Nikolay Zagoruiko Irina Borisova, Vladimir Dyubanov, Olga Kytnenko

5. Data Mining Cup 2009 http:www.prudsys.deServiceDownloadsbin Prognosis of data at absolure scale To predict 19344 cells 1 . . . . . . . 2418 C O N T R O L 1 . . . 84% = 0 . . A = 0 - 2300 . 2394 T R A I N I N G 1…8 1…………………………………………1856

6. DMC 2009 618 teams from 164 Universities of 42 countries participated 231 have sent decisions, 49 were selected for rating NN Teams Errors NN Teams Errors 1938612 FH Hannover 49 23488 Isfahan University of Technology 15 77551 Warsaw School of Economics 48 23277 Budapest University of Technology 14 45096 Uiversity of Edinburgh 39 21780 RWTH Aachen_I 11 32841 Technical University of Kosice 38 21195 KTH Royal Institute of Technology 10 28670 Anna University Coimbatore 34 21064 Uni Hamburg_ 9 28517 Indian Institute of Technology 32 20767 Hochschule Anhalt 8 26254 University of Central Florida 26 20140 FH Brandenburg_II 7 25829 Telkom Institute of Technology 25 19814 FH Brandenburg_I 6 25694 University of Southampton 24 18763 Uni Karlsruhe TH_ I 5 24884 University Laval 20 18353 Novosibirsk State University 4 23952 Zhejiang University of Sc. and Tech 19 18163 TU Dresden 3 23796 Uni Weimar_I 18 17912 TU Dortmund 2 23626 TU Graz 16 17260 Uni Karlsruhe TH_ II 1

12. Projection of training set on 2-dim. space 2641 and 4049 ALL AML

15. Measures of Similarity

16. Similarity is not absolute, but a relative category Is a object b similar to a or it is not similar? Whether objects a and b belong to one class? a b a b c a b c We should know the answer on question: In competition with what?

17. F unction of Concurrent ( Ri val) S imilarity ( FRiS ) r1 r2 -1 z A +1 B d2 F A B z r1 r2

18. All pattern recognition methods are based on hypothesis of compactness Braverman E.M. , 1962 The patterns are compact if -the number of boundary points is not enough in comparison with their common number; - compact patterns are separated from each other refer to not too elaborate borders. Compactness

19. Compactness Similarity between objects of one pattern should be maximal Similarity between objects of different patterns should be minimal

20. Maximal similarity between objects of the same pattern Compact patterns should satisfy to condition of the Defensive capacity: Compactness

21. Tolerance: Compactness Maximal difference of these objects with the objects of other patterns Compact patterns should satisfy to the condition

22. Selection of the standards (stolps) Algorithm FRiS-Stolp

28. Censoring of the training set

29. Censoring of the training set

30. Censoring of the training set

31. Censoring of the training set H P =argmax |r|(H,P) = 1,2,…7 1.0.8689 -90(90)-20 2.0.8902 -90(90)-20 3.0.9084 -90(90)-20 4.0.9167 -90(90)-20 5.0.8903 - 90(90)-20 6.0.7309 -88(90)-9 7.0.2324 -86(90)-7

32. Informativeness by Fisher for normal distribution Compactness has the same sense and can be used as a criteria of informativeness, which is invariant to low of distribution and to relation of NM Results of comparative researches have shown appreciable advantage of this criterion in comparison with commonly used number of errors at Cross-Validation Criteria

38. Value of FRiS for points on a plane

39. Classification (Algorithm FRiS-Class) FRiS-Cluster divides a objects on clusters FRiS-Tax unites a clusters to classes ( taxons ) Using FRiS-function allows: - To make a taxons of any form ; - To search a optimal number of taksons. r 1 r 2 * r 1 r 2 *

41. Examples of taxonomies by a algorithm FRiS-Class

42. Примеры таксономии алгоритмом FRiS-Class

43. Comparison the FRiS-Class with other algorithms of taxonomy K