A Class-Information-based SNMF Method for Selecting Characteristic Genes

Transcription

1 A Class-Informaon-based SNMF Mehod for Selecng Characersc Genes Jn-Xng Lu School of Informaon Scence and Engneerng Emal: Chun-Xa Ma School of Informaon Scence and Engneerng Emal: Yng-Lan Gao Lbrary of Qufu Normal Emal: Jan Lu School of Communcaon 6com Chun-Hou Zheng College of Elecrcal Engneerng and Auomaon, Anhu, Hefe, Chna E-mal: Absrac he sgnfcan advanage of sparse mehods s o reduce he complcacy of genes expresson daa, hch makes hem easer o undersand and nerpre In hs paper, e propose a novel Class-nformaon-based Sparse Non-negave Marx Facorzaon (CISNMF) mehod hch nroduces he class nformaon by he oal scaer marx Frsly, he oal scaer marx s obaned va combnng he beeen-class and hn-class scaer marces Secondly, a ne daa marx s consruced va sngular values and lef sngular vecors hch can be obaned va decomposng he oal scaer marx Fnally, e decompose he ne daa marx by usng sparse Non-negave Marx Facorzaon and exrac characersc genes In he end, resuls on gene expresson daa ses sho ha our mehod can exrac more characersc genes n response o aboc sresses han convenonal gene selecon mehods Keyords marx facorzaon; scaer marces; gene expresson daa; gene selecon; aboc sresses I INRODUCION Envronmenal aboc sresses have caused many unfavorable effecs on plan groh, such as hea, osmoc sress In order o reduce he negave mpac of hese envronmenal condons, plans have evolved a varey of sraeges and hey can able o cope h hese envronmenal condons, ncludng sal, cold, osmoc sress, uv-b lgh, drough and so on [] he fundamenal concep s ha hey have some neracng genes respondng o each aboc sress herefore, s one of he umos sgnfcan opcs ho o comprehend he aboc sresses responses n plan scence [] Many convenonal mehods, such as R-PCR [3] or Norhern blong [4, 5] have been used o sudy he genes respondng o aboc sresses Hoever, hese mehods have one defec ha only a small par of genes can be suded a he same me So, he mcroarray echnology has been pu forard o overcome hs shorcomng he echnology makes hs ork as suppored n par by he NSFC under gran Nos and ; he Chna Posdocoral Scence Foundaon funded proec, No04M56064; he Shandong Provncal Naural Scence Foundaon, under gran Nos ZR03FL06 and ZR0FM03; Shenzhen Muncpal Scence and echnology Innovaon Councl (NosJCYJ and JCYJ ) possble o monor gene expresson levels on a genomc scale [6] Wh he boomng of mcroarray echnology, a large number of mahemacal mehods have been used o analyze gene expresson daa [7-6], such as, prncpal componen analyss (PCA), ndependen componen analyss (ICA) and sngular value decomposon (SVD) In gene expresson daa analyss, PCA s an unsupervsed mehod o search he useful egenassay or egengene [7] ICA [0] s a useful exenson of PCA Huang e al nroduced a penalzed dscrmnan mehod based on ICA for umor classfcaon [] Aler e al pu forard o use SVD for modelng and processng he gene expresson daa [7] Alhough hese mehods have been dely used n gene expresson daa, hey have some drabacks For example, hey are no sparse, hch makes hard o nerpre he expresson daa herefore, he correspondng sparse algorhms are proposed by researchers o overcome hese drabacks For example, Journée e al proposed an SPCA mehod by usng generalzed poer mehod [8] Lu e al proposed he Weghng Prncpal Componens by Sngular Values o exrac characersc genes [5] In [4], Wen