Subgroup detection in genotype data using invariant coordinate selection

Fische e al. BMC Bioin o ma ics (2017) 18:173 DOI 10.1186/s12859-017-1589-9 METHODOLOGY ARTICLE Open Access Subg oup de ec ion in geno ype da a using in a ian coo dina e selec ion Daniel Fische 1* , Me i Honka ukia1, Ma ia Tuiskula-Haa is o1, Klaus No dhausen2,4, Da id Ca e o3, Rudol P eisinge 3and Johanna Vilkki1 Abs ac Backg ound: The cu en gold s anda d in dimension educ ion me hods o high- h oughpu geno ype da a is he P inciple Componen Analysis (PCA). The p esence o PCA is so dominan , ha o he me hods usually canno be ound in he analys ’s oolbox and hence a e only a ely applied. Resul s: We p esen a mode n dimension educ ion me hod called ’In a ian Coo dina e Selec ion’ (ICS) and i s applica ion o high- h oughpu geno ype da a. The mo e commonly known Independen Componen Analysis (ICA) is in his amewo k jus a special case o ICS. We use ICS on bo h, a simula ed and a eal da ase o demons a e i s some de iciencies o PCA and how ICS is capable o eco e he co ec subg oups wi hin he simula ed da a. Second, we apply he ICS me hod on a chicken da ase and also de ec he e wo subg oups. These subg oups a e hen u he in es iga ed wi h espec o hei geno ype o p o ide u he e idence o he biological ele ance o he de ec ed subg oup di ision. Fu he , we compa e he pe o mance o ICS also o i e o he popula dimension educ ion me hods. Conclusion: The ICS me hod was able o de ec subg oups in da a whe e he PCA ails o de ec any hing. Hence, we p omo e he applica ion o ICS o high- h oughpu geno ype da a in addi ion o he es ablished PCA. Especially in s a is ical p og amming en i onmen s like e.g. R, i s applica ion does no add any compu a ional bu den o he analysis pipeline. Keywo ds: ICS, PCA, Geno ype da a, Classi ica ion, Dimension educ ion Backg ound The as p og ess in analyzing a ia ions in he genome by deep sequencing has led o a ple ho a o high densi y geno yping a ays in many li es ock species. The eby also, he amoun o single nucleo ide polymo phism (SNP) da a ha is a ailable o analyzing he gene ic ela ionships be ween di e en samples is cons an ly g owing. One common app oach o handle his ype o da a and o iden- i y e.g. subpopula ions, is he applica ion o dimension educ ion me hods such as P inciple Componen Analy- sis (PCA). Cu en ly PCA is es ablished o be he s anda d app oach in clus e ing geno ype da a, see e.g. [1]. How- e e , as we will demons a e wi h an simula ion example, he e a e d awbacks and pi alls in he PCA app oach. In a PCA, he p inciple componen s a e o de ed acco ding o *Co espondence: [email p o ec ed] 1Na u al Resou ces Ins i u e Finland (LUKE), Mylly ie 1, Jokioinen, Finland Full lis o au ho in o ma ion is a ailable a he end o he a icle he a iance hey explain, bu he e is no heo e ical jus- i ica ion ha he componen wi h he la ges explained a iance also con ains he in o ma ion equi ed, e.g. o sepa a e subg oups wi hin he da a. A i id coun e ex- ample is a la ge hambu ge . I i is la ge enough, he componen wi h he la ges a ia ion goes h ough he diame e o he bu ge , bu o sepa a e he subg oups, one would need a di ec ion om bo om o op. Tha means, e en in his simple h ee-dimensional case he in e es - ing componen would be only he second one. Hence, he in e es ing componen s migh explain only a small ac- ion o he a iance and consequen ly a e easily missed bycheckingonly he ew i s o las componen s.Fo an o e iew and a mo e heo e ical backg ound on he applica ion o PCA in geno ype da a, see [2] o [3]. O he dimension educ ion me hods, such as In a i- an Coo dina e Selec ion (ICS), a e no commonly applied o genomic da a. ICS is a mode n mul i a ia e me hod © The Au ho (s). 2017 Open Access This a icle is dis ibu ed unde he e ms o he C ea i e Commons A ibu ion 4.0 In e na ional License (h p://c ea i ecommons.o g/licenses/by/4.0/), which pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided you gi e app op ia e c edi o he o iginal au ho (s) and he sou ce, p o ide a link o he C ea i e Commons license, and indica e i changes we e made. The C ea i e Commons Public Domain Dedica ion wai e (h p://c ea i ecommons.o g/publicdomain/ze o/1.0/) applies o he da a made a ailable in his a icle, unless o he wise s a ed. Fische e al. BMC Bioin o ma ics (2017) 18:173 Page 2 o 9 o iginally in oduced as gene alized PCA in [4], bu hen es ablished as ICS in he seminal pape [5] o a oid a name misma ch wi h a di e en gene alized PCA app oach, see e.g. [6]. The basic