A robust clustering algorithm with f uzzy directional similarity

Transcription

1 3 1 Vol CAA I Trasatios o Itelliget Systems Feb. 2008,, (,214122) :,, FDSC,,, RFDSC. RFDSC. : ;;; : TP :A : (2008) A robust lusterig algorithm with f uzzy diretioal similarity ZHU Li, WAN G Shi2tog, XIU Yu ( Shool of Iformatio Egieerig,Jiaga Uiversity, Wuxi , Chia) Abstrat :Oe of the importat harateristis of text lusterig i dataset s is t hat eah luster eter i t he dataset has a diretio t hat is differet from that of all ot her luster eters. This diretioal iformatio should be iorporated i lusterig aalysis. I t his paper, a ew robust f uzzy diretioal similarity lus2 terig algorit hm ( RFDSC) is proposed by itroduig membership ostrait s. The ew objetive f utio was ostruted. Fially, t he robust ess ad overgee of t he proposed algorit hm were aalyzed f rom t he viewpoit of o mpetitive learig. Experimetal test s of text lusterig i dataset s usig RFDSC dem2 ostrate it s effetiveess. Keywords :lusterig algorit hm ; diretio al similarit y ; ro bust ess ; o mpetitive learig,.,,,., ( K2meas Claras Frem) ( Chame2 leo Brih) ( WaveCluster Stg Clique) (Dbsa Optis).,, : :863 (2006AA10Z313) ; ( ; ) ; (A ) ; (105087). :. E2mail om... [122 ]2 SP Kmeas [1 ] movmf [2 ],2,. [ 3 ],,.,,,,. (f uzzy diretioal similarity luste2 rig,fdsc),,,, (robust f uzzy diretioal similarity lusterig,rfdsc),.

2 (DSCM) [3 ] ( diretioal similarity2 based lusterig algorit hm,dscm) S ( xj, wi ) xj wi : S ( xj, wi ) = e kx T j w i,,2,,,,2,,, k. S ( xj, wi ) xj wi. DSCM J S = S ( xj, wi) = e kx T j w i. (1) DSCM,wi,, ( ag2 glomerative hierarhial lusterig,a HC),. DSCM,,A HC.,, DSCM,. DSCM ( FDSC),, : J FDSC = u m ij e kx T j w i. (2) : uij = 1,0 < uij <, uij [0,1 ], : m,,2,,,,2,,, k. 1 ui,0 < uij <, uij [0,1 ], w T i w,fdsc J FDSC = u m ij (e kx T j w i ) : 1) uij uij = (e kx T j w i ) - 1/ ( m - 1) / (e kx T j w i ) - 1/ ( m - 1). (3) 2) wi. (4) (2), ( FDSC) uij (3) wi (4). FCM, FDSC, xj wi, (3) - 1/ ( m - 1) > 0,m < 1,, 0 < m < 1. FDSC wi, J FDBC,. 212 W TA (wier2take2 all) W TM ( wier2take2more) 2, (hard ompetitive learig) ( soft ompetitive learig) [425 ]. W TA :, (dead odes) (uder2utilizatio)., W TM,,,,. [ 6 ] ( RPCL ),,, ( ),. ( RPCL ), FDSC, RFDSC. xj, : f ( u1, u2,, u) = ui ( u m- 1 i - 1), : J RFDSC = u m ij (e kx T j w i ) - aj uij ( u m- 1 ij - 1). (5) (5) aj (1 j ). m (0,1), uij = 1,0 <

3 1,: 45 uij <, uij [0,1 ]. xj,: f ( u1, u2,, u) = ui ( u m- 1 i 0 ui - 1) : 2 f ( u1, u2,, u), 1, ui = 1, m (0,1), ui (,2,, ) 1/, f ( u1, u2,, u) 1 - m - 1 ;ui (,2,, ) uk 1, ui ( i k) 0, f ( u1, u2,, u) 0,0 f ( u1, u2,, u) 1 - m - 1., J RFDSC,f ( u1, u2,, u), uk 1,ui ( i k) 0. 1, ui.,. 213 RFDSC RFDSC,. 3 ui,0 < uij <, uij <, uij [0,1 ], w T i w m (0,1), RFDSC J RFDSC = u m ij (e kx T j w i ) - aj uij ( u m- 1 ij - 1) : 1) uij : uij = (e kx T j w i - aj ) - 1/ ( m- 1) / (e kx T j w i - aj ) - 1/ ( m- 1). (6) e kx T j w i - aj < 0,, uij. aj, e kx T j w i - aj. aj = mi{ e kx T j w j i { 1,, } } -, (> 0), (6) : uij = (e kx T j w i - mi e kx T j w 3 + ) - 1/ ( m- 1) / (e kx T j w i - mi e kx T j w 3 + ) - 1/ ( m- 1). (7) 2) wi :. (8) 3 m k. m, FCM, FDSC RFDSC, xj wi,m < 1,, 0 < m < 1.,m 1,,m 019. k, k ( k > 1) ( k < 1) xj wi.,k 15,,k 3.,,;,., 1/.,,, ;,, [7 ]. RFDSC, uij,,, RFDSC FDSC. RFDSC