e al proposed a penalzed marx decomposon, hch as used o analyze plans gene expresson daa by Lu e al [9, 8] Hoever, hey have some common defecs: hey allo he negave componen exss and need o sandardze he orgnal daa o seek a beer soluon, Lee and Seung frsly nroduced Non-negave Marx Facorzaon (NMF) mehod o decompose mage marx n [9] NMF decomposes a nonnegave daa marx no o non-negave facors hereno one marx s called bass marx, he oher s defned as he coeffcen marx of he correspondng bass marx In addon, NMF usually nvolves some smple operaons, so has a loer compuaonal cos So far, many algorhms of NMF have been proposed [0, ] In addon, he correspondng sparse NMF algorhms have been proposed o gve a reasonable sparse represenaon, such as sparse NMF [], Fsher NMF [3] and Non-negave Marx Facorzaon h Sparse Consrans (SNMF) [4] NMF has been dely used n gene expresson daa analyss [5] he sparse NMF and Fsher NMF have a common sde-effec ha he sparsy canno be conrolled Hoever, SNMF, hch as frs Qngdao, Chna, Ocober 4 7, 04

2 nroduced by Park O Hoyer [4], can conrol he sparsy accuraely SNMF has been appled o mages processng [6], genes selecon [7, 8] and so on In order o mprove he analycal performance of gene expresson daa, e pu forard a Class-Informaon-based Sparse Non-negave Marx Facorzaon (CISNMF) mehod, hch nroduces he class nformaon by usng he oal scaer marx he scheme of CISNMF s gven as follos: Frsly, he oal scaer marx s obaned by combnng he hn-class and beeen-class scaer marces; Secondly, e decompose he oal scaer marx by usng sngular value decomposon (SVD) and consruc a ne daa marx by sngular values and lef sngular vecors; hrdly, e decompose he ne daa marx by a SNMF and exrac he genes accordng o he sparse loadng vecors hs paper s srucured as follos In secon II, e descrbe he mehodology of CISNMF Secon III provdes expermenal resuls and dscusson Secon IV concludes he paper II MEHODS A he Mahemacal Defnon of Scaer Marces On he bass of a smlary measure, he pendng classfcaon paern se { x, x,, xn} s dvded no c caegores he classfed paern denoed as ( ) { x ; =,,, c; =,,, n} hree marces are defned as: he hn-class scaer marx J, he beeen-class marx J b and he oal scaer marx J For all he samples of all classes, he hree scaer marces can be ren as follos: ) he frs s called hn-class scaer marx J hch s descrbed as: here sample n class, of classes c n = -z -z = = J ( x )( x ), () x s he -h sample n class ; n s he number of z s he mean of class, c s he number ) he nex s called beeen-class scaer marx J b hch s gven by c ( )( ) J = n z -z z -z, () b = here z s he mean of all classes 3) he goal of cluserng makes he hn class dsance as small as possble, he dsance beeen classes as bgger as possble So, he oal scaer marx J can be denoed by J = Jb ξ J, (3) here ξ 0 s an adusable parameer ha sems from a rade-off beeen J b and J he am of cluserng s: r[ b ] max [ ] mn J or/and r J and he races of scaer marces could measure he beeen-class and hn-class dsances hey are ren as follos: n r r z z = = = λ + λ + + λ c ( J) = ( x )( x ) k r r n z z z z = λ + λ + + λ c ( Jb) = ( )( ) = b b bk Here, r( J ) s used o measure he close degree of he samples hn he classes Whle r( Jb ) s used o measure he degree of separaon beeen he classes Hence, he adusable parameer ξ n (3) can be ren as follos [9]: r( Jb ) ξ = r( J ) B Mahemacal Defnon of CISNMF In order o exrac he characersc genes