FUNCTION OF RIVAL SIMILARITY IN A COGNITIVE DATA ANALYSIS

FUNCTION OF RIVAL SIMILARITY IN A COGNITIVE DATA ANALYSIS Nikolay Zagoruiko Irina Borisova, Vladimir Dyubanov, Olga Kytnenko Institute of Mathematics of the Siberian Devision of the Russian Academy of Sciences, Pr. Koptyg 4, 630090 Novosibirsk, Russia, [email_address]

Data Analysis, Pattern Recognition, Empirical Prediction, Discovering of Regularities, Data Mining , Machine Learning, Knowledge Discovering, Intelligence Data Analysis, Cognitive Calculations The special attention involves ability of the person - To estimate similarities and distinctions between objects, - To make classification of objects, - To recognize a belonging of new objects to available classes, To discover natural dependences between characteristics and To use these dependences (knowledge) for forecasting

Specificity of Data Mining tasks: Polytypic attributes Quantity of attributes>> numbers of objects Presence of noise, spikes and blanks Absence of the information on distributions

Some real tasks DM Task K M N Medicine: Diagnostics of Diabetes II type 3 43 5520 Diagnostics of Prostate Cancer 4 322 17153 Recognition of type of Leukemia 2 38 7129 Physics: Complex analysis of spectra 7 20-400 1024 Commerse : Forecasting of book sealing (Data Mining Cup 2009) - 4812 1862

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

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

Comparison with 10 methods Jeffery I.,Higgins D.,Culhane A. Comparison and evaluation of methods for generating differentially expressed gene lists from microarray data. // http://www.biomedcentral.com/1471-2105/7/359 9 tasks on microarray data. 10 methods the feature selection . Independent attributes . Selection of n first (best) . Criteria – min of errors on CV: 10 time by 50%. Decision rules: Support Vector Machine ( SVM ), Between Group Analysis ( BGA ), Naive Bayes Classification ( NBC ), K - Nearest Neighbors ( KNN ).

Methods of selection Methods Results Significance analysis of microarrays (SAM) 42 Analysis of variance (ANOVA) 43 Empirical Bayes t-statistic 32 Template matching 38 maxT 37 Between group analysis (BGA) 43 Area under the receiver operating characteristic curve (ROC) 37 Welch t-statistic 39 Fold change 47 Rank products 42 FRiS-GRAD 12 Empirical Bayes t-statistic – for middle set of objects Area under a ROC curve – for small noise and large set Rank products – for large noise and small set

Results of comperasing Задача N0 m1/m2 max of 4 GRAD ALL 1 12625 95/33 100.0 100.0 ALL2 12625 24/101 78.2 80.8 ALL3 12625 65/35 59.1 73.8 ALL4 12625 26/67 82.1 83,9 Prostate 12625 50/53 90.2 93.1 Myeloma 12625 36/137 8 2 . 9 8 1 . 4 ALL/AML 7129 47/25 95.9 100.0 DLBCL 7129 58/19 94.3 89.8 Colon 2000 22/40 88.6 89.5

Recognition of two types of Leukemia - ALL and AML ALL AML Training set 38 27 11 N = 7129 Control set 34 20 14 I . Guyon, J . Weston, S . Barnhill, V . Vapnik Gene Selection for Cancer Classification using Support Vector Machines. Machine Learning. 2002, 46 1-3: pp. 389-422.

Training set 38 Test set 34 N g V suc V ext V med T suc T ext T med P 7129 0,95 0,01 0,42 0,85 -0,05 0,42 29 4096 0,82 -0,67 0,30 0,71 -0,77 0,34 24 2048 0,97 0,00 0,51 0,85 -0,21 0,41 29 1024 1,00 0,41 0,66 0,94 -0,02 0,47 32 512 0,97 0,20 0,79 0,88 0,01 0,51 30 256 1,00 0,59 0,79 0,94 0,07 0,62 32 128 1,00 0,56 0,80 0,97 -0,03 0,46 33 64 1,00 0,45 0,76 0,94 0,11 0,51 32 32 1,00 0,45 0,65 0,97 0,00 0,39 33 1,00 0,25 0,66 1,00 0,03 0,38 34 8 1,00 0,21 0,66 1,00 0,05 0,49 34 4 0,97 0,01 0,49 0,91 -0,08 0,45 31 2 0,97 -0,02 0,42 0,88 -0,23 0,44 30 1 0,92 -0,19 0,45 0,79 -0,27 0,23 27 Pentium T=3 hours Name of gene Weight 2641/1 , 4049/1 33 2641/1 32 On the 27 first rules P =34/34 The 10 best rules Pentium T=13 sec I . Guyon, J . Weston, S . Barnhill, V . Vapnik Zagoruiko N., Borisova I., Dyubanov V., Kutnenko O. F RiS Decision Rules P 0,72656 537/1 , 1833/1 , 2641/2 , 4049/2 34 0,71373 1454/1 , 2641/1 , 4049/1 34 0,71208 2641/1 , 3264/1 , 4049/1 34 0,71077 435/1 , 2641/2 , 4049/2 , 6800/1 34 0,70993 2266/1 , 2641/2 , 4049/2 34 0,70973 2266/1 , 2641/2 , 2724/1 , 4049/2 34 0,70711 2266/1 , 2641/2 , 3264/1 , 4049/2 34 0,70574 2641/2 , 3264/1 , 4049/2 , 4446/1 34 0,70532 435/1 , 2641/2 , 2895/1 , 4049/2 34 0,70243 2641/2 , 2724/1 , 3862/1 , 4049/2 34