idea o ICS is o use wo di e en sca e ma ices and o compa e how hey di e . Di e en choices o sca e ma ices lead hen o di e en applica ions o ICS. Cu en ly, ICS has been e.g. applied o nea - eal ime e ie al o low s a i o m cloud co e age [7]. Fu he , ICS was used o enhance he disc imina ion be ween snow and ice clouds and de ec ion o b oken, hin clouds [8] and also o s udies o de elopmen al canaliza ion and he iden i ica ion o di e gen and s abilizing selec ion [9]. To discuss possible p oblems wi h PCA, we will i s p esen a basic coun e example o show ha PCA does no necessa ily iden i y clus e s uc u es in a da ase and a e ha apply PCA and ICS on a eal example geno ype da ase . Fu he , o bo h da ase s we will com- pa e he wo me hods also wi h o he me hods used by he Bioin o ma ics communi y. Fo ha we apply also - dis ibu ed S ochas ic Neighbo Embedding ( -SNE) [10], Isomap [11], Locally Linea Embedding (LLE) [12], ke - nel PCA (kPCA) [13] and Di usion Maps (DM) [14] o he simula ed and he eal da a. Fo comple eness, we also check he pe o mance o a Linea Disc iminan Analysis (LDA) o he simula ion example. Me hods Simula ed da a Fi s we simula ed a da ase as an example ha PCA is no always capable o de ec ing clus e s in high-dimensional da a. Conside h ee 10- a ia e no mal popula ions wi h N10(μi,),whe e μ1=(−μ∗,μ∗,0,0,0,0,0,0,0,0 ), μ2=(μ∗,0,0,0,0,0,0,0,0,0 )and μ3=(0, −μ∗,0,0,0,0,0,0,0,0 )and =diag 1 5,1 5,1,1,1,2,2,2,2,2 wi h μ∗=2. F om each popula ion we simula ed hen 100 samples. In o de o hide he clea ly isible subpopula ions, we u he o a ed he simula ed obse a ions wi h a andom o hog- onal ma ix. No e ha he o a ion has no impac on he pe o mance o PCA as he me hod is o a ion in a ian . Addi ional ile 1: Figu e S1 shows he simula ed da a be o e he o a ion and Addi ional ile 1: Figu e S2 he da a a e i . In he la e one, he g oups a e clea ly no isible anymo e. Chicken da a The high-densi y geno ype da a consis s o 749 chicken om 4 gene a ions. The las gene a ion is he la ges g oup wi h 603 samples. The o he gene a ions con ain 50, 46 and 50 samples. The da a consis s o sequence based a ia ion da a om 7 genomic egions, co e - ing app ox. 35% o he genome. The egions ha e been p eselec ed based on p e ious s udies as con aining loci a ec ing egg-quali y ai s, see [15] and [16]. As e e ence genome we used galgal4. In o al he e we e 157,528 geno ypes measu ed in hose egions. See Addi ional ile 1: Figu e S3 o he loca ions o he used egions on he chicken e e ence genome. In addi ion o he geno ype da a, also a se o 15 di e en b eeding alues was a ailable o all chicken. These we e, besides o he s, egg p oduc ion in pe iod 3 o 7, egg p o- duc ion in pe iod 9 o 12 and eed in ake. We use his da a as eal da a example and will ollow up on he biological indings only o one de ec ed subg oup in o de o keep he ocus on he me hod. In a ian coo dina e selec ion ToexplainICSweneed i s oin oduce heconcep o sca e ma ix. Fo a p- a ia e andom ec o xany p×p ma ix- alued es ima o S(x)is called a sca e ma ix i i a ine equi a ian in he sense ha S(Ax +b)=AS(x)A, o any ull- ank p×pma ix Aand any p- a ia e ec- o b. Clea ly he egula co a iance ma ix COV is a sca e ma ix. Bu especially in he obus s a is ics li - e a u e many o he sca e ma ices we e in oduced. Fo mo e de ails abou how sca e ma ices gene alize he co a iance ma ix and many ela ed e e ences see [17]. A sca e ma ix we will use la e is he so-called sca e ma ix o ou h momen s COV4(x)=1 p+2E 2(x−E(x))(x−E(x)), whe e =||COV(x)−1/2(x−E(x))|| and || · || deno es he F obenius no m. The main idea o ICS is o compa e wo di e en sca - e ma ices S1(x)and S2(x)by sol ing he ollowing eigen ec o -eigen alue p oblem S−1 1(x)S2(x)B(x)=B(x)D(x), whe e D(x)is hen he diagonal ma ix con aining he peigen alues o S−1 1(x)S2(x)in dec easing o de . The ows o B(x)con ain hen he co esponding eigen ec o s. Fo con enience o no a ion we will deno e om now on S1(x)=S1,S2(x)=S2,B(x)=Band D(x)=D. The ICS equa ion abo e can be seen as he p oblem o join ly diagonalizing he wo sca e ma ices, i.e. ind B and Dsuch ha BS1B=Ipand BS2B=D. An in e p e a ion can hen be gi en as ollows. Fi s S1 is used o whi en he da a, i.e. unco ela e he a iables Fische e al. BMC Bioin o ma ics (2017) 18:173 Page 3 o 9 and s anda dize he scales. Then pe o m on he whi ened da a PCA using S2. The e o e he idea is o see i S2 inds s ill some in e es ing s uc u e a e emo ing second o de in o ma ion as measu ed by S1. The ans o ma ion B(x)xyields hen an in