effecvely, e nroduce a supervsed learnng mehod he ne daa marx s obaned by he oal scaer marx J hen he ne daa marx s decomposed no o non-negave enres by SNMF Frsly, he scaer marx J s decomposed by usng SVD I can be ren as follos: (4) (5) (6) J UΛV, (7) = here Λ = dag( Λ, Λ,, Λr ) s a dagonal marx ha consss of sngular values and r s he rank of J U and V are orhogonal feaure vecors Secondly, for reducng he compuaonal complexy, e consruc a ne marx, and he ne daa marx s consruced as follos: / Q = UΛ (8) Qngdao, Chna, Ocober 4 7, 04

3 Fnally, L s he ranspose of Q, and L s decomposed by usng Sparse Non-negave Marx Facorzaon (SNMF) L ~ FP, (9) here L s an m n non-negave marx, F s an m k non-negave marx, P s a k n non-negave marx and k < mn m,n ( ) he opmzaon problem can be descrbed as he follong: mnmze L - FP = mnmze ( L - ( FP) ), F, P > 0, (0) F,P s oponal consrans: F,P sparseness( F ) = ϕ, () sparseness( P ) = γ, () here F s he -h column of F, P s he -h ro of P C he Algorhm he deals of he CISNMF algorhm are lsed as follos: ) he oal scaer marx J s obaned va (3) ) he U, Λ and V are obaned va decomposng J by SVD n (7) 3) Consruc a ne daa marx Q accordng o (8) 4) ranspose Q as L, and L s decomposed no F and P by SNMF 5) Inalze F and P o random posve marces 6) Ierae unl convergence or reach he larges number of eraon a) Sparse consrans on P, In hs algorhm, ξ 0 s an adusable parameer ha sems from a rade-off beeen J b and F (ϕ ) and P ( γ ) are n he range beeen (0, ) J he sparseness of δ f and δ p are small posve consans (sepszes) and he o parameers need no be se by he user D Exracng Characersc Genes by CISNMF In he research, our goal s o gan he characersc genes respondng o he aboc sresses Here, e ranspose he gene expresson daa marx Q and defned as L Hence, L = Q and he sze of L s m n, ros represens he expresson level of he n genes n m samples, each column of L represens he expresson level of a gene across all samples So, he L can be ren as: L ~ FP, here F s an m k non-negave marx, P s a k n non-negave marx and k < mn(m,n) he opmzaon problem s convex n F and P separaely and mnmze he reconsrucon error beeen L and FP Varous error funcons have been esfed n [30], and he squared error (Eucldean dsance) funcon s gven as follos: L - FP = ( L - ( FP) ), F, P > 0 (3) he sample expresson profle l k = by (9) can be denoed as: l = f p, =,,,m (4) Here l s a lnear combnaon of he measamples p } and l s he ro of L, f s he enry of F Here, e can ve he ros of F as he encodng coeffcens and he k ros of P as bass vecors (measamples) he daa marx L, coeffcens marx F and bass marx P are shon n Fg { P : = P F ( FP L) δ p ( ) ( ) F : = F LP / FPP b) Sparse consrans on F, ( ) F : = F FP L P δ f ( ) ( ) P: = P FL/ FFP Fg he graph descrpon of he marx L h he facors F and P In Fg, l s he samples characerscs of he marx L, r represens he feaure vecors of L, a shos he expresson level of he -h gene n he -h sample ˆ l s he -h egensamples of F, r ˆ s he column vecor of F and 3 Qngdao, Chna, Ocober 4 7, 04

