Quick algorithm f or computing core attribute

Μέγεθος: px

Εμφάνιση ξεκινά από τη σελίδα:

Download "Quick algorithm f or computing core attribute"

Φωτινή Βασιλειάδης
8 χρόνια πριν
Προβολές:

1 24 5 Vol. 24 No. 5 Cont rol an d Decision May 2009 : (2009) a, 2, 1b (1. a., b., ; 2., ) :,,.,.,. : ; ; ; : TP181 : A Quick algorithm f or computing core attribute GE H ao 1a, L I L ong2shu 2, YA N G Chuan2j i an 1b (1a. Department of Electronic and Information Engineering, 1b. Department of Computer Science, Chuzhou University, Chuzhou , China ; 2. School of Computer Science, Anhui University, Hefei , China. Correspondent : GE Hao, E2mail : com) Abstract : The algorithms for computing the core have following shortcoming : The core acquired f rom these algorithms is not the core based on positive region, and the time complexity and space complexity are not good. Therefore, a new approach for computing core is provided and proved that the core is equivalent to the core based on positive region. The partition of the equivalence class is the key step for computing the core. An efficient algorithm for computing the equivalence class is designed with the approach based on radix sort by using distributing counting. On the foundation, the quick algorithm for computing the core is designed. The experimental result shows that the algorithm is correct and efficient. Key words : Rough set ; Equivalence class ; Positive region ; Core attribute 1 [ 1 ] Pawlak 1982.,,.. Hu [2 ] Skowron [3 ],, O( C U 2 ). [4 ] Hu,, O( C U 2 ). [5 ],,:,Hu. [6 ], O( C 2 U log U ), O( U ),,.,, [7210 ] : [7 ],, O( C U 2 ) ; [8 ], max{ O( C U log U ), O( C U POSC ( D) ) } O( C U POSC ( D) ) ; [9 ],, max{ O( C U/ C 2 ), O( C U ) } max{ O( U ), O( C U/ C 2 ) }. [7210 ] : ; : : ( ) ; ( KJ2008B117). : (1976 ),,,,, ; (1956 ),,,,,.

2 5 : 739,,,,..,,., U/ C, U/ C O ( C U ).,O( C 2 U ), O( U ). 2 1 [11 ] S = (U, A,V, f ). :U,,U = { x1, x2,, x n} ; A, A = { a1, a2,, am, d}, A 2, A = C D C D =, C, D, D D = { d} ;V,V = { V a1,v a2,,v am, V d} ; f f :U A V, Πa A, x U, f ( x, a) V a. 2 [11 ] S = (U, A, V, f ), R Α A, ind ( R) = { ( x i, x j ) f ( x i, b) = f ( x j, b), Πb R} S.,, x [ x ]ind( R) [ x ] R. R U U/ ind ( R) U/ R. 3 [11 ] S = (U, A, V, f ), R Α A, R- X = { x U [ x ]ind( R) Α X} X R ; R - X = { x U [ x ]ind( R) X } X R ; POSR ( X) = R- X X R. 4 [11 ] S = (U, C D, V, f ), P Α C, D P POSP ( D), POS P ( D) = P - ( X). X U/ D D P U ind ( P) D. 5 [11 ] S = (U, C D, V, f ), a C, POSC ( D) = POSC- { a} ( D), a C D ;, a C D. C C D, Core ( C). 6 [11 ] S = (U, C D, V, f ),x i, x j U, i j, f ( x i, C) = f ( x j, C) f ( x i, D) f ( x j, D),, x i x j ( ) ;,. 3, Hu ;, Hu.,.. 7 S = (U, C D,V, f ), a C, GCore ( C) GCore ( C) = { a a C}, ConSet ( C - { a} ) > ConSet ( C) ; <, ot herwise. ConSet ( C) = { x i x i U, ϖ x j, f ( x i, C) = f ( x j, C) f ( x i, D) f ( x j, D) }., ConSet ( C), ConSet ( C) ConSet ( C). 7,ai,,ai ;, ai. 1 S = (U, C D, V, f ), Core ( C) = GCore ( C). U/ C = { X1, X2,, X n},u/ D = { Y1, Y2,, Y m}. 1) GCore ( C) Α Core ( C). Πa GCore ( C),7, a, ConSet. x ConSet ( C), x ConSet ( C - { a} ),y [ x ] C y [ x ] C- { a}, f ( x, D) f ( y, D). x Y q, y Y p, y Y q, y [ x ] C- { a} y Y q,x ( C - { a} ) - Y q, x POSC- { a} ( D). x S x Y q, x C- Y q, x POSC ( D), POSC ( D) POSC- { a} ( D). a Core ( C)., GCore ( C) Α Core ( C). 2) Core ( C) Α GCore ( C). Πa Core ( C), POSC ( D) POSC- { a} ( D),x [ x ] C Α Y k [ x ] C- { a} Y k. ϖ y, y [ x ] C- { a} y [ x ] C. f ( x, C - { a} ) = f ( y, C - { a} ) f ( x, D) f ( y, D)., a. x S.. z, z, x [ x ] C Α Y k f ( x, D) f ( z, D), x, z U/ D, z, x [ x ] C Α Y k, x S., a, ConSet ( C - { a} ) > ConSet ( C), a

