Journal of Chemical and Pharmaceutical Research, 2014, 6(5): Research Article

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1 Avalable ole Joural of Cheal a Pharaeutal Researh, 04, 6(5: Researh Artle ISSN : CODEN(USA : JCPRC5 Stuy o swar optzato lusterg algorth Zuo Yg Lu a Xa We Southwest Uversty Chogqg, Cha ABSTRACT Ths artle stues the applato of swar algorth to fuzzy -eas lusterg algorth. The author proposes the fuzzy erel herarhal lusterg algorth base o swar optzato. Ths prove algorth uses the erel futo etho a the ut set fator s ae to t. The algorth optzes the target perforae futo a uses bary tree splt etho to luster ata saple what. The eperetal results show that the algorth a effetvely overoe the weaesses of FCM algorth. Key wors: swar algorth; lusterg; algorth optzato; Partle Swar Optzato algorth (PSO INTRODUCTION. The oept of lusterg algorths Clusterg refers to the proess of vg the olleto osstg of ultple ata saple eleets to ultple set ategores opose of slar saple eleets aorg to erta rules. [] Clusterg aalyss eas vg the ata eleets set reasoably aorg to erta lassfato rules orer to etere the ategory eah eleet belogs to. I fferet lusterg algorths, Eulea stae, vetor Agle ose a soe other easureet ethos are use to esrbe fferet slarty futo. [].. Har -eas lusterg algorth Aog lusterg algorths, fuzzy lusterg algorth base o the obetve futo has bee wely apple prate. Fuzzy lusterg algorth[3] s oe fuzzy lusterg algorth whh s ore ature theoretal researh a ore wely use aog lusterg algorths base o target futo. Fuzzy lusterg algorth X { a be aheve by provg the obetve futo of har lusterg algorth. Suppose,, 3, 3, } (,, 3, 3, s represets a set of lte easure ata saples of oel spae, represets the, egevetors of easure saple ata s the ata value of the -eso feature. The lusterg aalyss o a gve saple set X of easureet ata s partto o the saple set X a the proess to obta lusterg results. U [ u ] V { v, v, v, 3, v } Suppose s a lusterg partto atr, 3 s the lusterg eter a s ts lusterg uber, the the obetve futo of har -eas lusterg a be epresse the followg equato: (, ( J UV st.. U M h The har partto spae orrespog to the ata saple set X s epresse the followg equato: 743

2 Zuo Yg Lu a Xa We J. Che. Phar. Res., 04, 6(5: h M { U R {0,},, ;, ; 0 < <, } I the equato, represets the uber of X eleets the ataset whle s the uber of lusterg eters(<< a s the storto egree betwee the ata saple pot a the lusterg eter V a t s easure by stae. V s R (. s the ebershp value of the ata saple pot belogg to the lusterg eter. The bgger the ebershp value s, the hgher egree the slarty betwee the ata saple pot a ts lusterg eter s, the ore easly the ata saple pot s ve to the ategory etere by the lusterg eter. The error su squares betwee ata saple pots all ategores a the typal ata saple pots s epresse as the relato J( UV,. The a proeure of HCM (har -eas algorth s as follows: The talzato of algorth: s the uber of lusterg lassfato,, represets the uber of ata the ata saple. Set the terato stop presoε >0 a talze V(0, the terato outer 0; Step : Calulate the followg upate atr ( ( { } ( { ( 0 other Step: Calulate the upate atr V(+; ( +. V +,,, 33 ( ( + ( ( Step3: f + V V < ε, stop the alulato; or set +, retur to step. The algorth a also tae talzg ebershp atr U (0 lusterg algorth as a oto to start a e. The proeure s slar to the above steps, oly that the ebershp futo s use as the rtero futo of lusterg. Fuzzy -eas lusterg algorth I har -eas lusterg algorth, t a be fou that ts ebershp s or 0. So whether the partto s reasoable or ot, eah ata saple a always be orporate to a ategory. The weaess of the algorth s that t aot show learly the relato betwee ata saples a lusterg eter, a prate t s har to f a proble eee to be stgushe so strtly. To eal wth ths of probles ore effetvely, the oept of fuzzy set s troue a the lusterg algorth FCM base o obet futo s propose. Fuzzy set theory s to ete the rage of ebershp futo values har partto fro {0, } to the lose terval [0, ] a eue the fuzzy partto, the ths lusterg partto spae s show as follows: f M { U R [0,],, ;, ; 0 < <, } J( UV, ( st.. U M f ( (-3 Its a ea s ag a fuzzy weghte e fuzzy lusterg obetve futo to otrol the fuzzy egree of atr U. The bgger s, the hgher fuzzy egree of the target futo s. The lusterg's obet s to get the J ( UV, u of the atheatal epresso ; { J ( UV, } ( ( { ( } (-5 Naely, whe eetg the equato, get the etree value of the above equato so that the ultplato etho Lagrage a be use to get the etree value of ostrat otos ; J ( UV, whe satsfes the