4 ndcaes he -h vecor n k genes of F l and r refer o he -h sample vecor and -h feaure of P hch consss of n genes n k samples In order o reduce he dmenson of L, e choose par of he sample characerscs o replace L Due o he marx P conans all genes and s one subse of measamples of L, he marx P s called he bass vecors Hence, e can exrac characersc genes from he bass marx P So, l can be replaced by p By conrollng he parameers of SNMF, he sparse marx P can be ganed So, he characersc genes can be exraced from he non-zero enres n he marx P In he end, e summarze n geng characersc genes va he CISNMF mehod as he follong: Gan he oal scaer marx J Decompose he scaer marx J by SVD Gan a ne marx Q va execung he SVD, and ranspose Q no L Oban he marx P accordng o SNMF Exrac he characersc genes va he non-zero enres n P Explo he GO o check he exraced characersc genes III RESUL AND DISCUSSION In hs secon, e ll sho he resuls of explong CISNMF mehod In hs secon, he resuls on gene expresson daa ses are gven Our mehod ll compared h SNMF [4], SPCA [8] and PMD [9] mehods n hs secon A Daa Source he gene expresson daa are donload from he NASCArrays [hp://affyarabdopssnfo/], reference numbers are: NASCArrays-4, drough sress; NASCArrays-40, sal sress; NASCArrays-44, uv-b lgh sress; NASCArrays-38, cold sress; NASCArrays-46, hea sress; NASCArrays-39, osmoc sress; NASCArrays-37, conrol [3] Here, each sample conans 80 genes and he sample numbers of each sress are lsed n able I ABLE I HE NUMBER OF EACH SRESS YPE IN HE DAA SE sress ype drough sal uv-b cold hea osmoc conrol number he background lgh nose of hese daa can be adused by usng he GC-RMA mehod hch as proposed by Wu e al [3] he GC-RMA resuls are colleced n a marx o be furher processng In hs paper, he o labels are seleced by o daa ses (excep he conrol ses) o consruc he marx J For drough se n roo, e assgn he drough samples o he frs class and he oher samples as he second class We use SNMF o process hese daa, and he exraced genes are verfed by GO ools B Selecon of he Parameers In [7, 8] he bes resuls are obaned hen he sparseness conrollng parameer ϕ s se o 05 So n our expermen, parameer ϕ s se o 05 and he adused parameer γ s conrolled n range (0-) [4] For comparson, 500 genes are seleced by CISNMF, SNMF, PMD and SPCA mehods C Gene Onology (GO) Analyss erms are he basc concep of Gene Onology (GO) Each enry n GO has a unque dgal label he Gene Onology erm enrchmen ool, ncludng meanngful shared GO erms, can search hose genes ha may have n common [33] he analyss of GO erm Fnder s modular, hch offers valuable nformaon of hgh-hroughpu expermens n bologcal scence feld In hs research, our mehod ll be evaluaed by GO ermfnder, hch s freely used a <hp://goprnceonedu/cg-bn/goermfnder> [34] he hreshold parameers are se as lsed belo: mnmum number of gene producs s se o and maxmum p-value s se o 00 ABLE II RESPONSE O SIMULUS (GO: ) IN ROO SAMPLES sress CISNMF SNMF PMD SPCA ype PV SF PV SF PV SF PV SF drough 36E- 33 *, 39E- 38, 367E- 87, 39E- 89, 84 67% % % % sal 39E- 307, 554E- 36, 9E- 33, 4E- 37, 79 64% 95 65% 84 66% % uv-b 59E- 88, 38E- 86, 878E- 43, 956E- 0, % 64 57% % 40% cold 98E- 3, 379E- 309, 506E- 9, 54E- 8, 84 65% 8 68% 68 58% 6 564% hea 306E- 48, 37E- 09, 8E- 05, 3E- 00, % 48% 9 40% 7 400% osmoc 459E- 39, 65E- 60, E-6, 49E- 37, % 47 5% 44% % In hs able, he background frequency of response o smulus (GO: ) n AIR se s 8% (669/3034) And n he sample frequency, 33* denoes havng 33 genes o response o smulus n he 500 selecon genes PV: p-value, and SF: sample frequency In roo sample, he response o smulus (GO: ) s lsed n able II In AIR se, he correspondng background frequency s 8% (669/3034) In hs expermen, 500 genes are seleced by CISNMF, SNMF, PMD and SPCA mehods able II lss he p-value and