4 46 3,,., x wi , , RFDSC. RFDSC : 1) (2 N ), ( l = 1 ) m k T, w 1 i ; 2) (7) u l + 1 ij ; 3) (8) w l + 1 i ; 4) u l + 1 ij - u ( ij l), l = l + 1, 2) ; <l > T, 5),wi u ij. 3,, SP K2 meas [ 1 ] soft2movmf [ 2 ] FDSC RFDSC 4,. DSCM,,,,DSCM. 311, 2. 1, ( ormalized mut ual iformatio, NMI) F,. 2, AA (averaged auray or rad idex) J aard,,2, [8 ]. :( Reall) ( Preisio)., [9 ]. NMI [10 ] AA [11212 ] 2. X, Y, NMI NMI ( X, Y) = I ( X ; Y) H ( X) H ( Y), I ( X ; Y ) X, Y, H ( X), H ( Y) X Y. AA :AA ( X, Y) = a + b ( - 1) / 2, a 2 X Y, b 2,. NMI AA [0,1 ],, 2, X Y,NMI AA Newsgroup s [13 ] CL U TO [ 14 ] , 5 832, , 3, 20,. N G20 20,Bow toolkit [ 15 ] 202Newsgroup s N G17219 N G20,,. CL U TO [14 ], Table 1 Summary of text datasets Data Soure d w K balae N G20 202Newsgroups N G overlappig/ subgroups from NG ohsal O HSUMED klb WebACE hiteh Sa Jose Merury( TREC) la12 LA Times( TREC) tr11 TREC tr23 TREC tr41 TREC tr45 TREC : d (), w ( ), k, balae,.

5 1,: 47, L , SP Kmeas soft2movmf FDSC RFDSC 4.,, 20.,FDSC RFDSC k m. 2 3 FDSC k N G17219 tr45 NMI AA. m k FDSC NG17219 Table 2 The results of FDSC o NG17219 datasets with the hage of k k RFDSC tr45 Table 5 The results of RFDSC o tr45 datasets with the hage of RFDSC m N G17219 tr45 NMI AA. 0115, k 3. 6 m RFDSC NG17219 Table 6 The results of RFDSC o NG17219 datasets with the hage of m m k FDSC tr45 Table 3 The results of FDSC o tr45 datasets with the hage of k k RFDSC N G17219 tr45 NMI AA. m 019, k 3. 4 RFDSC NG17219 Table 4 The results of RFDSC o NG17219 datasets with the hage of m RFDSC tr45 Table 7 The results of RFDSC o tr45 datasets with the hage of m m ,k m 019, FD2 SC RFDSC. SP Kmeas soft2movmf FDSC RFDSC NMI.

