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1 Bonformaton by Bomedal Informats Publshng Group Predton Model Iteratve loal Gaussan lusterng for expressed genes dentfaton lnked to malgnany of human oloretal arnoma Ito Wasto, *, St Zaton M Hashm and Sr Sukmanngrum 2 Department of Software Engneerng, Faulty of Computer Sene and Informaton Systems, Unversty Tehnology Malaysa, Skuda, Johor Bahru, Malaysa; 2 Faulty of Bology, Unversty of Jenderal Soedrman Purwokerto, Central Java, Indonesa; Ito Wasto* - E-mal: to@gmx.o.uk; *Correspondng author reeved Deember 4, 2007; aepted Deember 28, 2007; publshed onlne Deember 30, 2007 Abstrat: Gene expresson proflng plays an mportant role n the dentfaton of bologal and lnal propertes of human sold tumors suh as oloretal arnoma. Proflng s requred to reveal underlyng moleular features for dagnost and therapeut purposes. A non-parametr densty-estmaton-based approah alled teratve loal Gaussan lusterng (ILGC), was used to dentfy lusters of expressed genes. We used expermental data from a prevous study by Muro and others onsstng of,536 genes n 00 oloretal aner and normal tssues. In ths dataset, the ILGC fnds three lusters, two large and one small gene lusters, smlar to ther results whh used Gaussan mxture lusterng. The orrelaton of eah luster of genes and lnal propertes of malgnany of human oloretal aner was analysed for the exstene of tumor or normal, the exstene of dstant metastass and the exstene of lymph node metastass. Keywords: gene expresson; unsupervsed lusterng; Gaussan kernel; oloretal aner Bakground: Gene expresson proflng s an effetve approah to extrat useful nformaton from a large number of smultaneously expressed genes wthn spef ell types. Ths approah s not only useful for nvestgatng a known bologal ell, t also an be appled to explore unknown bologal ells n relaton to spef gene funtons []. Comprehensve profles of mrna levels an be obtaned and used to dsrmnate aner ells from normal ell, and to provde sub-lasses of tumor types. The possblty of measurng thousands of smultaneously expressed genes represents a hallenge n terms of analyss and nterpretaton. One useful applaton s the dentfaton of genes whose expresson levels are assoated wth human oloretal arnoma where there s stll lmted knowledge of the bologal and lnal propertes of malgnany [4]. Ths sold tumor s one of the most prevalent and wellharaterzed human aners, and, n spte of reent advanes n dagnoss and therapeuts, s stll a leadng ause of death [3]. Clusterng s a powerful exploratory tehnque for the analyss of gene expresson profles. In the past deades, a number of lusterng algorthms have been proposed n ths ontext nludng Herarhal Clusterng [, 2] and Gaussan Mxture Clusterng [3]. The Herarhal luster analyss s probably the most popular and powerful method for unvelng underlyng features of gene expresson profles. However, beause of a lak of vald statstal evaluaton methods, the results are subjet to nterpretaton by the nvestgator. Gaussan Mxture Clusterng s also another powerful approah. Bonformaton 2(5): 75-8 (2007) 75 Ths parametr lusterng method has been appled to gene expresson lnked to malgnany of human oloretal arnoma wth promsng results [3]. However, ths luster analyss requres pror nformaton about the number of lusters n the dataset, whh s often not realstally possble. In ths paper, a densty-based lusterng method for unoverng underlyng strutures of gene expresson data wll be explored. The advantages of of ths method alled Iteratve Loal Gaussan Clusterng (ILGC) nludes the smplty of the tehnque, no need for pror nformaton on the number of lusters, and the requrement of only one parameter, the nearest neghbour. Methodology: Through densty-based estmaton, we try to approxmate the true densty of genes. Basally, there are two man approahes to mplement densty estmaton: parametr and non-parametr. The frst approah was mplemented by Muro et al [3] usng Gaussan Mxture lusterng and Bayesan framework wth promsng results. However, to avod the requrement for nformaton wth regards number of lusters n advane, we used the nonparametr-based approah to determne the densty of genes. The orgnal form of densty based approah an be formulated as n equaton () (see supplementary materal) 2007 Bomedal Informats Publshng Group

