Lower bounds on performance of metric tree indexing schemes for exact similarity search in high dimensions

Proceedings - 4th International Conference on SImilarity Search and APplications, SISAP 2011

Volumn , Issue , 2011, Pages 25-32

  Pestov, Vladimir ^a,b  

^a FEDERAL UNIVERSITY OF SANTA CATARINA   (Brazil)

^b UNIVERSITY OF OTTAWA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

AVERAGE CASE PERFORMANCE; COMPLEXITY ASSUMPTIONS; CURSE OF DIMENSIONALITY; DATA SETS; DATAPOINTS; DECISION FUNCTIONS; HIGH DIMENSIONS; INDEXING SCHEME; INTRINSIC DIMENSIONS; LOWER BOUNDS; METRIC TREES; NEAREST NEIGHBOUR; QUERY POINTS; RIGOROUS MODEL; SIMILARITY SEARCH; STATISTICAL LEARNING THEORY; VC DIMENSION;

ASYMPTOTIC ANALYSIS; INFORMATION RETRIEVAL; PLANT EXTRACTS; PROBABILITY DISTRIBUTIONS;

INDEXING (OF INFORMATION);

EID: 79960962823     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1995412.1995419     Document Type: Conference Paper

References (42)

1. A. Andoni, P. Indyk, M. Pǎtrascu, On the optimality of the dimensionality reduction method, in: Proc. 47th IEEE Symp. on Foundations of Computer Science, pp. 449-458, 2006. (Pubitemid 351175533)
2. M. Anthony and P. Bartlett. Neural Network Learning: Theoretical Foundations. Cambridge University Press, Cambridge, 1999.
3. O. Barkol and Y. Rabani. Tighter lower bounds for nearest neighbor search and related problems in the cell probe model. In: Proc. 32nd ACM Symp. on the Theory of Computing, 2000, pp. 388-396.
4. K. Beyer, J. Goldstein, R. Ramakrishnan, and U. Shaft. When is "nearest neighbor" meaningful?, in: Proc. 7-th Intern. Conf. on Database Theory (ICDT-99), Jerusalem, pp. 217-235, 1999.
5. A. Borodin, R. Ostrovsky, and Y. Rabani. Lower bounds for high-dimensional nearest neighbor search and related problems, in: Proc. 31st Annual ACS Sympos. Theory Comput., 312-321, 1999.
6. E. Chávez, G. Navarro. A compact space decomposition for effective metric indexing. Pattern Recognition Letters 26:1363-1376, 2005. (Pubitemid 40644699)
7. E. Chávez, G. Navarro, R. Baeza-Yates and J. L. Marroquín. Searching in metric spaces. ACM Computing Surveys 33:273-321, 2001. (Pubitemid 33768485)
8. P. Ciaccia, M. Patella and P. Zezula. M-tree: An efficient access method for similarity search in metric spaces. In Proc. 23rd Int. Conf. on Very Large Data Bases (VLDB'97), (Athens, Greece), 426-435, 1997.
9. P. Ciaccia, M. Patella and P. Zezula. A cost model for similarity queries in metric spaces, in: Proc. 17-th ACM Symposium on Principles of Database Systems (PODS'98), Seattle, WA, 59-68, 1998.
10. K.L. Clarkson. Nearest-neighbor searching and metric space dimensions. In: Nearest-Neighbor Methods for Learning and Vision: Theory and Practice, MIT Press, 2006, pp. 15-59.
11. A. Faragó, T. Linder, and G. Lugosi, Fast nearest neighbor search in dissimilarity spaces, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 18, pp. 957-962, 1993. (Pubitemid 23703599)
12. P.W. Goldberg and M.R. Jerrum, Bounding the Vapnik-Chervonenkis dimension of concept classes parametrized by real numbers, Machine Learning 18:131-148, 1995.
13. M. Gromov and V.D. Milman, A topological application of the isoperimetric inequality. Amer. J. Math. 105, 843-854, 1983.
14. J. M. Hellerstein, E. Koutsoupias, D. P. Miranker, C. Papadimitriou, and V. Samoladas. On a model of indexability and its bounds for range queries. Journal of the ACM (JACM), 49(1):35-55, 2002.
15. P. Indyk. Nearest neighbours in high-dimensional spaces. In: J.E. Goodman, J. O'Rourke, Eds., Handbook of Discrete and Computational Geometry, Chapman and Hall/CRC, Boca Raton-London-New York-Washington, D.C. 877-892, 2004.
16. Piotr Indyk, Rajeev Motwani, Approximate nearest neighbors: towards removing the curse of dimensionality, Proceedings of the thirtieth annual ACM symposium on Theory of computing, pp. 604-613, 1998, Dallas, Texas.
17. N. Katayama and S. Satoh, The SR-tree: An index structure for high-dimensional nearest neighbour queries, in: Prof. 16-th Symposium on PODS, pp. 369-380, Tuscon, AZ, 1997. (Pubitemid 127456800)