3 Zuo Yg Lu a Xa We J. Che. Phar. Res., 04, 6(5: F ( + ( (-6 The otos for havg etree values are: F [ ( t ]( t 0 t (-8 F 0 (-7 t Fro the above equatos, the followg equato a be got: Plug the above equato to (-6, the followg equatos a be got: [ ] ( t (-9 l l lt l l ( lt l ( lt l ( ( [ ] ( { [ ] (-0 l [ ] ( lt (- I the proess of alulatg, the value of s ot 0. For. a be 0, so aalyze t uer the two ases whe s 0 or Slarly, the value of V( a be got the sae way whe the epresso s u. Set The followg equato a be got: V ( ( - J ( UV, 0 V It a be see fro (-4 that the obet futo of fuzzy -eas lusterg algorth s the sae as that of har -eas lusterg algorth whe equals. Therefore, fuzzy -eas lusterg algorth s the sae as har -eas lusterg algorth whe equals. Whe, the bgger s, the larger the fuzzy egree of the lusterg results fuzzy lusterg algorth s. The lusterg results are the ost fuzzy whe s fte. Matr U fuzzy -eas lusterg algorth orrespos to the fuzzy lassfato of ata saple set X. FCM algorth s sestve to the hoe of tal value a easly falls to loal etreu pots. To prove FCM algorth, fuzzy erel herarhal lusterg algorth s propose the artle. Fuzzy erel herarhal lusterg algorth The prove FCM algorth propose the artle s alle fuzzy erel herarhal lusterg algorth base o partle swar algorth. The a proveet s that the algorth tegrates the erel lusterg etho to solve the olear separable probles. I orer to aheve the quess of lusterg, the assebly operator a the bary tree splt are ae to obta herarhy lusterg a optze the perforae of target futo by usg partle swar algorth.. Kerel futo etho Wth the rap evelopet of support vetor ahe theory, t has broa applato prate. Kerel futo etho s a etho appg the ata saple fro the tal put spae Rp to hgh-esoal feature spae Rq through the use of olear trasforato φ( a og researh the hgh esoal feature spae []. If the relatoshp betwee the varous eleets the ata set the algorth s oly og atheatal er prout alulato, the spef atheatal for of φ( ee ot be ow. To get the orrespog olear algorth the orgal put spae, oly erel futo wth Merer ature s eee to substtute the er prout for the algorth. The alulato beoes very sple a oveet through erel futo wth Merer ature Defto Gra Matr []: set that a gve futo eets the atheatal relato : ( the relato, K equals C or R a,, X K ( (,, the atr; s alle the ulear 745