6 48 3 SPKmeas soft2movmf FDSC RFDSC 8 NG20 NG17219 ohsal k1b hiteh Table 8 NMI results o NG20, NG17219, ohsal, k1b, hiteh datasets N G20 N G17219 ohsal k1b hiteh la12 tr11 tr23 tr41 tr45 Table 9 NMI results o la12,tr11,tr23,tr41,tr45 datasets SPKmeas soft2movmf FDSC RFDSC la12 tr11 tr23 tr41 tr AA. 10 NG20 NG17219 ohsal k1b hiteh Table 10 AA results o NG20, NG17219,ohsal, k1b, hiteh datasets N G20 N G17219 ohsal k1b hiteh SP Kmeas soft2movmf FDSC RFDSC la12 tr11 tr23 tr41 tr45 Table 11 AA results o la12,tr11,tr23,tr41,tr45 datasets la12 tr11 tr23 tr41 t r45 SP Kmeas soft2movmf FDSC RFDSC ,RFDSC, FDSC RFDSC, FDSC RFDSC,.,, RFDSC,,, RFDSC m k,. 4 DSCM, FDSC,,, RFDSC,RFDSC,DSCM. 1 FDSC (2) J FDSC, uij = 1,0 < uij <, uij [0,1 ] w T i w, Lagrage, b. Lagrage L (w,, b) : L (w,, a, b) = u ij m (e kx T j w i ) + j ( uij - 1) + bi (w T i wi - 1). (9) L (w,, b) uij, - j uij = [ ] 1/ ( m- 1). (10) m (e kx T j w i ) (10) uij = 1, ( - j ) / m uij = (e kx T j w i ) - 1/ ( m- 1) / (e kx T j w i ) - 1/ ( m- 1). (11) L (w,, b) wi, 9L 9wi = kx T j u ij m e kx T j w i + 2 bi 0. (12) kx T j u ij m e kx T j w i / ( - 2bi). (13) w T i w,(13) :..

7 1,: 49 2 : 1) 0 ui 1,0 < m < 1, i - 1) i - 1) 0, f ( u1, u2,, u) 0. f ( u1, u2,, u) = 0 i - 1) 0, i - 1) = 0 (0 i ), ui = 0 ui = 1. ui = 1, f ( u1, u2,, u) = 0 u, uk = 0 ( k i). 2) f ( u1, u2,, u) = ui ( u m- 1 i - 1) (0 ui 1) ui = 1. : G = ( ui - 1). 9 G 9 u1 u2 = u = 1,= m1 - m - 1. i - 1) -, 9 G,, 9 G 0, u1 = 9 u2 9 u f ( u1, u2,, u) [0, 1 ], f ( u1, u2,, u),. f ( u1, u2,, u ). 1 - m ) u1 = u2 = u = 1, f ( u1, u2,, u ) = 2) [0,1 ] ( u1, u2,, u), u1, u2,, u p (1 p ) ui 0, q(0 q 1) ui 1. p + q =, p + q <,ui i - 1) = 0. = 0,1 f ( u1, u2,, u),,p + qu i 0 1, f ( u1, u2,, u) - p - q ui ( u m- 1 i i = p+ q+1-1). ui ( u m- 1 i i = p+ q+1-1) < 1 - m - 1., f ( u1, u2,, u) u1 j = u2 j = uj = m RFDSC (5) J RFDSC, uij = 1, 0 < uij <, uij [0,1 ] w T i w, Lagrage, b. Lagrage L (w,, a, b) : L (w,, a,b) = u ij m (e kxt j w i ) - i =1 j =1 aj j =1 j ( uij - 1) + i =1 uij ( u m- 1 ij - 1) + bi (w T i wi - 1). (14) L (w,, a, b) uij, - aj - j uij = [ m (e kx T j w i - aj ) ]1/ ( m- 1). (15) (15) uij = 1, ( - aj - j ) / m uij = (e kx T j w i - aj ) - 1/ ( m- 1) / (e kx T j w i - aj ) - 1/ ( m- 1). (16) e kx T j w i - aj < 0,, uij. aj, e kx T j w i - aj. aj = mi{ e kx T j w i i { 1,, } } -, (> 0), (10) uij = (e kx T j w i - mi e kx T j w 3 + ) - 1/ ( m- 1) / (e kx T j w i - mi e kx T j w 3 + ) - 1/ ( m- 1). (17) L (w,, a, b) wi, : 9L 9wi = kx T j u ij m e kx T j w i + 2 bi 0. (18) kx T j u ij m e kx T j w i / ( - 2 bi). (19) w T i w, (19) : :.. [1 ]D HILLON I S, MOD HA D S. Coept deompositios for large sparse text data usig lusterig [J ]. Mahie Learig, 2001, 42 (1) : [2 ]BAN ERJ EE A, D HILLON I S, GHOST J, et al. Ge2 erative model based lusterig of diretioal data [ C ]/ / Coferee o Kowledge Disovery i Data. Washig2 to, DC, [3 ]L I H X, WAN G S T, XIU Y. Applyig robust dire2 tioal similarity based lusterig approah RDSC to las2

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