a ian coo - dina e sys em in he sense ha B(x)x=B(Ax)(Ax), whe e equali y holds up o ma ginal signs o any ull ank p×pma ix A.Thenew ec o z=B(x)xis hen usually e e ed o as he in a ian coo dina es. The uni a ia e concep o ku osis can be seen as he a io o wo (s anda dized) scale measu es and simila ly S−1 1S2can hence be seen as a mul i a ia e ex ension o his concep . The e o e he eigen alues con ained in Dcan be in e p e ed as gene alized ku osis alues as measu ed by S1and S2.In hespecialcaseo S1=COV and S2= COV4i can be shown ha he diagonal elemen s in Da e a linea unc ion o he classical measu es o ku osis o he componen s in z[18]. And o example when sea ching clus e s i is well- known ha la ge clus e s can be ound o en in di ec ions wi h small ku osis and ou lie s and small clus e s in di ec ions wi h la ge ku osis. This means ha in a ian coo dina es a e e y sui able o sea ching o g oups as he componen s a e o de ed acco ding o hei (gene al- ized) ku osis. As ac ually [5] show, in he con ex o mix- u es o ellip ical dis ibu ions wi h p opo ional sca e ma ices, ICS inds Fishe ’s linea disc iminan subspace wi hou knowing he g oup membe ships. Hence, when using ICS o explo a o y da a analysis usually mos a en- ion is paid o he componen s wi h ex eme gene alized ku osis alues, like o example he i s 3–5 and las 3–5 componen s. Fo mo e de ails abou ICS see [4, 5, 18, 19]. As p ac ical conside a ions we would howe e like o poin ou ha he e is no gene al bes combina ion o sca - e ma ices and he pe o mance migh depend on he choice o S1and S2.ThechoiceS1=COV and S2= COV4is howe e well-es ablished and o example also a solu ion o he independen componen p oblem (ICA) i x ollows i (see eg [20] o u he de ails). ICA has been applied in he con ex o gene ic da a e.g. in [21]. Fu he mo e, ICS is howe e cu en ly limi ed o he case when p<n−1 as o he wise sca e ma ices a e always p opo ional o each o he , see [22] o de ails. The e o e i p≥n−1, hen one can o example i s pe o m dimension educ ion using PCA, esul ing in a n×nma ix whe e he n- h eigen alue is ze o. Then ICS is only applied o a subspace which is known o ha e a i- a ion and is o smalle dimension han n−1. This is o example s anda d p ac ice in many mul i a ia e me hods which a e limi ed o he p≥n−1 case, like o example he high-dimensional noisy ICA app oaches [23]. Dis ance measu e, dis ance g oups and s a is ical es ing Fo he simula ed da a he classi ica ion decision based on he sca e plo ma ices om PCA and ICS was done by applying a k-means algo i hm o he desi ed componen s. The classi ica ion esul s o he di e en dimension educ- ion me hods we e hen e alua ed using he adjus ed Rand index [24]. In he eal da a example, he classi ica ion decision was done by isual inspec ion o he igu es. In o de o calcula e he gene ic dis ance o wo di - e en g oups in a egion o in e es , we ollowed a basic app oach. Assuming wo subpopula ions Aand Bha e been iden i ied in he da a, we de e mined i s a each loci l=1, 2, ... he mos common geno ypes o bo h g oups and deno e hese ˜ GA,l espec i e ˜ GB,l.Then,wecompa ed i hese geno ypes ma ch be ween he wo g oups, by se - ing Gl=1, i ˜ GA,l=˜ GB,land 0 else. A e wa ds we calcula ed a mo ing a e age o leng h 1000 ac oss he da a and calcula ed in each window he a e age le el o ag ee- men . Le W=w1,w2,... be he se o all windows o leng h 1000 wi h w1=l1,...,l1000,w2=l2,...,l1001, he a e age le el o ag eemen in window iis hen ¯ xwi= ∀l∈wiGl/1000. Fo he sake o simplici y, we calcula ed he mo ing a e age also ac oss ch omosomal bo de s. Fo all windows wiwi h le el o ag eemen be ween wo subpopula ions ¯ xwi≤0.4, he indi idual dis ance o each indi iduum in he one g oup was calcula ed o he a e age o he o he g oup. Fo ha , we use again he mos com- mon geno ype o each loci in he subpopula ion coded as 0,1,2 and hen we calcula ed he Manha an dis ance o each indi iduum om he s anda d popula ion o ha . Tes ing o di e ences in he b eeding alues be ween he wo subpopula ions has been done by applying a wo- sided Mann-Whi ney es . Signi ican b eeding alues (p- alue ≤0.05) a e u he in es iga ed wi h a di ec- ional es , as p oposed by [25] and implemen ed in he R-package gMWT [26]. The indi idual dis ance measu e o he chicken om he main popula ion o he subpop- ula ion showed h ee ypes o chicken, hose which a e gene ically close (c), hose ha a e medium (m)and hose ha a e a ( ) away om he subpopula ion. Le Fp,c,Fp,m and Fp, be he dis ibu ions o he h ee g oups o a gi en pheno