4 Zuo Yg Lu a Xa We J. Che. Phar. Res., 04, 6(5: atr K for,,. Defto Postve Defte Matr[] Postve Defte Matr for a atr K of, suppose all C q 0 eet,, the the atr s Postve Defte Matr. Defto 3 Postve Defe Kerel: Set X s a oepty set a has a futo efe X X, a Postve Defte Gra Matr s geerate for all N N,, a X, the the futo s alle ' ' ' ( T f ( ((, f ( Postve Defe Kerel. The equato T geerates operator, the futo s T alle erel futo of. N,,,, Defto 4 Merer erel: Set ata saple set R l, s appe to feature spae H through olear trasforato φ( φ (, φ (,, φ (, a get the relato l the put er prout operato betwee spae ata saples after appg to feature spae H s epresse wth Merer erel K(, ( φ( as, (, All ata saple fors a erel atr K K, erel lusterg etho s usg Merer erel to aheve the appg trasforato of two spaes. Frst ap saple put spae for to the feature spae for, the luster a aalyze the saples the feature spae. Ay futo K a get the haraterst futo a haraterst value ( φ (, of the erel futo K as log as t eets Merer oto. Its erel futo N H Ky (, φ ( φ( y, a be epresse as N H the equato eotes the esos of the feature spae. Slarly, φ( a be epresse the followg equato: T φ( ( φ (, φ (,, N H φ NH ( (- Eul stae (, H y a be epresse the followg equato: (, (, (, (, H y y+ yy (- Gaussa erel futo eetg Merer oto s use; Ky (, ep( β y, β > 0 (-3 The K ( X, X,the equato(6-0 a be hage to the followg equato: (, (, H y y (-4. Cut Set fator Mappg the orgal ata saple set to hgh-esoal feature spae through erel futo a ag trap/cut Set fator to the hgh-esoal feature spae at the sae te solves the owershp proble of ata (,,, saples whe the ebershp are lose to eah other, at the sae te ehaes the overgee apaty of the algorth a aelerates the overgee spee of the algorth. Defto 5 Suppose A X eotes a fuzzy set X, a [0,]. If A eets the atheatal epresso A { A } s, the set A s alle trap/cut Set fator of A. Set the vg atr of X s epresse [0,], Z, [ z ] as U [ ] z, U {,,,, } 0 a ust eet the followg otos:, geerates fuzzy partto, the t 746

5 Zuo Yg Lu a Xa We J. Che. Phar. Res., 04, 6(5: , U φ z U w 0, U φ z U U φ (-5 I the above equato, / a,a > 0 eotes a postve trap/cut Set fator. I the geeral ases, the uber of ategores of ata saples after lusterg s.whe a, [0.5,] ; Whe a, /..3 Optzato of obet futo Covert ata saple set fro the put spae to hgh-esoal feature spae Rq through olear appg φ( a use Eul stae feature spae at the sae te, the the epresso of obetve futo of fuzzy erel lusterg a be epresse as: J( UV, (, φ( φ( v ( (, (, y + v (, v, (-8 Optze the obetve futo by usg partle swar algorth. Ky (, ep( β y, β 0 Use Gaussa erel futo >. Slarly, aorg to the requreet of the FCM algorth, the ebershp futo of fuzzy erel lusterg algorth has to eet the followg equato: ( ( v, ( ( v, l (-9 Itroue Cut Set fator to hgh-esoal spae a 0.5 +/ z 0 < (-0 U {,,,, } (-, U φ z a{ U w 0, U φ z a{ U U φ (- The the lusterg eter hgh-esoal feature spae s epresse as: φ( φ( v,,, (-3 After alulatg, the followg results are got: K(, K(, v φ( φ( v φ φ l l l l Kv (, v ( v ( v ( ( K (, /( ( (-4 (-5 Therefore, the ebershp futo hgh-esoal feature spae s epresse as: ( ( v, (/ (, v (, + v (, v ( (/ (, v (, + v (, v l ( v, (-6.4 Herarhal Clusterg etho Herarhal Clusterg etho s a lusterg etho wely use prate a ts relate theory s ostat 747

Zuo Yg Lu a Xa We J. Che. Phar. Res., 04, 6(5:743-749 evelopet.