2 Bonformaton by Bomedal Informats Publshng Group Predton Model Due to ts smplty, the K-nearest neghbour based s one of the most popular non-parametr-based approah [5,6,7]. In ths report, we extend the K-nearest neghbour (KNN) densty estmaton ombned wth Gaussan kernel funton. In the proposed method, the KNN would ontrbute n determnng the best loal genes teratvely for Gaussan kernel densty estmaton. The loal best s defned as the set of neghbours genes that maxmzes the Gaussan kernel funton. Ths leads to an alternatve non-parametr lusterng approah that s alled teratve loal Gaussan lusterng (ILGC). Iteratve loal Gaussan lusterng Basally, Gaussan kernel funton for genes lusterng has bas form as n equaton (2) (see supplementary materal) There are two man rules to deal wth ths problem of seletng the best loal genes: KNN-rule and Bayesanrule. In ordnary KNN densty estmaton, the KNN-rule s appled to assgn a target gene to a ertan luster based on the majorty of number of gene neghbours rteron. On other hand, ILGC mplements a Bayesan deson rule suh that the target gene wll be assgned to the -th luster, f the majorty of k-neghbours of the target gene maxmzes the densty funton, K (x). To do ths, we perform the rule teratvely usng the nequalty llustrated n equaton (3) (see supplementary materal). Note that we do not use the sale parameter term expltly n the equaton as t wll be determned n k- nearest neghbour seleton proess. The teratve loal Gaussan lusterng algorthm an be summarzed follows: ILGC Algorthm (Database, k neghbours). Set the number lusters to the N nformatve gene seleted 2. Eah gene x (=..N) wth k neghbours s assgned to luster as n equaton (4) (see supplementary materal) 3. If there s no hanges n the luster struture, teratons have onverged. Re-ndex the lusters and stop. Otherwse go to step Re-alulate luster membershp n Equaton (3) (supplementary materal) then go to step 2. Data mputaton To mplement ILGC algorthm, there are number of mssng entres n the orgnal datasets whh we fll n. We apply the INI algorthm [6, 7] to mpute these mssng data entres. Ths method s based on a least squares prnple. Ths approah mnmzes the sum of squared dfferenes between the data entres and those reonstruted va blnear modellng whh s akn to the sngular value deomposton (SVD) of a data matrx. Detals of INI algorthm an be obtaned elsewhere [6, 7]. Gene seleton Another ssues addressed n our mplementaton of luster analyss s the nosy gene whh s not so nformatve. We use a Correlaton Rato (CR) method as llustrated n equaton (5) n the supplementary materal to selet the nformatve genes [3]. Dsusson: In ths work, we used the nformatve genes seleted by Muro et al [3] whh onssts of 34 genes out 536 genes and 00 anerous samples and normal samples wth ther lnal parameters. Usng ILGC wth 0 number of nearest neghbour and 95% of rate onvergene, three lusters were found, smlar to the Gaussan Mxture Clusterng results of Muro et al [3]. However, the ILGC unovers a dfferent struture of lusters ompared to those found by the Gaussan Mxture method. The struture of lusters an be vsualzed n 2-D graph based on plottng the frst and seond omponent of prnpal omponent analyss (PCA) as shown n Fgure. The results show that there are two large numbers of genes lusters and one small luster. Bonformaton 2(5): 75-8 (2007) Bomedal Informats Publshng Group

3 Bonformaton by Bomedal Informats Publshng Group Predton Model Fgure : The struture of lusters those to be found by ILGC algorthm. Green, blue and red represent luster I, luster II and luster III, respetvely. For the two large numbers of lusters, luster I and luster II, further analyss was arred out to detet any relatonshp to the aner lnal parameters: anerous or normal, dstant metastases and lymph node metastass. Correlaton Rato (CR) analyss was used, based on the followng proedure: (a) Calulate CR value for eah gene n luster I and II; (b) Sort genes wth key CR value from (a); () Permute sample poston for eah gene, then alulate CR of the permuted samples; and (d) Draw all CR values from (b) and (). Fgure 2 shows that luster I and II orrelate to the dfferenes between ell tssues that ontan tumour or normal. Fgures 3a and 3b show that the luster I and II have sgnfant orrelaton wth the exstene of dstant metastass n ell tssues. However, luster I and luster II have no orrelaton to the exstene of lymph-node metastass n ell tssues (Fgure 4a and 4b). Sne luster III ontans only a small number of genes (7), we use the dfferene orrelaton analyss tehnque. Sne ths luster ontans TCL (tumor lassfer) genes, ths luster appears to orrelate wth the exstene of tumor. Fgure 5 shows that when dstant metastass exsts, luster III orrelates to the thrd oloretal lnal parameter. Bonformaton 2(5): 75-8 (2007) Bomedal Informats Publshng Group