3 GCore ( C). Core ( C) Α GCore ( C). 1) 2) Core ( C) = GCore ( C). 1,. U, C,., ;,. O( C U 2 ). 1 S = (U, A,V, f ), x i, x j U C Πa A, f ( x i, a) = f ( x j, a). 2, 1. 1,S C ; S,. [6 ], O( C U log U ) ; [9 ], O( C U )., C S. O( C U ), O( U ),. : S = (U, C D), C = { ai i = 1,, m}, D = { d},, S = { S i i = 1,, n}, S i m + 2, S i = ( x i, a1, a2,, am, d). : S i x i, S i a j i a j, S i d i. C S, ai S., ai, [1 e], 0 < e U ;, count Pos[0 e],count Pos ind ( ai), ind ( ai), count Po s S i., 2,count Pos, sorteds. 1 : S = (U, C D,V, f ),U = { x i i = 1,, n}, C = { ai i = 1,, m} ; :U/ C. Step1 : for i = 1 to C Do / / Step1. 1 : { count Pos : count Pos[0 e] = 0. Step1. 2 : ind ( ai),,count Pos. Step1. 3 : for j = U to 1 Do Step : { S j a i, count Pos S j pos; po s ; Step : S j sorteds Step : [ S j a i ]ind( a i ) () ; } ) Step2 : s = 1, E1 } / / end_for_ i Step3 : for i = 2 to U Do } = { x1 } ; / / s {if ( x i x i- 1 C t hen Es = Es { x i} ; else s = s + 1, Es = { x i} ; Step4 : E( U/ C) s. 1, Step1 O( e) + O( U ) + O( U ) = O( U ). O( C ), Step1 O( C U ), Step3 O( U ). Step1, count Pos U + 1, Step3 sorteds 2 U., 2 O( U ). 1 O( C U ) + O( U ) = O( C U ), O( U ) , : 2 :S = (U, A,V, f ). : U ; A, A = C D C D = ; C ; D. E s. : Core ( C). Step1 : Core ( C) =, ConSet ( C) =. Step2 : 1,C S, Step3 : count Po s,, count Pos. Step4 : for j = 1 to s Do if ( ( Ej x t x k x t d

4 5 : 741 x k d) t hen ConSet ( C) = ConSet ( C) Ej. Step5 : for i = 1 to C Do Step5. 1 : { 1,C - { ai} S, E s ; Step5. 2 : count Pos,, count Pos ; x k d) Step5. 3 : ConSet ( C - { ai} ) Step5. 4 : for j = 1 to s Do - { ai} ) Ej ; = ; if ( Ej x t x k x t d t hen ConSet ( C - { ai} ) = ConSet ( C Step5. 5 : if ( ConSet ( C - { ai} ) > ConSet ( C) ) then Core ( C) = Core ( C) { ai} ; } / / end_for_ i. Step6 : Core ( C). Step7 :. 2, Step2 O( C U ), Step3 Step4 O( U ). Step5. 1 O( C U ), Step5. 2 Step5. 4 O( U ), Step5 O( C U ) + 2O( U ) = O( C U ), Step5 C, Step5 O( C 2 U )., 2 O( C U ) + 2O( U ) + O( C 2 U ) = O( C 2 U ), O( U ) Hu, O( C U 2 ),., O( C 2 U log U ) O( U ),. max{ O( C U log U ), O( C U POSC ( D) ) } O( C U POSC ( D) ) ; max{ O( C U/ C 2 ), O( C U ) } max{ O( U ), O( C U/ C 2 ) },, U, U/ C POSC ( D) C, UCI Car evaluation 1 728, C 6, U/ C = 972, POSC ( D) = 1 196, U, U/ C POSC ( D) C., , [4 ] , 5, C = { a, b, c}, D. 1 S1 U a b c D x x x x x , x1 x2, x3 x4., ConSet ( C) = { x1, x2, x3, x4 } ; ConSet ( C - { a} ) = { x1, x2, x3, x4 }, ConSet ( C - { b} ) = { x1, x2, x3, x4, x5 }, ConSet ( C - { c} ) = { x1, x2, x3, x4 }., ConSet ( C - { b} ) > ConSet ( C), Core ( C) = { b} , C = { a, b, c}, D. 2 S2 U a b c D x x x x , ConSet ( C) = { x2, x3 } ; ConSet ( C - { a} ) = { x1, x2, x3 }, ConSet ( C - { b} ) = { x1, x2, x3, x4 }, ConSet ( C - { c} ) = { x2, x3 }., ConSet ( C - { a} ) > ConSet ( C) ConSet ( C - { b} ) > ConSet ( C), Core ( C) = { a, b} [6 ]UCI 6, Petium GHz, RAM 512 M, EAB KF, 3. AL G1,AL G2 EAB KF, AL G3, AL G4,