18. E. Kushilevitz, R. Ostrovsky, Y. Rabani, Efficient Search for Approximate Nearest Neighbor in High Dimensional Spaces. SIAM Journal on Computing 30:457-474, 2000.
19. M. Ledoux. The Concentration of Measure Phenomenon, volume 89 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2001.
20. S. Mendelson, A few notes on statistical learning theory. In: S. Mendelson, A.J. Smola, Eds., Advanced Lectures in Machine Learning, LNCS 2600, pp. 1-40, Springer, 2003.
21. V.D. Milman and G. Schechtman, Asymptotic Theory of Finite Dimensional Normed Spaces, volume 1200 of Lecture Notes in Mathematics. Springer, 1986.
22. P.B. Miltersen, Cell probe complexity - a survey. In: 19th Conference on the Foundations of Software Technology and Theoretical Computer Science (FSTTCS), 1999. Advances in Data Structures Workshop.
23. Gonzalo Navarro, Analysing metric space indexes: what for? Invited paper, in: Proc. 2nd Int. Workshop on Similarity Search and Applications (SISAP 2009), Prague, Czech Republic, 2009, 3-10.
24. R. Panigrahy, K. Talwar, U. Wieder, A geometric approach to lower bounds for approximate near-neighbor search and partial match, in: Proc. 49th IEEE Symp. on Foundations of Computer Science, pp. 414-423, 2008.
25. M. Pǎtrascu, M. Thorup, Higher lower bounds for near-neighbor and further rich problems, in Proc. 47th IEEE Symp. on Foundations of Computer Science, pp. 646-654, 2006. (Pubitemid 351175552)
26. V. Pestov. On the geometry of similarity search: dimensionality curse and concentration of measure. Inform. Process. Lett., 73:47-51, 2000. (Pubitemid 30563374)
27. V. Pestov. An axiomatic approach to intrinsic dimension of a dataset. Neural Networks, 21:204-213, 2008.
28. V. Pestov. Indexability, concentration, and VC theory. - A full version of SISAP'2010 invited article, submitted to Journal of Discrete Algorithms. Available from arXiv:1008.5105v4 [cs.DS].
29. V. Pestov and A. Stojmirović. Indexing schemes for similarity search: an illustrated paradigm. Fund. Inform., 70:367-385, 2006. (Pubitemid 43760897)
30. H. Samet. Foundations of Multidimensional and Metric Data Structures. Morgan Kaufmann Publishers Inc., San Francisco, CA, 2005.
31. S. Santini, Exploratory Image Databases: Content-Based Retrieval, Academic Press, Inc. Duluth, MN, USA, 2001.
32. U. Shaft and R. Ramakrishnan. Theory of nearest neighbors indexability. ACM Transactions on Database Systems (TODS), 31:814-838, 2006. (Pubitemid 44600827)
33. A. Stojmirović and V. Pestov. Indexing schemes for similarity search in datasets of short protein fragments. Information Systems, 32:1145-1165, 2007. (Pubitemid 47379494)
34. J.K. Uhlmann. Satisfying general proximity/similarity queries with metric trees, Information Processing Letters 40:175-179, 1991.
35. V.N. Vapnik. Statistical Learning Theory. John Wiley & Sons, Inc., New York, 1998.
36. S.S. Vempala. The Random Projection Method. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 65, Amer. Math. Soc., Providence, R.I., 2004.
37. M. Vidyasagar. Learning and Generalization, With Applications to Neural Networks. Second Ed. Springer-Verlag, London, 2003.
38. I. Volnyansky and V. Pestov, Curse of dimensionality in pivot-based indexes. - Proc. 2nd Int. Workshop on Similarity Search and Applications (SISAP 2009), Prague, Czech Republic, 2009, pp. 39-46.
39. R. Weber, H.-J. Schek, and S. Blott, A quantatitive analysis and performance study for similarity-search methods in high-dimensional spaces. in: Proceedings of the 24-th VLDB Conference, New York, pp. 194-205, 1998.
40. D.A. White and R. Jain, Similarity indexing with the SS-tree, in: Proc. 12th Conf. on Data Engineering (ICDE'96), La Jolla, CA, pp. 516-523, 1996.
41. P. Yianilos. Data structures and algorithms for nearest neighbor search in general metric spaces, in: Proc. 3rd Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 311-321, 1993. (Pubitemid 23612715)
42. P. Zezula, G. Amato, Y. Dohnal, and M. Batko. Similarity Search. The Metric Space Approach. Springer Science + Business Media, New York, 2006.