4 Bonformaton by Bomedal Informats Publshng Group Predton Model Fgures 2: Cluster I and II have orrelaton to the dfferenes between ell tssues that ontan tumor or normal. The vertal axs represents CR-value of the dfferenes of ell tssues whh ontans aner and normal n luster I (a) and luster II (b). The horzontal axs represents sorted genes based on ther CR-values. The top blue lne represents lusters found by ILGC, others represent permuted samples. Fgure 3: The vertal axs represents the CR-value of the dfferenes of ell tssues whh ontan dstane metastass: luster I (a) and luster II (b). The horzontal axs represents sorted genes based on ther CR-values. The top blue lne represents lusters found by ILGC; others represent permuted samples. Bonformaton 2(5): 75-8 (2007) Bomedal Informats Publshng Group

5 Bonformaton by Bomedal Informats Publshng Group Predton Model Fgure 4: The vertal axs represents CR-value of the dfferenes of ell tssues whh ontan lymph node metastass: luster I (a) and luster II (b). Horzontal axs represents sorted genes based on ther CR-values. No orrelaton to the exstene of lymph-node metastass n ell tssues s observed. Fgure 5: Lnkage of the lusters of expressed genes to the exstene of dstant metastass n luster III usng the dfferene orrelaton analyss tehnque. Conluson: Bonformaton 2(5): 75-8 (2007) Bomedal Informats Publshng Group

6 Bonformaton by Bomedal Informats Publshng Group Predton Model In ths paper, we explored a non-parametr densty based lusterng tehnque whh s alled teratve loal Gaussan lusterng (ILGC). The advantages of ILGC nludes: the smplty of the tehnque, no requrement for pror nformaton on the number of lusters and the use of a sngle parameter, the nearest neghbour. Aknowledgement: Ths work was supported by a researh grant from the Hgher Eduaton Dretorate General, Mnstry of Eduaton of Indonesa, The authors gratefully aknowledge many helpful omments by revewers that have been very helpful n mprovng the publaton. ILGC algorthm has been tested on the oloretal arnoma database of Muro et al, 2003 [3]. The results show that the proposed method produed the same number of lusters as those found by Muro et al. In addton, the lusters found by ILGC were able to be lnked to malgnany of human oloretal arnoma whh nlude the exstene of tumor and dstant metastass. Further work s needed to ompare ILGC expermentally wth other exstng lusterng tehnques suh as Herarhal lusterng, Gaussan Mxture lusterng and K-Means for dentfaton of other aners. Referenes: [0] P. O. Brown & D. Botsen, Nature Genets Supplement., 2: 33 (999) [02] M. B. Esen, et al., Pro. Natl. Aad. S., 95: 4863 (995) [03] S. Muro, et al., Genome Bology, 4 (2003) [04] D. A. Notterman, et al., Caner Res., 6: 324 (999) [05] N. Tranh, et al., Computatonal Statsts and Data Analyss, 5: 53 (2006) [06] I. Wasto & B. Mrkn, Informaton Senes, : (2005) [07] I. Wasto & B. Mrkn, Computatonal Statsts and Data Analyss, 50: 926 (2006) Edted by O. Motto, T. W. Tan & S. Ranganathan Ctaton: Wasto, et al., Bonformaton 2(5): 75-8 (2007) Lense statement: Ths s an open-aess artle, whh permts unrestrted use, dstrbuton, and reproduton n any medum, for non-ommeral purposes, provded the orgnal author and soure are redted. Bonformaton 2(5): 75-8 (2007) Bomedal Informats Publshng Group

7 Bonformaton by Bomedal Informats Publshng Group Predton Model Supplementary materal Equatons p( x) = V Where K p n = K ( x) (), V and K represent densty estmaton, volume of data and kernel funton, respetvely. n (2) / 2( x x ) ( ) 2 x = e n = where x, n and K are -th gene, number of genes n -th luster and densty funton of the -th luster. The man ssue of ths framework s the seleton of the best loal genes to maxmze K (x). (3) x e x x ) 2 > / 2( x x ) 2 / 2( x j e where x and are target genes and the -th luster, respetvely where j Clus = Max( p ( x )) (4) pˆ ( x ) x where s a lass-ondtonal densty funton at for eah luster. ( CR ) Where 2 n = C n (( = j J, j ) / n M s the number ( xof genes, j j= x ) (5) Correlaton Rato (CR) n a partular lass J; s the expresson level of gene n sample j; and s the average expresson level of gene. x x ) 2 2 x j x Bonformaton 2(5): 75-8 (2007) Bomedal Informats Publshng Group