ype p, we ha e hen he ollowing wo es ing p oblems in mind H0:Fp,c=Fp,m=Fp, s H1:Fp,cs Fp,ms Fp, o H0:Fp,c=Fp,m=Fp, s H2:Fp, s Fp,ms Fp,c wi h s being he s ochas ical o de ing o he wo dis- ibu ions. Two dis ibu ions F1and F2a e s ochas ically o de ed, i F1(x)≥F2(x)∀x∈Rand we w i e F1s F2. These di ec ional hypo heses ha e been used o es o a di ec ional ela ionship be ween he simila i y g oup and he di e en pheno ypes. Fische e al. BMC Bioin o ma ics (2017) 18:173 Page 4 o 9 Resul s To e alua e he pe o mance o he di e en dimension educ ion me hods o un a el he o iginal clus e s uc- u e, we i s clus e ed he plain simula ed da a using k-means wi h he cons ain o h ee classes (k=3). Fo he classi ica ion esul , we hen calcula ed he adjus ed Rand Index o he 3 ×3 able be ween he o iginal class labels and he esul o he k-means clus e ing. Nex , we pe o med a PCA, ollowed again by a k-means clus e ing using he i s wo componen s o classi ica ion. Also o his classi ica ion esul able we calcula ed he adjus ed Rand index. Then we applied ICS on o he da ase and calcula ed in he same way again he Rand index o he k-means applied o he las wo componen s. To compa e he esul s o o he popula dimension educ ion me h- ods, we applied also -SNE, Isomap, LLE, kPCA and DM o he simula ion da a and calcula ed he co esponding Rand indices. Fu he , we sea ched wi h each dimension educ ion me hod he same dimensionali y, ha was d= 2 o he simula ed and d=7 o he eal chicken da a. The Rand index o he clus e ing using he o iginal da a is 0.20, he index o PCA is 0.48 and o ICS i is 0.94. In o he wo ds, he k-means clus e ing applied o he aw da adoesno de ec anyo heo iginalg oupsand he PCA only de ec s wo g oups, bu mixes he second and hi d one. The ICS me hod, howe e , eco e s he o iginal clus e s uc u e o a la ge ex en , indica ed by an adjus ed Rand index o nea ly one. See also Fig. 1 ha isualizes he clus e labels in he p ojec ed da ase s o he k-means classi ica ions applied o he di e en me hods. The esul s o he o he dimension educ ion me hods we e a he weak. Whe eas he -SNE me hod was almos as good as he ICS (Rand-index 0.93), he ou o he s clea ly we e ou pe o med by hese wo mo hods. Isomap had a Rand index o 0.71, LLE had a alue o 0.48, DM had also only 0.50 and he kPCA me hod had wi h 0.42 e en a alue smalle han he PCA had. Tha means, none o hese me hods was able o ully eco e he o iginal da a. The co esponding Figu es S4–S11 can be ound in he Addi ional ile 1. To calcula e he -SNE we used he R-Package sne [27], Isomap is implemen ed in he R-Package RDRToolbox [28] and LLE in lle [29]. Fo kPCA we used he ke nmap package [30] and o DM he des iny package [31]. The lda unc ion applied o he simula ion da a esul ed in an e o - ee sepa a ion o he da a and had consequen ly a Rand index o 1. Howe e , he ICS me hod is wi h 0.94 no oo a away om ha op imum. In abso- lu e numbe s, 6 ou o 300 obse a ions we e mislabeled using he ICS unc ion. LDA canno be applied o he eal example da a, as he iden i ica ion o subg oups is done wi hou any p io knowledge and as such supe ised me hods like LDA canno be applied o he p oblem. To analyze he eal chicken da a using PCA, we applied he snpgdsPCA unc ion o he SNPRela e [32] R- package o i . Figu e 2 shows he sca e plo ma ix o he en i s componen s, bu no pa icula subg oup could be iden i ied. The PCA iden i ies only wo s ongly de ia ing indi iduals. Nex we de e mined he numbe o eigen ec- o s ha accoun o a o al a iance o 80%. Fig. 1 Clus e labels o he k-means clus e ing o mixed da a (le ), he i s wo p inciple componen s (middle) and he las wo ICS componen s ( igh ). The ue class labels a e colo ed acco dingly and he k-means classi ica ion is ep esen ed wi h di e en symbols Fische e al. BMC Bioin o ma ics (2017) 18:173 Page 5 o 9 Fig. 2 Sca e plo ma ix o he PCA analysis. No pa icula subg oup could be iden i ied. The i s componen de ec s only wo ou lying obse a ions We plugged he co esponding ma ix wi h he i s 169 eigen ec o s om he eigen-decomposi ion o he PCA in o he ics unc ion o he ICS [19] R-package. We applied he ics unc ion using he egula co a iance ma ix and he co a iance ma ix o o h o de momen s (de aul ), as desc ibed abo e. By using his me hod we could clea ly iden i y wo subg oups in he las compo- nen s o he ICS as well as de ia ing indi iduals in he i s componen s. One subpopula ion is sepa a ed by he an epenul ima e componen (Numbe 167). This subpop- ula ion o 20 indi iduals is ma ked in ed and g een in he sca e plo