sample frequency of varous sresses In our mehod, 33 genes for drough sress are exraced and he sample frequency s 67%, 307 genes for sal sress are exraced (64%), 88 genes for uv-b sress are exraced (576%), 3 genes for cold sress are exraced (65%), 48 genes for hea sress are exraced (496%), and 39 genes for osmoc sress are exraced (638%) Whle n SNMF mehod, 38 genes for drough sress are exraced (636%), 36 genes for sal sress are exraced (65%), 86 genes for uv-b sress are exraced (57%), 309 genes for cold sress are exraced (68%), 09 genes for hea sress are exraced (48%) and 60 genes for osmoc sress are exraced (5%) In able II, only o of hese sresses 4 Qngdao, Chna, Ocober 4 7, 04

5 (drough sress and sal sress) ha SNMF mehod s superor o our mehod In oher sresses, our mehod ouperforms SNMF Obvously, he bold fons n able II sho ha our mehod s far superor o PMD mehod and SPCA mehod From Fg, e can see ha our mehod surpasses oher mehods In shoo samples, he sample frequences of response o smulus (GO: ) are shon n Fg 3 I can be seen ha only n drough sress and uv-b sress daa pons, SNMF mehod s superor o our mehod In he four remanng daa pons, our mehod s beer han SNMF mehod he specfc resuls are lsed n able III In addon, n he sx daa ses, our mehod has prory over PMD mehod and SPCA mehod Fg he response o smulus (GO: ) n roo samples Fg 4 he response o sress (GO: ) n roo samples Fg 3 he response o smulus (GO: ) n shoo samples ABLE III RESPONSE O SIMULUS (GO: ) IN SHOO SAMPLES sress CISNMF SNMF PMD SPCA ype PV SF PV SF PV SF PV SF droug h 346E , 66% 58E , 684% 809E , 606% 545E , 540% sal 8E- 85, 0E- 68, 43E- 56, 959E- 6, % 5 537% 45 5% 49 54% uv-b 0E- 33, 79E- 375, 64E- 36, 3E- 33, 9 647% 4 750% 8 7% 0 664% cold 3, 04E- 30, 8E- 94, 354E- 79, 6E-8 6% 8 60% % % hea 34E- 30, 48E- 04, 369E- 0, 804E- 65, % 9 408% 6 440% 5 530% osmo 47E- 335, 97E- 33, 367E- 94, c 03 67% 9 646% % 3E-49 63, 56% Fg 5 he response o sress (GO: ) n shoo samples Fg 4 and 5 depc he correspondng sample frequency of response o sress (GO: ) n roo and shoo samples, respecvely As shon n Fg 4, he sal sress pon of SNMF mehod s hgher han ours In oher daa pons, our mehod ouperforms oher mehods Fg 5 shos ha only n drough sress and uv-b sress daa pons, SNMF mehod ges ahead of our mehod In he resduary daa pons, our mehod has an advanage over oher mehods he numbers e selec and p-value of response o sress (GO: ) n roo and shoo samples, respecvely, are lsed n able IV and able V In AIR se, he background frequency of response o sress s 33% (408/3034) In able IV, our mehod s superor o oher four mehods excep he sal sress daa se SNMF mehod excels our mehod n he drough sress and uv-b sress daa ses, and he dealed 5 Qngdao, Chna, Ocober 4 7, 04

6 conens are lsed n able V In oher daa ses, our mehod ouperforms oher mehods ABLE IV RESPONSE O SRESS (GO: ) IN ROO SAMPLES sress CISNMF SNMF PMD SPCA ype PV SF PV SF PV SF PV SF drough 8E-94 60, 5% 5E-9 58,, 3, 989E-64 49E-70 56% 444% 46% sal 57E-8 45, 60, 46, 77, 457E-94 48E-8 365E % 50% 49% 354% uv-b 57E-5 06, 03, 59E-50 4% 406% cold 479E-79 4, 7E-79 hea 43E-44 65, 53, 36E-7 38E- 330% 306% 4, 33, 3, 403E-7 7E % 466% 448% 485% 94, 68, 70, 53, 59E-9 98E-30 47E- 388% 336% 340% 306% osmoc 99E-8 45, 0, 59, 69, 78E-49 55E-4 07E-9 490% 403% 38% 338% ABLE V RESPONSE O SRESS (GO: ) IN SHOO SAMPLES sress CISNMF SNMF PMD SPCA ype PV SF PV SF PV SF PV SF droug 