pac nearest neighbor queries: Approximate and controlled search in high-dimensional and metric spaces. In: Proc. 16th Intl. Conf. on Data Engineering (ICDE 2000), pp. 244–255. IEEE Computer Society Press, Los Alamitos (2000)
Ciaccia, P., Patella, M., Zezula, P.: M-tree: an efficient access method for similarity search in metric spaces. In: Proc. of the 23rd Conference on Very Large Databases (VLDB 1997), pp. 426–435 (1997)
Clarkson, K.: Nearest neighbor queries in metric spaces. Discrete Computational Geometry 22(1), 63–93 (1999)
Fagin, R., Kumar, R., Sivakumar, D.: Comparing top k lists. SIAM J. Discrete Math. 17(1), 134–160 (2003)
Hjaltason, G., Samet, H.: Index-driven similarity search in metric spaces. ACM Trans. Database Syst. 28(4), 517–580 (2003)
Navarro, G.: Searching in metric spaces by spatial approximation. The Very Large Databases Journal (VLDBJ) 11(1), 28–46 (2002)
Vidal, E.: An algorithm for finding nearest neighbors in (approximately) constant average time. Pattern Recognition Letters 4, 145–157 (1986)
White, D., Jain, R.: Algorithms and strategies for similarity retrieval. Technical Report VCL-96-101, Visual Computing Laboratory, University of California, La Jolla, California (July 1996)
Yianilos, P.: Excluded middle vantage point forests for nearest neighbor search. In: ALENEX (1999)
Yianilos, P.N.: Locally lifting the curse of dimensionality for nearest neighbor search. Technical report, NEC Research Institute, Princeton, NJ (June 1999)
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Chávez, E., Figueroa, K., Navarro, G. (2005). Proximity Searching in High Dimensional Spaces with a Proximity Preserving Order. In: Gelbukh, A., de Albornoz, Á., Terashima-Marín, H. (eds) MICAI 2005: Advances in Artificial Intelligence. MICAI 2005. Lecture Notes in Computer Science(), vol 3789. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11579427_41
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DOI: https://doi.org/10.1007/11579427_41
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