ma ix o he ICS componen s, see Fig. 3. Fu he , we could also iden i y ano he possible subg oup o size 10 by p ojec ing he da a on o he penul ima e componen (Numbe 168), indica ed in blue. We do no ollow up on he indi idual ou lie s iden i ied in he i s componen s as he cu en goal was subg oup de ec ion. Be o e analyzing he pheno ypical pa icula i ies o he iden i ied subg oup, we also es he pe o mance o he o he dimension educ ion me hods on he eal chicken da a. He e, kPCA and LLE a e able o iden i y he same clus e s as ICS does, bu -SNE and Isomap ail o iden i y Fische e al. BMC Bioin o ma ics (2017) 18:173 Page 6 o 9 Fig. 3 Sca e plo ma ix o he ICS analysis. Clea subg oups could be iden i ied in componen 167 and 168. All membe s o he subg oup 167 ha e he same a he , bu wo di e en mo he s, indica ed by ed (n=19) and g een (n=1). Ano he subg oup could be iden i ied in componen 168 (blue,n=10) any clea clus e s uc u es. In case o -SNE we ied bo h k=7 and k=2, bu in nei he case any ob ious subg oup could be iden i ed. Di usion map, howe e , appa en ly iden i ies ano he subg oup. The co esponding sca e - plo ma ices can also be ound in he Addi ional ile 1. We used he de aul se ings and p o ocols as p o ided by he di e en packages. Tha means, e.g. o LLE we calcula ed he op imal numbe o neighbo s as 17. Membe s o he ed subg oup, iden i ied by he ICS me hod a e all o sp ings om he same a he and mainly om he same mo he . F om he 20 membe s o he subg oup only one indi idual (indica ed by g een) has a di e en mo he . The subpopula ion indica ed in blue is also o med by a amily. Se en chicken om his popula- ion ha e he same a he and mo he . Fu he , he a he o hose 7 chicken can also be ound in his g oup. A egion o app oxima e leng h 4Mb (Ch 2:70,348,413- 74,448,870), con aining 1340 SNPs was iden i ied by calcula ing he gene ic simila i y be ween he de ia ing ( ed) amily and he emaining popula ion. The gene ic Fische e al. BMC Bioin o ma ics (2017) 18:173 Page 7 o 9 simila i y was calcula ed wi h a mo ing a e age using windows o size 1 kb. A eas, whe e he a e age le el o ag eemen d ops below 0.4 a e conside ed o be he majo cause o he di e ence be ween he di e gen ed am- ily and he main popula ion. Addi ional ile 1: Figu e S12 shows he le el o ag eemen ac oss he conside ed ch o- mosomal egions. Also o he blue subpopula ion we could iden i y in a candida e egion a simila way. Nex , we calcula ed o each chicken wi hin he main popula ion he Manha an dis ance be ween he mode geno ype alues o he de ia ing ed amily in he egion o in e es and he indi idual geno ypes. The e we could clea ly iden i y h ee subg oups wi hin he main popula- ion, see Addi ional ile 1: Figu e S13. We deno e hose subg oups as close,in e media e and a . When b eeding alues o 15 p oduc ion alues we e compa ed be ween he ed subpopula ion and he main popula ion, signi ican di e ences we e seen in 10 ai s (The wo-sided Mann-Whi ney es was signi ican a le el α=0.05). These we e hen es ed u he using a gene alized Mann-Whi ney es o di ec ional al e na- i es. This means, we es ed o a di ec ional end o he pheno ypes wi h espec o he close, he in e media e and he a g oup. Fo six b eeding alues a di ec ional ela ionship in he main popula ion could also be e i ied. Especially he p oduc ion alues ollowed a di ec ional o de , see he co esponding boxplo s in Fig. 4. In de ails ha means ha he ed subg oup had a signi ican highe egg p oduc ion compa ed o he main g oup and wi hin he main g oup he chicken ha a e gene ically close o he subg oup in an iden i ied egion also had a highe p oduc ion com- pa ed o hose ha a e gene ically u he away. Howe e , he inc eased p oduc ion alues occu ed wi h a highe eed in ake. Discussion We applied he mode n dimension educ ion me hod ICS o a simula ion example and compa ed i o he commonly used PCA me hod o isualize some de iciency o he PCA app oach. Fu he , we applied he o he , mode n dimen- sion educ ion me hods -SNE, Isomap, LLE, kPCA and DM o he simula ion da a. He e, in he con olled en i- onmen we could clea ly see ha he PCA me hod was no able o iden i y all h ee ue g oups in he simula ed da a,bu heICSme hod,howe e ,was.F om heo he es ed me hods, only -SNE was able o eco e all h ee subg oups, bu all o he ou es ed me hods ailed doing so. Some o hem sepa a ed a single subg oup, bu mixed he emaining wo g oups in o a single la ge clus e . When he me hods we e hen applied o a high-densi y geno- ype chicken da a, he PCA me hod could no iden i y any