An approximate nearest neighbours search algorithm based on the extended general spacefilling curves heuristic

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1451, Issue , 1998, Pages 697-706

  Pérez, Juan Carlos ^a   Vidal, Enrique ^a  

^a UNIVERSITAT POLITÈCNICA DE VALÈNCIA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

CURVE FITTING; MAPPING; PATTERN RECOGNITION; TREES (MATHEMATICS); VECTOR SPACES;

MULTI-DIMENSIONAL SPACE; NEAREST NEIGHBOUR; ONE DIMENSION; REAL VALUES; REAL VECTOR SPACE; SEARCH ALGORITHMS; SPACE-FILLING CURVE; TEST POINTS;

NEAREST NEIGHBOR SEARCH;

EID: 22044444648     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/bfb0033294     Document Type: Conference Paper

References (28)

1. Bartholdi, J.J.; Platzman, L.K. (1983) "A Fast Heuristic Based on Spacefilling Curves for Minimum-Weight Matching in the Plane", Information Processing Letters, 17. pp. 177-180.
2. Bartholdi, J.J.; Platzman, L.K. (1988) "Heuristics Based on Spacefilting Curves for Combinatorial Problems in Euclidean Space", Management Science, 34. pp. 291-305.
3. Bentley, J.L.; Weide, B.W.; Yao, A.C. (1980). "Optimal Expected Time Algorithms for Closest Point Problems", ACM Transactions on Mathematical Software, Vol. 6, pp. 563-580.
4. Bern, M. (1993). "Approximate Closest-Point Queries in High Dimensions", Pattern Recognition, Vot. 45, pp. 95-99.
5. Fukunaga, K.; Narendra, P.M. (1975). "A Branch and Bound Algorithm for Computing k-Nearest Neighbors", IEEE Transactions on Computers, Vol. 24, No. 7, pp. 750-753.
6. Friedman, J.H.; Baskett, F.; Shustek, L.J. (1975). "An Algorithm for Finding Nearest Neighbors", IEEE Tr. on Computers, Vol. 24, No. 10, pp. 1000-1006.
7. Friedman, J.H.; Bentley, J.L.; Finkel, R.A. (1977). "An Algorithm for Finding Best Matches in Logarithmic Expected Time", ACM Transactions on Mathematical Software, Vol. 3, No. 3, pp. 209-226.
8. Fukunaga, K. (1990). "Introduction to Statistical Pattern Recognition", Academic Press, San Diego, CA.
9. Hilbert, D. (1891). "Ueber die steitge Abbildung einer Linie auf ein Flaechenstueck", Math. Ann, Vol. 38, pp. 459-460.
10. Imai, H. (1986). "Worst-Case Analysis for Planar Matching and Tour Heuristics with Bucketing Techniques and Spacefilling Curves", Journal of the Operations Research Society of Japan, Vol. 29, No. 1, pp. 43-67.
11. Jain, A.K.; Dubes, R.C. (1988). "Algorithms for Clustering Data", Prentice Hall.
12. Kalantari, I.; McDonald, G. (1983). "A Data Structure and an Algorithm for the Nearest Point Problem", IEEE Trans. on Software Engineering, Vol. 9, No. 5, pp. 631-634.
13. Kim, B.S.; Park, S.B. (1986). "A Fast k-Nearest Neighbor Finding Algorithm Based on the Ordered Partition", IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 8, No. 6, pp. 761-766.
14. Miclet, L.; Dabouz, M. (1983). "Approximative Fast Nearest Neighbor Recognition", Pattern Recognition Letters', Vol. 1, No. 5/6, pp. 277-285.
15. Murphy, O.J.; Selkow, S.M. (1990). "Finding Nearest Neighbors with Voronoi Tessellations", Information Processing Letters, Vol. 34, pp. 37-41.
16. Omohundro, S.M. (1990). "Geometric Learning Algorithms", Physica D, 42. pp.307-321.
17. Peano, G. (1890). "Sur une Courbe qui Remptit Toute une Aire Plane", Math. Ann., Vol. 36, pp. 157-160.
18. Pérez, J.C.; Vidal, E. (1994). "Métodos Geométricos de Aprendizaje Supervisado",.Ph.D. Thesis (In spanish) DSIC. Univ. Politécnica de Valencia.
19. Pérez, J.C.; Vidal, E. (1997). "The Extended General Spacefilling Curves Heuristic" Technical Report, Dept. DISCA. Universidad Politécnica de Valencia. http://www.disca.upv.es
20. Pérez, J.C.; Vidal, E. (1998). "The Extended General Spacefilling Curves Heuristic" Submitted to ICPR-98.
21. Poggio, T.; Girosi, F. (1990). "Networks for Approximation and Learning", Proceedings of the IEEE, Vol.78, no.9. pp.1481-1497.
22. Sethi, I.K. (1981). "A Fast Algorithm for Recognizing Nearest Neighbors", IEEE Transactions on Systems, Man and Cybernetics, Vol. 1 t, No. 3, pp. 245-248.
23. Shasha, D.; Wang, T. (1990). "New Techniques for Best-Match Retrieval", ACM Transactions on Information Systems, Vol. 8, No, 2, pp. 140-158.
24. Sierpinski, M.W. (1912). "Sur une Nouvelle Courbe Continue qui Remplit Toute une Aire Plane", Bull. Acad. Sci. de Cracovie, pp. 462-478.
25. Skubalska, E.; Krzyzak, A. (1996). "Fast k-NN Classification Rule Using Metric on Space-Filling Curves", Proceedings oflCPR-96, pp. 121-I25.
26. Vidal, E. (1986). "An Algorithm for Finding Nearest Neighbours in (Approximately) Constant Average Time", Pattern Recognition Letters, Vol. 4, pp. 333-344.
27. Yao, A.C.; Yao, F.F. (1985). "A General Approach to d-dimensional Geometric Queries", Proceedings of the 17th Annual ACM Symposium on the Theory of Computing, 163-168.
28. Yunck, T.P. (1976). "A Technique to Identify Nearest Neighbors", IEEE Transactions on Systems, Man, and Cybernetics', Vol. 6, No. 10, pp. 678-683.