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

Diabetes of II type Ordering of patients M=43 17+8+18 , N=5520 Average similarity F av of patients to healthy people Healthy Patients Group of risk The group of risk did not participate in training It is useful for early diagnostics of diseases and for monitoring process of treatment F=+1 F=-1

The reason for abundance of methods - Absence of the uniform approach to the solution of tasks of different type Types of scales, dependences of features, lows of distribution, linear-nonlinear decision rules, small or big training set, … Uniform approach can be founded on next hypothesis: Basic function, used by the person at the classification, recognition, feature selection etc. consists in method of estimation of similarity between objects .

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?

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

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

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

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

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

Selection of the standards (stolps) Algorithm FRiS-Stolp

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

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

Comparison of the criteria (CV - FRiS) Order of attributes by informativeness ... . ... ... . ... C = 0,661 ... . ... ... . ... C = 0,883 noise N =100 M =2*100 m t =2*35 m C =2*65 +noise noise Criteria

Algorithm GRAD It based on combination of two greedy approaches : forward and backward searches . At a stage forward algorithm Addition is used At a stage backward algorithm Deletion is used GRAD

Algorithm AdDel To easing influence of collecting errors a relaxation method it is applied. n1 - number of most informative attributes, add-on to subsystem ( Addition ), n2<n1 - number of less informative attributes, eliminated from subsystem ( Deletion ). AdDel Relaxation method: n steps forward - n/2 steps back Algorithm AdDel. Reliability (R) of recognition at different dimension space. R (AdDel) > R (DelAd) > R (Ad) > R (Del) GRAD

Algorithm GRAD AdDel can work with not single attributes only, but also with groups of attributes ( granules ) of different capacity m=1,2,3,…: , , ,… The granules can be formed by the exhaustive search method. But: Problem of combinatory explosion! Decision : orientation on individual informativeness of attributes Dependence of frequency f hits in an informative subsystem from serial number L on individual informativeness It allows to granulate a most informative part attributes only GRAD L f

Algorithm GRAD (Granulated AdDel) 1. Independent testing N attributes Selection m1<<N first best (m1 granules power 1) 2. Forming combinations Selection m2<< first best (m2 granules power 2) 3. Forming combinations Selection m3<< first best (m3 granules power 3) M =< m1,m2,m3 > - set of secondary attributes ( granules) AdDel(M) selects m*<<|M| best granules, which included n* attributes GRAD

Value of FRiS for points on a plane

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 *

Examples of taxonomies by a algorithm FRiS-Class

Примеры таксономии алгоритмом FRiS-Class

Comparison the FRiS-Class with other algorithms of taxonomy K

Universal classification Unlabeled Semilabeled Labeled (Clastering) ( ТРФ ) (Pattern Rec) ================================= FRiS-TDR

New methods of DM, using FRiS - function Quantitative estimation of compactness Choice of informative attributes Construction of decision rules Censoring of the training set Universal classification Filling of blanks (inputation) Forecasting Detection of spikes

Unsettled problems Censoring of training set Recognition with boundary Stolp+corridor (FRiS+LDR) Imputation Associations Unite of tasks of different types (UC+X) Optimization of algorithms Realization of program system (OTEX 2) Applications (medicine, genetics,…) … ..

Conclusion FRiS-function : 1. Provides effective measure of similarity, informativeness and compactness 2. Provides invariance to parameters of tasks, low of distribution, relation M:N 3. Provides high quality of decisions

Conclusion FRiS-function : 1.Provides effective measure of similarity, informativeness and compactness 2.Provides unification of methods 3.Provides high quality of decisions Publications: http://math.nsc.ru/~wwwzag

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FUNCTION OF RIVAL SIMILARITY IN A COGNITIVE DATA ANALYSIS

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