subg oups. The ICS me hod clea ly iden i ied wo sub- g oups consis ing o 20, espec i e 10 samples, ha sha e he same amily backg ound. Two (kPCA and LLE) o he i e o he me hods, howe e , also de ec ed he same sub- g oups in he eal chicken da a. The o he h ee me hods ailed o iden i y any clea clus e s uc u es. In he sca e plo ma ices some ou lying obse a ions could be iden i ied by -SNE (see Addi ional ile 1), bu no as e iden as in he ICS case. A close look a compo- nen 3 showed e.g., ha some o he chicken wi h a alue la ge 25 a e ela ed bu he mos o hem a e un ela ed. In e ms o calcula ion imes, he ICS needed a ound 0.2 s, whe eas he -SNE un ook a ound h ee minu es. The o he used me hods needed a mos only a ew seconds o he calcula ion. We conside ed also he ed subg oup iden i ied by ICS close . I was supe io in mo e han hal o he a ail- able b eeding alues compa ed o he s anda d chicken popula ion. Wi hin he s anda d chicken popula ion we Fig. 4 Boxplo o p oduc ion alues P2 (le )andP3( igh ). A clea di ec ional ela ionship be ween he subpopula ion and he h ee dis ance g oups close, medium and a . In bo h p oduc ion pe iods ha e chickens ha a e in he iden i ied egion close o he subpopula ion also highe p oduc ion alues Fische e al. BMC Bioin o ma ics (2017) 18:173 Page 8 o 9 could iden i y h ee subg oups ha we e ei he gene - ically close, in e media e o a away om his sub- g oup based on he mos de ia ing ch omosomal egion. In addi ion, hese h ee g oups o he main popula- ion showed a di ec ional end in many ai s, espe- cially in he impo an p oduc ion alues P2 and P3. Also he blue subg oup is de ia ing in i e b eeding al- ues om he main popula ion, including he p oduc ion alues P3. The e we e no o he combina ions wi h hose pa en s in he da a a ailable so ha no u he in es iga ions could be conduc ed o iden i y he eason o he subg oups o beha e in such a di e en way. The biological explana ion o he di e ence is beyond he scope o his pape . The iden i ica ion o h ee g oups (main g oup and wo subg oups) wi hin he da a is ema kable. As all he chicken o igina e om he same line, one would no assume any subpopula ion s uc u es and by applying a PCA o i , we did no iden i y any. ICS iden i ied wo subpopula ions ha we e he ea e also seen o di e om he main popula ion o some o he pheno ypes o p oduc ion ai s. Fu he , we could iden i y s ongly de ia ing gene ic egions be ween he subpopula ions and he main g oup and ollowed exempla y up on he one ha co esponds o he ed subg oup. Wi hin ha , we calcula ed hen he gene ic dis ance o he emaining chicken o he iden i- ied subpopula ion and could see ha chicken gene ically mo e simila wi h ega d o he de ia ing egion o he subpopula ion also ha e be e p oduc ion alues. Mo e- o e , we could iden i y a di ec ional ela ionship be ween he gene ic simila i y in ha egion and ce ain p oduc- ion alues. Conclusion We p esen ed he e an al e na i e dimension educ ion me hod ha is al eady used in o he scien i ic ields, bu ha has no ye made i s way o he genomic communi y. Howe e , al hough ICS is supe io o e PCA in he cu - en scena io, i s pu pose is no o eplace PCA o any o he dimension educ ion me hod, bu i is a he consid- e ed o be ano he ool in he dense geno ype da a analysis oolbox. I s good esul s o bo h, he simula ion and he eal da ase encou age i s use also o o he genomic da ase s o u he e alua e i s pe o mance in a la ge scale. Com- pa ed o o he , mode n dimension educ ion me hods, we saw ha he e is a la ge a ia ion in he pe o - mance o each me hod, depending on he da ase . Fo ou da a, only ICS showed good esul s in he simula ion as well as in he eal da a se , Isomap and Di usion map had he weakes esul s o bo h se ups. -SNE only pe - o med well in he simula ion se up and LLE only o he eal da a. Addi ional ile Addi ional ile 1: The supplemen al ma e ial con ains addi ional Figu es. Included igu e iles a e p o ided below. Figu e S1. Sca e plo ma ix o he unmixed simula ion da a. Figu e S2. Sca e plo ma ix o he o a ed simula ion da a. Figu e S3. Visualiza ion o genomic egions ha ha e been used o he analysis. Figu e S4. Sca e plo wi h clus e labels o he k-means clus e ing o -SNE, Isomap and he LLE. Figu e S5. Sca e plo wi h clus e labels o he k-means clus e ing o Di usion Maps and ke nel PCA. Figu e S6. Sca e plo ma ix o -SNE ou pu wi h k=7 applied o he eal chicken da a. Figu e S7. Sca e plo ma ix o -SNE ou pu wi h k=2 applied o he eal chicken da a. Figu e S8. Sca e plo ma ix o he i s 7 componen s o he LLE