6 Zuo Yg Lu a Xa We J. Che. Phar. Res., 04, 6(5: evelopet. It a be ve to the botto-up oesg herarhal lusterg etho a the top-ow splt herarhal lusterg etho aorg to the fferet retos of the eoposto herarhal lusterg etho [3]. The a prple of splt herarhal lusterg etho s asrbg all the ata obets to a ategory frst, the vg the ategory to two aorg to soe rules a repeatg the sae vg etho the ewly-geerate ategores utl the algorth eets erta e otos. The algorth ths artle uses the ea of bary tree splt algorth a obes wth the prove fuzzy erel lusterg algorth. I the algorth,,,a the lusterg eter of the bary tree whh s less tha the u or the au epth of the bary tree whh s greater tha the au TLa s use as the e otos of the algorth. I orer to prove the spee of the algorth, 5 s set as the au epth, erge a aust the lusterg eters aorg to ther staes whe the algorth es. Fgure. s the eo fgure of fuzzy herarhal lusterg algorth base o partle swar algorth. D v Fgure. Deo Fgure of Kerel Herarhal Clusterg Proess.5 The eperetal ata a aalyss IRIS ata are use to test the fferet perforaes of FCM algorth a fuzzy lusterg algorth. IRIS ata are a staar test saple set. IRIS ata saple set are opose of 50 ata saple pots a they represet a four-esoal ata set. Eah ata saple set s represete respetvely by four opoets Petal Legth,Petal Wth,Sepal Legth a Sepal Wth. I the eate, the whole ata saple set s opose of three IRIS ategores Setosa,Versolor a Vrga. Eah ategory s opose of 50 saples. K (, y ep( β y, β>0. The a of ths eperet s usg fuzzy erel herarhal lusterg algorth base o partle swar algorth a FCM to luster IRIS ata set, opare ther lusterg auray a spee. The results are show as follows: Table Results of lusterg IRIS ata Clusterg Frst Seo Thr Average Te(s algorth ategor ategor ategor uber of y y y teratos FCM , IRIS To overoe the weaesses of FCM algorth, the fuzzy erel herarhal lusterg algorth base o partle swar algorth s propose. Copare wth FCM algorth, the ew algorth s gue by the prple of au ebershp a t uses the prove partle swar algorth to optze obetve futo. It ot oly atas the avatages of fuzzy lusterg but also proves the overgee spee a prevets loal optu. The algorth apples the ea of erel futo a the herarhal lusterg of bary tree proves the lassfato spee a auray. Eperetal results prove that ts perforae s superor to the latter /FCM algorth. CONCLUSION Ths artle aalyzes the weaesses of Fuzzy C lusterg algorth a proposes a prove lusterg algorth----fuzzy erel herarhal lusterg algorth base o partle swar algorth. The a proveet s that the algorth eteres lusterg uber autoatally a troues erel lusterg algorth. Assebly operator operato s ae to the algorth a the algorth uses the prove partle swar optzato (pso algorth for global optzato. The eperetal results show that the algorth a effetvely overoe the weaesses of FCM algorth. 748

7 Zuo Yg Lu a Xa We J. Che. Phar. Res., 04, 6(5: REFERENCES [] Gao Xbo Xe We.. Chese See Bullet,00,(44:4-47 []lu zhao. Researh & Applato of Clusterg Algorth.[D].Chagsha Uubersty of See &Tehology,03. [3]He lg. researh a applato of oputer 007(:0-3 [4]Du J C. IEEETras.SMC,974,4(3:30-33 [5]Beze J C.Patter Reogto wth Fuzzy Obetve Futo Algorths. Pleu Press,New Yor,98 [6]L R P,Muaoo M.A au-etropy approh to fuzzy lusterg. FUZZ-IEEE 95, [7]Beze J C. Patter Reogto, 00,5(:-7. [9]Beze J C, Hathaway R J,et al. IEEE Tras. PAMI,0,7(5: [0]L Zhogwe. Harb Egeerg Uversty,00.(: 7-9. [] L Yg Zhag Yag. Coputer egeerg a Applatos,00 (7:4- []Shege et. Coputer egeerg a Applatos 0,43(3:

A Weighted Sample s Fuzzy Clustering Algorithm With Generalized Entropy

A Weighted Sample s Fuzzy Clustering Algorithm With Generalized Entropy A Weghted Saple s Fuzzy Clusterg Algorth Wth Geeralzed Etropy Ka L Hebe uversty Shool of atheats ad oputer Baodg, Cha Eal: Lka {at} hbu.edu. Lua Cu Hebe uversty Lbrary Baodg, Cha Abstrat Cobed wth weght