403E- 59, 503E- 86, 43E- 47, 75E- 96, h 93 58% 8 57% % 46 39% sal 973E- 7, 66E- 05, 77E- 75, 366E- 68, % 5 4% % 9 336% uv-b 84E- 67, 89E- 37, 965E- 95, 56E- 49, % % 8 590% % cold 7E-77 39, 396E- 3, 0E- 3, 348E- 8, 480% % 57 46% 6 436% hea E- 4,45 805E- 6, 97E- 74, 34E- 86, 65 % 6 34% 3 348% 39 37% osmo E- 77, 494E- 60, 6, 5E- 9, E-66 c % 94 50% 45% 4 38% ABLE VI SAMPLES RESPONSE O WAER DEPRIVAION (GO: ) IN ROO sress CISNMF SNMF PMD SPCA ype PV SF PV SF PV SF PV SF drough 6E- 64, 487E- 60, 54E- 5, 54E- 44, 39 8% 35 0% 6 0% 9 88% o sum up, our mehod ges ahead of ohers In order o furher sudy, he drough sress daa se respondng o aer deprvaon (GO: ) n roo samples s analyzed n able VI he background frequency of response o aer deprvaon s 4% hs able lss he numbers of response o aer deprvaon and p-value by he four mehods, Moreover, he negleced characersc genes by oher mehods are lsed n able VII he leraures of hose characersc genes and he auhors of hese leraures are noed n he able All hese genes are relevan o drough sress, and some are relevan o cold or sal and / or osmoc sress From able VI, e can see ha CISNMF mehod exracs more characersc genes han oher mehods ABLE VII REFERENCES ABOU CHARACERISIC GENES RESPONSE O WAER DEPRIVAION (GO: ) IN ROO SAMPLES Gene name Response o References Ag33380 Drough, cold Heyndrckx KS, e al (0) [35] A3g4540 Drough Bell, e al (993) [36] A4g34390 Drough Heyndrckx KS, e al (0) [35] Ag46680 Drough, cold Heyndrckx KS, e al (0) [35] A5g750 Drough Heyndrckx KS, e al (0) [35] Ag4530 Drough Heyndrckx KS, e al (0) [35] A5g6470 Drough Seo, e al (009) [37] A4g6070 Drough Xng, e al (008) [38] A3g9970 Drough Heyndrckx KS, e al (0) [35] A5g54490 Drough Heyndrckx KS, e al (0) [35] A5g740 Drough Heyndrckx KS, e al (0) [35] A3g63060 Drough, sal, osmoc Koops, e al (0) [39] A4g36990 Drough Heyndrckx KS, e al (0) [35] A4g440 Drough Heyndrckx KS, e al (0) [35] Ag73480 Drough, cold Heyndrckx KS, e al (0) [35] A5g67340 Drough, cold Heyndrckx KS, e al (0) [35] A4g7500 Drough Heyndrckx KS, e al (0) [35] Ag4430 Drough Kyosue, e al (994) [40] A3g5400 Drough, cold Heyndrckx KS, e al (0) [35] A4g0500 Drough Heyndrckx KS, e al (0) [35] Ag4670 Drough, sal Heyndrckx KS, e al (0) [35] A4g6080 Drough, cold Heyndrckx KS, e al (0) [35] A5g57050 Drough, cold Heyndrckx KS, e al (0) [35] A3g57530 Drough, cold Heyndrckx KS, e al (0) [35] A4g3470 Drough Heyndrckx KS, e al (0) [35] In a ord, hese expermens and analyses sho our mehod can exrac more genes han oher mehods herefore, our mehod has more advanages of exracng characersc genes han oher mehods IV CONCLUSIONS A ne mehod (CISNMF) s proposed o exrac genes n hs paper CISNMF mehod nroduces he classfcaon nformaon by scaer marx, so can ge more comprehensble and nerpreable resuls he exraced characersc genes are analyzed by GO ools For gene expresson daa, CISNMF can exrac more characersc genes han oher mehods he expermens demonsrae ha our mehod s effecve and suable for selecng characersc genes In fuure, e ll focus on he bologcal nerpreaon of he characersc genes REFERENCES [] G J Allen, S P Chu, K Schumacher, C Shmazak, D Vafeados, A Kemper, e al, "Aleraon of smulus-specfc guard cell calcum oscllaons and somaal closng n Arabdopss de3 muan," Scence, vol 89, pp , 000 [] Hrayama and K Shnozak, "Research on plan aboc sress responses n he pos genome 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