ou pu applied o he eal chicken da a. Figu e S9. Sca e plo ma ix o he i s 7 componen s o he Isomap ou pu applied o he eal chicken da a. Figu e S10. Sca e plo ma ix o he i s 7 componen s o he kPCA ou pu applid o he eal chicken da a. Figu e S11. Sca e plo ma ix o he i s 7 componen s o he DM ou pu applied o he eal chicken da a. Figu e S12. The alues o he le el o ag eemen ac oss he egions o in e es . Figu e S13. The indi idual gene ic dis ances be ween main popula ion o he mode o he subpopula ion. (PDF 2130 kb) Abb e ia ions DM: Di usion maps; ICA: Independen componen analysis; ICS: In a ian coo dina e selec ion; kPCA: ke nel PCA; LDA: Linea disc iminan analysis; LLE: Locally linea embedding; PCA: P inciple componen analysis; SNP: Single nucleo ide polymo phism; -SNE: -Dis ibu ed s ochas ic neighbo embedding Acknowledgemen s The au ho s would like o hank e e yone a S e en Weigend’s g oup a he F ied ich Loe le Ins i u e, G ei swald, Ge many, o p epa ing he aw geno ype da a. Fu he , we would like o hank he anonymous e iewe s o hei aluable commen s. Funding This esea ch was inancially suppo ed by Lohmann Tie zuch GmbH, he design analysis and conclusions o he s udy we e done by he au ho s, and he ma e ial was ecei ed om he Lohmann Tie zuch b eeding p og amme. A ailabili y o da a and ma e ials Da a is no publicly sha ed, as i is only used as an example and no di ec esul s a e de i ed om i . The da a is, howe e , a subse o a la ge s udy ha will be published la e . Au ho s’ con ibu ions DF, KN and JV w o e he manusc ip . DF and KN implemen ed he R-sc ip s. MH, MTH and JV p o ided he gene ical backg ound and in e p e a ion. DC and RP p o ided and p ocessed he used da a. All au ho s ead and app o ed he inal manusc ip . Compe ing in e es s The au ho s decla e ha hey ha e no compe ing in e es s. Consen o publica ion No applicable. E hics app o al and consen o pa icipa e Chicken lines a e owned by he b eeding company, Lohmann Tie zuch (LTZ). The p ogeny o hese bi ds a e used o in a-communi y ade and expo s. EU Di ec i e 158/2009 equi es he examina ion o blood samples o ce ain pa hogens. Fu he es ing is equi ed o mul iple heal h ce i ica es o hi d coun ies. Blood samples ob ained om his ou ine heal h moni o ing, a e used o ex ac DNA o geno ype animals. The men ioned DNA we e ex ac ed om ou ine blood samples in he in-house labo a o y a LTZ. All bi ds a e kep and supe ised in s ic compliance o he animal wel a e laws o Lowe Saxony, Ge many. All s a aking he blood samples egula ly pa icipa e in aining p og ams o adecua e sampling in s ic obse a ion o cu en animal wel a e egula ions. Fische e al. BMC Bioin o ma ics (2017) 18:173 Page 9 o 9 Publishe ’s No e Sp inge Na u e emains neu al wi h ega d o ju isdic ional claims in published maps and ins i u ional a ilia ions. Au ho de ails 1Na u al Resou ces Ins i u e Finland (LUKE), Mylly ie 1, Jokioinen, Finland. 2Uni e si y o Tu ku, Depa men o Ma hema ics and S a is ics, Tu ku, Finland. 3Lohmann Tie zuch GmbH, Am Seedeich 9-11, 27454, Cuxha en, Ge many. 4Uni e si y o Tampe e, School o Heal h Sciences, Medisiina inka u 3, 33014, Tampe e, Finland. Recei ed: 9 Augus 2016 Accep ed: 9 Ma ch 2017 Re e ences 1. Solo ie N, Ha ley SW, Baldwin CT, Pe ls TT, S einbe g MH, Sebas iani P. Clus e ing by gene ic ances y using genome-wide snp da a. BMC Gene . 2010;11:. doi:10.1186/1471-2156-11-108. 2. Pa e son N, P ice AL, Reich D. Popula ion s uc u e and eigenanalysis. PLoS Gene . 2006;2:190. doi:10.1371/jou nal.pgen.0020190. 3. Ma S, Dai Y. P incipal componen analysis based me hods in bioin o ma ics s udies. B ie Bioin o ma. 2010;12:714–22. doi:10.1093/bib/bbq090. 4. Caussinus H, Ruiz A. In e es ing P ojec ions o Mul idimensional Da a by Means o Gene alized P incipal Componen Analyses In: Momi o i´ cK, Mildne V, edi o s. Comps a : P oceedings in Compu a ional S a is ics, 9 h Symposium held a Dub o nik, Yugosla ia, 1990. Heidelbe g: Physica-Ve lag HD; 1990. p. 121–6. doi:10.1007/978-3-642-50096-1_19. 5. Tyle DE, C i chley F, Dümbgen L, Oja H. In a ian co-o dina e selec ion. J R S a Soc Se ies B. 2009;71:549–92. doi:10.1111/j.1467-9868.2009.00706.x. 6. Vidal R, Ma Y, Sas y SS. Gene alized P incipal Componen Analysis. New Yo k: Sp inge ; 2016. 7. Musial JP, Hüsle F, Sü e lin M, Neuhaus C, Wunde le S. Day ime low s a i o m cloud de ec ion on a h image y. Remo e Sensing. 2014;6(6): 5124. doi:10.3390/ s6065124. 