5 U/ C POSC (D) / ms AL G1 AL G2 AL G3 AL G4 AL G5 [ 6 ] Patient data Flare data Balance data Monkey data Car evaluation data Led17 data AL G5 ( 2). 3, AL G5 AL G1 AL G4,,AL G5,. 6, Hu.,,.,, U/ C, O ( C U ) O ( U )., O( C 2 U ) O ( U ).,. ( References) [ 1 ] Pawlak Z. Rough set s [ J ]. Int J of Computer and Information Science, 1982, 11 (5) : [2 ] Hu X H, Cercone N. Learning in relational databases : A rough set approach [J ]. Computational Intelligence, 1995, 11 (2) : [ 3 ] Skowron A, Rauszer C. The discernibility matrices and f unctions in information systems [ C ]. Intelligent Decision Support2handbook of Applications and Advances of the Rough Sets Theory. Dordrecht : Kluwer Academic Publisher, 1991 : [4 ],. [J ]., 2002, 30 (7) : ( Ye D Y, Chen Z J. A new discernibility matrix and the computation of a core [ J ]. Acta Electronica Sinica, 2002, 30 (7) : ) [5 ]. [J ]., 2003, 26 (5) : ( Wang G Y. Calculation methods for core attributes of decision table [ J ]. Chinese J of Computers, 2003, 26 (5) : ) [6 ],,,. [J ]., 2003, 24 (11) : ( Zhao J, Wang G Y, Wu Z F, et al. An efficient approach to computer feature core [ J ]. Mini2Micro Systems, 2003, 24 (11) : ) [7 ],. [J ]., 2005, 26 (11) : ( Yan D Q, Liu F F. Discernibility matrix and approximate quality in attribute reduction [ J ]. Mini2 Micro Systems, 2005, 26 (11) : ) [ 8 ],. [J ]., 2004, 43 (5) : ( Yang M, Sun Z H. Improvement of discernibility matrix and the computation of a core [ J ]. J of Fudan University, 2004, 43 (5) : ) [9 ],,,. [J ]., 2006, 42 (6) : 426. (Xu Z Y, Yang B R, Song W, et al. Quick computing core algorithm based on discernibility matrix [ J ]. Computer Engineering and Applications, 2006, 42 ( 6) : 426. ) [10 ],. [J ]., 2007, 21 (8) : ( Yang M, Yang P. Fast updating algorithm of computation of a core based on discernibility matrix [J ]. Control and Decision, 2007, 21 (8) : ) [11 ],,,. [ M ]. :, (Zhang W X, Wu W Z, Liang J Y, et al. Theory and method of rough set [ M ]. Beijing : Science Press, )

Σχετικά έγγραφα

ER-Tree (Extended R*-Tree)

ER-Tree (Extended R*-Tree) 1-9825/22/13(4)768-6 22 Journal of Software Vol13, No4 1, 1, 2, 1 1, 1 (, 2327) 2 (, 3127) E-mail xhzhou@ustceducn,,,,,,, 1, TP311 A,,,, Elias s Rivest,Cleary Arya Mount [1] O(2 d ) Arya Mount [1] Friedman,Bentley