8. Musial JP, Hüsle F, Sü e lin M, Neuhaus C, Wunde le S. P obabilis ic app oach o cloud and snow de ec ion on ad anced e y high esolu ion adiome e (a h ) image y. A mos Meas Tech. 2014;7(3):799–822. doi:10.5194/am -7-799-2014. 9. Books ein FL, Mi e oecke P. Compa ing co a iance ma ices by ela i e eigenanalysis, wi h applica ions o o ganismal biology. E ol Biol. 2013;41(2):336–50. doi:10.1007/s11692-013-9260-5. 10. an de Maa en LJP, Hin on GE. Visualizing high-dimensional da a using -sne. J Mach Lea n Res. 2008;9:2579–605. 11. Tenenbaum JB, de Sil a V, Lang o d JC. A global geome ic amewo k o nonlinea dimensionali y educ ion. Science. 2000;290:2319–23. 12. Roweis S, Saul L. Nonlinea dimensionali y educ ion by locally linea embedding. Science. 2000;290:2323–6. 13. Schölkop B, Smola A, Mülle KR. Nonlinea componen analysis as a ke nel eigen alue p oblem. Neu al Compu . 1998;10:1299–319. 14. Coi man RR, La on S, Lee AB, Maggioni M, Nadle B, Wa ne F, Zucke SW. Geome ic di usions as a ool o ha monic analysis and s uc u e de ini ion o da a: Di usion maps. PNAS. 2005;102:7426–31. 15. Tuiskula-Haa is o M, Honka ukia M, P eisinge R, Schmu z M, de Koning DJ, Wei WH, Vilkki J. Quan i a i e ai loci a ec ing eggshell ai s in an 2 popula ion. Animal Gene . 2011;42:293–9. 16. Honka ukia M, Tuiskula-Haa is o M, A ango J, Tabell J, Schmu z M, P eisinge R, Vilkki J. Q l mapping o egg albumen quali y in egg laye s. Gene Sel E ol. 2013;45:31. 17. No dhausen K, Tyle DE. A cau iona y no e on obus co a iance plug-in me hods. Biome ika. 2015. doi:10.1093/biome /as 022. 18. No dhausen K, Oja H, Ollila E. Mul i a ia e Models and he Fi s Fou Momen s. Singapo e: Wo ld Scien i ic; 2011, pp. 267–87. doi:10.1142/9789814340564_0016. 19. No dhausen K, Oja H, Tyle DE. Tools o explo ing mul i a ia e da a: The package ICS. J S a So w. 2008;28(6):1–31. doi:10.18637/jss. 028.i06. 20. Mie inen J, Taskinen S, No dhausen K, Oja H. Fou h momen s and independen componen analysis. S a is Sci. 2015;30(3):372–90. doi:10.1214/15-STS520. 21. Tapio M, Tapio I, G islis Z, Holm LE, Jeppsson S, Kan anen J, Miceikiene I, Olsake I, Viinalass H, Ey ho sdo i E. Na i e b eeds demons a e high con ibu ions o he molecula a ia ion in no he n eu opean sheep. Mol Ecol. 2005;14(13):3951–63. doi:10.1111/j.1365-294X.2005.02727.x. 22. Tyle DE. A no e on mul i a ia e loca ion and sca e s a is ics o spa se da a se s. S a P obab Le . 2010;80(17–18):1409–13. doi:10.1016/j.spl.2010.05.006. 23. Oja H, No dhausen K. Independen Componen Analysis In: El-Shaa awi A-H, Piego sch W, edi o s. Encyclopedia o En i onme ics. New Je sey: John Wiley & Sons; 2012. p. 1352–1360. 24. Rand WM. Objec i e c i e ia o he e alua ion o clus e ing me hods. J Am S a Assoc. 1971;66(336):846–50. 25. Fische D, Oja H, Schleu ke J, Sen PK, Wahl o s T. Gene alized Mann-Whi ney ype es s o mic oa ay expe imen s. Scand J S a . 2014;41:672–92. doi:10.1111/sjos.12055. 26. Fische D, Oja H. Mann-Whi ney ype es s o mic oa ay expe imen s: The R package gMWT. J S a So w. 2015;65(1):1–19. doi:10.18637/jss. 065.i09. 27. Donaldson J. Tsne: T-Dis ibu ed S ochas ic Neighbo Embedding o R ( -SNE). 2016. R package e sion 0.1-3. h p://CRAN.R-p ojec .o g/ package= sne. Accessed 30 No 2016. 28. Ba enhagen C. RDRToolbox: A Package o Nonlinea Dimension Reduc ion wi h Isomap and LLE. 2014. R package e sion 1.20.0. h ps:// www.bioconduc o .o g/packages/ elease/bioc/h ml/RDRToolbox.h ml. Accessed 30 No 2016. 29. Died ich H, Abel M. Lle: Locally Linea Embedding. 2012. R package e sion 1.1. h p://CRAN.R-p ojec .o g/package=lle. Accessed 30 No 2016. 30. Ka a zoglou A, Smola A, Ho nik K, Zeileis A. ke nlab – an S4 package o ke nel me hods in R. J S a So w. 2004;11(9):1–20. 31. Ange e P, Hagh e di L, Bü ne M, Theis FJ, Ma C, Bue ne F. des iny – di usion maps o la ge-scale single-cell da a in R. Bioin o ma ics. 2015. doi:10.1093/bioin o ma ics/b 715. h p://bioin o ma ics.ox o djou nals. o g/con en /ea ly/2015/12/13/bioin o ma ics.b 715. ull.pd +h ml. 32. Zheng X, Le ine D, Shen J, Goga en S, Lau ie C, Wei B. A high-pe o mance compu ing oolse o ela edness and p incipal componen analysis o snp da a. Bioin o ma ics. 2012;28:3326–8. doi:10.1093/bioin o ma ics/b s606. • We accep p e-submission inqui ies • Ou selec o ool helps you o ind he mos ele an jou nal • We p o ide ound he clock cus ome suppo • Con enien online submission • Tho ough pee e iew • Inclusion in PubMed and all majo indexing se ices • Maximum isibili y o you esea ch Submi you manusc ip a www.biomedcen al.com/submi Submi you nex manusc ip o BioMed Cen al and we will help you a e e y s ep: