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1 Elsever Edtoral System(tm) for NeuroImage Manusrpt Draft Manusrpt Number: Ttle: Comparson of ampltude normalzaton strateges on the auray and relablty of group ICA deompostons Artle Type: Tehnal Note Seton/Category: Methods & Modellng Correspondng Author: Dr. Elena A Allen, Ph.D. Correspondng Author's Insttuton: The Mnd Researh Network Frst Author: Elena A Allen, Ph.D. Order of Authors: Elena A Allen, Ph.D.; Erk Barry Erhardt, Ph.D.; Srnvas Rahakonda, MS; Tom Ehele, Ph.D.; Andrew R Mayer, Ph.D.; Vne D Calhoun, Ph.D. Abstrat: In the study of modularty and onnetvty wth fmri, group ndependent omponent analyss (ICA) has emerged as a powerful multvarate tehnque to dsover spatal patterns of oherent atvty and ther varaton aross ndvduals. Lke other mult-subjet methods, group ICA ommonly requres that data from dfferent subjets are standardzed nto a ommon spae wth a ommon sale. Ths s partularly mportant for fmri data sne sgnal unts are arbtrary and varablty s hgh both wthn and between subjets. Currently, there s lttle onsensus on how data should be normalzed pror to group analyss and the urrent lterature provdes no dret omparson of proposed strateges. In the present study, we evaluate the performane of three ampltude normalzaton methods n the ontext of group ICA. These methods nlude no normalzaton (NN), ntensty normalzaton (IN) and varane normalzaton (VN). Usng both smulated and restng-state datasets, we ompare the effets of normalzaton methods on the auray and test-retest relablty of omponent features. We further onsder these methods n ombnaton wth two bak-reonstruton tehnques used to estmate omponent features of ndvdual subjets. Bak-reonstruton tehnques nlude GICA3, whh dretly 'bak-projets' group omponents nto the subjet subspae, and dual regresson (DR), whh ndretly estmates subjet-spef omponents by regressng group omponents onto the subjet data. Parallel results from smulatons and real data suggest that ) VN redues deomposton auray due to removal of mportant ampltude nformaton and ) IN, when used n onjunton wth GICA3, mproves the auray and relablty of estmated omponent magntudes between subjets. Notably, DR bak-reonstruton ompromses the relablty of omponent features and magntudes. These fndngs demonstrate the sgnfant nfluene of normalzaton and bak-reonstruton hoes on group ICA deompostons and mply that areful onsderaton of ther applaton may mprove the utlty of funtonal onnetvty metrs n lnal and bas researh applatons.

2 . Cover Letter Dear Edtors, We are submttng the manusrpt, Comparson of ampltude normalzaton strateges on the auray and relablty of group ICA deompostons, to be onsdered for publaton n NeuroImage. In the present study, we evaluate the performane of three ampltude normalzaton methods on fmri data n the ontext of group ndependent omponent analyss (ICA) methods. Lke other mult-subjet methods, group ICA ommonly requres that data from dfferent subjets are standardzed nto a ommon spae wth a ommon sale, yet, to our knowledge, a formal omparson between dfferent normalzaton strateges s not avalable n the lterature. Here, we use smulated and restng-state datasets to ompare the effets of normalzaton methods on the auray and test-retest relablty of omponent features. Our fndngs demonstrate the sgnfant nfluene of preproessng hoes on group ICA deompostons and provde mportant reommendatons for the growng number of users of mult-subjet ICA. Reommended revewers are provded n another attahment. We also request the followng people not be onsdered to revew ths work due to possble onflts of nterest: Chrstan F. Bekmann and Stephen M. Smth. Snerely, Elena Allen Postdotoral Fellow The Mnd Researh Network

3 *. Revewer Suggestons Kvnem, Vesa Ylopstonranta E, D-E rappu, 4. krs. 7 Kuopo Itä-Suomen ylopsto, Kuopon kampus, Tetoteknkkakeskus, PL 67, 7 Kuopo vesa.kvnem@uef.f Mhael P. Mlham, M.D., Ph.D. Leon Levy Assstant Professor of Chld and Adolesent Psyhatry; Assoate Dretor, Phylls Green and Randolph Cōwen Insttute for Pedatr Neurosene Mhael.Mlham@nyum.org () Koene R.A. van Djk, PhD Athnoula A. Martnos Center for Bomedal Imagng Department of Radology - Massahusetts General Hosptal 49 Thrteenth Street (Rm 3) Charlestown, MA 9 kvandjk@nmr.mgh.harvard.edu Mhael C. Stevens, Ph.D Department of Psyhatry Yale Unversty Shool of Medne Retreat Avenue Whtehall Buldng - Insttute of Lvng Hartford CT 66 Emal: msteven@harthosp.org Phone: , ext 755 Bharat Bswal, Ph.D. Assoate Professor Department of Radology 5 Bergen Street, UH C3 Newark, NJ 7 bswalbh@umdnj.edu Ph# (973)

4 *3. Manusrpt Clk here to vew lnked Referenes Comparson of ampltude normalzaton strateges on the auray and relablty of group ICA deompostons Elena A. Allen *, Erk B. Erhardt, Srnvas Rahakonda, Tom Ehele, Andrew R. Mayer,3, and Vne D. Calhoun,3 The Mnd Researh Network, Albuquerque, NM, USA Unversty of Bergen, Bergen, Norway 3 Unversty of New Mexo, Albuquerque, NM, USA * Correspondene to: Elena Allen The Mnd Researh Network, Yale Blvd. NE, Albuquerque, New Mexo 876, USA. phone: fax: e-mal: eallen@mrn.org Key words: group ICA; ampltude normalzaton; varane normalzaton; fmri; smulaton Runnng ttle: Effets of ampltude normalzaton on group ICA deompostons Page of 34

5 Abstrat In the study of modularty and onnetvty wth fmri, group ndependent omponent analyss (ICA) has emerged as a powerful multvarate tehnque to dsover spatal patterns of oherent atvty and ther varaton aross ndvduals. Lke other mult-subjet methods, group ICA ommonly requres that data from dfferent subjets are standardzed nto a ommon spae wth a ommon sale. Ths s partularly mportant for fmri data sne sgnal unts are arbtrary and varablty s hgh both wthn and between subjets. Currently, there s lttle onsensus on how data should be normalzed pror to group analyss and the urrent lterature provdes no dret omparson of proposed strateges. In the present study, we evaluate the performane of three ampltude normalzaton methods n the ontext of group ICA. These methods nlude no normalzaton (NN), ntensty normalzaton (IN) and varane normalzaton (VN). Usng both smulated and restng-state datasets, we ompare the effets of normalzaton methods on the auray and test-retest relablty of omponent features. We further onsder these methods n ombnaton wth two bak-reonstruton tehnques used to estmate omponent features of ndvdual subjets. Bak-reonstruton tehnques nlude GICA3, whh dretly bak-projets group omponents nto the subjet subspae, and dual regresson (DR), whh ndretly estmates subjet-spef omponents by regressng group omponents onto the subjet data. Parallel results from smulatons and real data suggest that ) VN redues deomposton auray due to removal of mportant ampltude nformaton and ) IN, when used n onjunton wth GICA3, mproves the auray and relablty of estmated omponent magntudes between subjets. Notably, DR bak-reonstruton ompromses the relablty of omponent features and magntudes. These fndngs demonstrate the sgnfant nfluene of normalzaton and bak-reonstruton hoes on group ICA deompostons and mply that areful onsderaton of ther applaton may mprove the utlty of funtonal onnetvty metrs n lnal and bas researh applatons. 49 Page of 34

6 5 Introduton The blood oxygenaton level dependent (BOLD) sgnal deteted wth funtonal magnet resonane (fmri) magng s the result of a omplex asade of neural, vasular and metabol reatons measured by varable sannng protools and feld strengths. The absolute sgnal ampltude s n arbtrary unts and s generally not nterpretable per se. Therefore, fmri responses are usually assessed and reported n relatve unts, most ommonly perent sgnal hange from the baselne (Glover, 999; Handwerker et al., 4; Mezn et al., ), or sometmes as standard devatons from the mean (Logothets et al., ) or fraton of the maxmum ntensty (Agurre et al., 998). Whle the mplatons of suh normalzng (.e., standardzng) transformatons are relatvely straghtforward for voxel-wse regressons or mpulse response estmatons, ther effet on multvarate spatotemporal fmri analyses are less lear and to our knowledge a formal omparson between dfferent strateges s not yet avalable n the lterature. In ths study, we ompare three potental methods of ampltude normalzaton n the ontext of a multvarate deomposton usng group ndependent omponent analyss (ICA). Spatal ICA s ommonly appled to fmri datasets to separate spatally ndependent patterns, or spatal maps (SMs), from ther lnearly mxed BOLD tme ourses (TC) va maxmzaton of mutual ndependene between spatal omponents (Calhoun et al., 9; MKeown et al., 998). The nvestgated normalzaton approahes nlude ) no normalzaton (NN), where data s left n ts raw ntensty unts, ) ntensty normalzaton (IN), whh apples voxel-wse dvson of the tme seres mean, equvalent to perent sgnal hange and 3) varane normalzaton (VN), where voxel-wse tme seres are z-sored to have a mean of zero and standard devaton of one. NN has been used n a large varety of sngle-subjet (Formsano et al., 4; MKeown et al., 998) and mult-subjet (Calhoun et al., ; Varoquaux et al., Page 3 of 34

7 ) spatal ICA approahes and s a frequent hoe for users of the group ICA of fmri toolbox (GIFT) ( (Calhoun, 4), though reently IN has also been onsdered, e.g. (Damaraju et al., ). VN s used as an ntal step n the probablst ICA (PICA) model under the assumpton of sotrop nose (Bekmann and Smth, 3, 4), and a type of VN s mplemented n the multvarate exploratory lnear optmzed deomposton nto ndependent omponents (MELODIC) software ( The effets of these normalzaton proedures on the outome of group ICA an manfest n several possble ways. Frst, beause IN and VN are appled n a voxelwse fashon, they may alter the relatve ontrbutons of dfferent regons to the SMs, affetng omponent shape. In addton, sne the sale of eah subjet s dataset wll be transformed separately, these methods an also affet the relatve ampltudes of deomposed omponents between subjets. Lastly, sne the mplementaton of mult-subjet ICA typally requres the use of PCA for data whtenng and reduton (Bekmann and Smth, 4; Calhoun et al., ; Varoquaux et al., ), pror applaton of IN or VN may alter the varane struture n datasets and affet the nformaton retaned n the ompressed data used for the ICA deomposton. For example, the prnpal omponents of NN or IN data may be based towards apturng the large varane n ventrles or areas wth movement-related artfats, whle omponents of VN data should be less suseptble to these effets gven the equvalent varane ontrbutons from eah voxel. Thus, dfferenes n the features aptured wth PCA may lead to dstntons n the multvarate deomposton, nludng omponent auray or omponent deteton. We evaluate the performane of normalzaton strateges through the omplementary use of smulated and real data. For smulated datasets, we ompare the wthn-subjet and betweensubjet auray of ICA deompostons, as well as the ablty to detet omponents at the group Page 4 of 34

8 level. For real fmri data, we make smlar omparsons based on the test-retest relablty of omponent features from two restng-state sans olleted approxmately four months apart. Beause the TCs and SMs of ndvdual subjets must be estmated, or bak-reonstruted, from the group omponents, we present the effets of normalzaton methods n ombnaton wth two ommonly used bak-reonstruton tehnques: GICA3, whh bak-projets the group omponents nto the subjet subspae (Calhoun et al.,, ; Erhardt et al., ), and dual regresson (DR), whh regresses the group omponents onto the subjet data (Bekmann et al., 9; Calhoun et al., 4; Flppn et al., 9). Our results from both smulated and restngstate datasets demonstrate that ICA deompostons are sgnfantly nfluened by ampltude normalzaton and that these effets addtonally nterat wth the method of bak-reonstruton. 6 7 Materals and Methods 8 9 Here we provde the detals of smulatons and data olleton, the mplementaton of group ICA (GICA) hghlghtng the aforementoned approahes to normalzaton and bakreonstruton, and the metrs used to assess the auray (for smulated data) and relablty (for real data) of omponent features Smulatons A general hallenge n evaluatng dfferent analyss methods, partularly blnd methods suh as ICA, s that the ground truth s typally unknown. Smulated data faltate evaluatons by establshng a ground truth aganst whh all estmates an be ompared. Here, smulatons are based on an fmri-lke dataset wth spatal soures that are ommon among subjets (Correa et al., 5), as dsussed n detal prevously (Erhardt et al., ). Brefly, data are smulated as Page 5 of 34

9 the produt of tme ourses (TCs) and spatal maps (SMs), denoted by the T -by- C matrx R and the C -by-v matrx S, respetvely, wth T tme ponts, V 36 voxels, and C 8 soure omponents. Three soures (S, S, and S6) have task-related TCs whle the remanng fve have TCs and SMs modeled after artfats ommon to fmri data. The SMs of sx soures are super-gaussan (leptokurtot) as typally seen n fmri data and one soure (S7) s sub- Gaussan (platykurtot). Thrty-two, M 3, realzatons of subjet data are reated from R and S templates by addng subjet-spef Gaussan nose to the TCs and SMs and by varyng the ampltude of the task-related TCs. Spefally, let of S, then subjet-spef data wth no nose (nn) are generated wth R be olumn of R and let S be row 7 C nn T a( )( ) Y R S R S, () 8 T where and are vetors whose elements are dstrbuted as Normal(, ) and s vared 9 between subjets and omponents. Component ampltude, a, s Unform(.5,.75) for ,,6 and equal to otherwse. In Fgure, we dsplay the true group mean of the smulated TC ( R ) and SM ( S ) for eah omponent. To better approxmate the propertes of fmri data, we sale the atvatons n smulated data, add Ran nose onsstent wth a realst SNR (Okada et al., 5) and multply by an 34 ntensty fator refletng the arbtrary magntude of aqured sgnals. For eah element n nn Y 35 over tme and voxels, Y nn ( tv, ), we ompute Y( t, v) f ( Y ( t, v) B ), where the nn 36 addtve baselne B Y to smulate % atvatons, and are both dstrbuted nn max /. tv, 37 as Normal(, ) wth nose Y / SNR and SNR=5, and ntensty fator f s nose 38 Unform(, ). Ths yelds the smulated data Y for subjets,, M. Page 6 of 34

10 Restng-state data The fmri data presented here were olleted as part of an ongong nvestgaton nto the stablty and relablty of restng-state networks. Twenty-three partpants (mean ± SD age: 9.7 ± 9.4 years, females) ompleted two fve mnute restng-state sans on the same 3 Tesla Semens Tro sanner durng vsts spaed approxmately 4 months apart. T * -weghted funtonal mages were olleted usng a sngle-shot, gradent-eho eho planar pulse sequene (TR = ms; TE = 9 ms; flp angle = 75 ; FOV = 4 mm; matrx sze = 64 64). Thrtythree ontguous, axal 4.55-mm thk sles were seleted to provde whole-bran overage (voxel sze: mm). In addton to two dummy sans, the frst two mages of eah run were also elmnated to aount for T equlbrum effets, leavng 48 mages for analyss. Subjets were requested to keep ther eyes open and fxate on a foveally presented ross (vsual angle =. ) and to keep head movement to a mnmum. Canonal preproessng of fmri magntude data was performed usng the Statstal Parametr Mappng (SPM5) pakage mplemented n MATLAB (MathWorks, In., Natk, MA, USA) and Analyss of Funtonal NeuroImages (AFNI) software. Analyss steps nluded sle-tmng orreton, moton orreton, de-spkng (performed n AFNI), spatal normalzaton to an EPI template n MNI spae, reslng to mm sotrop voxels, and spatal smoothng wth a Gaussan kernel (8 mm FWHM) Ampltude Normalzaton Let Y be the T -by-v data matrx for subjet ontanng the preproessed data where T tme ponts over V voxels are olleted on M subjets. The normalzng transformatons ntrodued earler, NN, IN, and VN, are defned here: Page 7 of 34

11 6 Y Y, [NN] 6 Y [IN] Y Y Y Y V V, and Y Y Y Y V V Y [VN], T T T ( Yt Y ) T ( YtV Y V ) t t where Y tv s the data value for subjet at tme t and voxel v, Y v s the olumn vetor of data for voxel v, Y v s the mean value over tme for voxel v, and s a olumn of ones Group ICA Group ICA was performed usng the GIFT toolbox (Calhoun, 4) whh uses a temporal onatenaton approah to spatal ICA as desrbed n detal elsewhere (Calhoun et al.,, ; Calhoun et al., 9). Here, we brefly desrbe the proedure and hoes made for the analyss of smulated and restng-state datasets. Let Y be the T -by-v data matrx ontanng the preproessed and normalzed data for 7 subjet. We frst use PCA to orthogonalze, whten, and redue subjet data. Let Y F Y 73 be the T -by-v PCA-redued data for subjet, where T F F s the T -by-t standardzed redung matrx and T s the number of prnpal omponents retaned for eah subjet. Note that n prate, the subjet data Y s demeaned aross spae for eah tme pont pror to PCA to mprove ondtonng of the ovarane matrx. For the analyses presented here, T was hosen to be T, sne a relatvely large number of subjet-spef prnpal omponents works well for subsequent bak-reonstruton and mtgates aganst PCA bas (Erhardt et al., ). We Page 8 of 34

12 79 8 should note, however, that addtonal analyses usng a smaller number of prnpal omponents ( T rangng from to 8 n the ase of smulatons and T 5, the maxmum of the mnmum 8 8 desrpton length (MDL) estmates aross subjets, for restng-state data) dd not hange results related to the performane of normalzaton methods. The subjet data are then onatenated n 83 the PCA projeted tme dmenson, Y [ Y,, Y ], and undergo a group data reduton. T T T M 84 Let the T -by-v PCA-redued aggregate data be where FY M M T T T T X G Y [ G,, G M ] G F Y X F M YM G s the T -by- MT standardzed redung matrx. Ideally, T C s seleted to be the true number of omponents for all subjets, and eah subjet has the same omponents. For smulatons, we vary T from 6 to (where C 8) to explore the effet of model order on omponent estmaton. For restng-state data, T s hosen to be 3, the mean of the MDL estmates aross subjets (L et al., 7). Note that t s the seond PCA step, redung the aggregate data from MT to T dmensons that wll be most senstve to the varane-based retenton of features., 93 Usng the Infomax ICA algorthm (Bell and Sejnowsk, 995), we ompute X AS ˆˆ, where  s the T -by-t mxng matrx related to subjet TCs and Ŝ s the T -by-v matrx of group aggregate SMs. To redue senstvty to ntal algorthm parameters we repeat the ICA deomposton 3 tmes usng ICASSO (Hmberg et al., 4) and the aggregate SMs are the entrotypes of omponent lusters. Page 9 of 34

13 Bak-reonstruton We ompare two dfferent tehnques to estmate subjet-spef SMs and TCs. These nlude GICA3, a bak-reonstruton tehnque based on PCA ompresson and projeton (Erhardt et al., ), and dual regresson (DR), based on the regresson of the aggregate spatal map onto the subjet data (Bekmann et al., 9; Calhoun et al., 4; Flppn et al., 9). In GICA3, subjet-spef TCs are defned as the subjet-spef PCA bak-projeted mxng 4 matrx, R F G G G ˆ A and subjet-spef SMs are defned by applyng the unmxng T ( ) 5 matrx ( A ˆ ) to the ompressed subjet data, S Aˆ X Aˆ G F Y. The GICA3 method T T 6 provdes that the aggregate SM s the sum of the subjet-spef SMs, M Sˆ S, analogous to a random effets model where the subjet-spef effets are zero-mean dstrbuted devatons from the group mean effet (Erhardt et al., ). In DR, we frst assume that all subjets share a ommon SM whh s the aggregate from ICA, S S ˆ,,, M, and wrte T T T T Y ˆ S R E. Note that the data matrx Y s always the orgnal data (.e., pror to any normalzaton), even f Y[IN] or Y [VN] are used n the ICA deomposton to obtan Ŝ. Subjet-spef TCs are then defned as the least-square estmate, 3 ˆ ˆ ˆ ˆ T T T T R ( SS ) SY ( YS ), where ˆ S s the Moore-Penrose pseudonverse of Ŝ. To alulate 4 subjet-spef SMs, S, we relax the ntal assumpton of ommon SMs and wrte 5 Y R S E, where least squares estmaton gves S R R R Y R Y YS Y. In T T ( ) ( ˆ ) 6 ontrast to GICA3, the relatonshp between the sum of the subjet-spef SMs and the 7 aggregate SM s not easly nterpreted, M ˆ T T ˆ ˆ T T S (( S ) Y YS ) ( S ) Y Y. M Page of 34

14 8 9 3 In prate, t s neessary to remove the relevant means from the data matrx Y before performng eah regresson, or to model the baselnes expltly wth a olumn of ones n eah desgn matrx. Here we hoose the removal of means, and for the frst regresson subtrat the mean aross spae for every tme pont, then for the seond regresson subtrat the mean aross tme for every voxel. It s also ommon to normalze the ampltude of the estmated TCs before performng the seond regresson. Ths s done to remove the potental bas of TC ampltude on 4 the estmaton of S and to apture sale nformaton n the SMs themselves (Chrstan Bekmann, personal ommunaton). Thus, before estmatng S we normalze eah olumn of R to have unt standard devaton. Note that t s unlkely that usng non-normalzed TCs n the seond regresson of DR would strongly affet our results, as ths analyss varant has been explored prevously and found to have mnmal mpat (Zuo et al., 9). 9.6 Component Analyss 3.6. Magntude 3 3 We wsh to quantfy the relatve magntudes of omponents between subjets. Beause ampltude nformaton an be shared aross TCs and SMs (refer to ()), we alulate omponent 33 magntudes, g, as the produt of the magntudes for TC and SM features. For subjet we ompute the salar g g( R ) g( S ), where TC magntude g( R ) s the standard devaton of the detrended subjet-spef TC (removng the mean, slope, and perod π and π snes and osnes), and SM magntude g( S ) s the loadng parameter of the frst prnpal omponent of 37 the V -by- M subjet-spef SM matrx S [ S,, S ], as reently suggested (Glahn et al., * T T M Page of 34

15 ). When usng GICA3 bak-reonstruton, estmated omponent magntudes g are omputed analogously, g g( R ) g( S ). Wth DR, we use a slghtly dfferent formulaton to aount for the fat that ampltude nformaton has been estmated twe (one n eah regresson, see Seton.5). In ths ase, we ompute omponent magntudes as the geometr mean of the magntudes obtaned for the TC and SM features, g g( R ) g( S ). We note that the ombned magntude s very smlar to the magntude of ether ndvdual feature (e.g., for NN restng-state data bak-reonstruted wth DR, the Pearson s orrelaton oeffent between g and gr ( ) s.96, and the orrelaton between g and gs ( ) s also.96), suggestng that when usng DR to estmate subjet-spef omponents, ether feature may be used to estmate omponent magntude. We also nvestgated other possble metrs of omponent magntude, nludng low frequeny ampltude for TCs and beta oeffents from the regresson of the aggregate map onto sngle-subjet maps (.e., S ˆ S ) for SMs. We note that these alternatve methods yelded smlar results (e.g., for NN restng-state data bak-reonstruted wth GICA3, the Pearson s orrelaton oeffent between the loadng parameter of the frst prnple omponent and the beta oeffent from regresson s.86) Auray 55 For smulated data, we ompare methods by evaluatng the smlarty between true and 56 estmated omponents usng the R statst, or oeffent of determnaton. For the group Page of 34

16 57 aggregate map, we alulate the measure of smlarty R V ( ˆ ˆ S S )( S S ) S S, v v ˆ v (, ) V V ˆ ˆ ( Sv S) ( Sv S) v v where S v and S ˆv are the true and estmated ntensty values for omponent at voxel v, and S and S ˆ are the means over voxels, respetvely. We alulate analogous statsts to ompare 6 the subjet-spef SMs, R ( S, S ), subjet-spef tme ourses, R ( R, R ), and 6 omponent magntudes, R ( g, g ) Test-retest relablty For the real data, where the true omponents are unknown, we ompare dfferent approahes by examnng the test-retest relablty of omponents aross vsts (Zuo et al., 9). For a gener metr p olleted over M subjets and K vsts, relablty s estmated usng the sample ntralass orrelaton oeffent (ICC), 67 ICC p MSb( p) MS w( p) MS ( p) ( K )MS ( p) b w () 68 (Shrout and Fless, 979). Here, b M MS ( p ) ( n ) K( p p) s the between-subjet mean 69 square and M K w ( p ) ( n( K )) ( pk p s the wthn-subjet mean square n a one k MS ) 7 way random effets model, wth K p K pk k and M p M p. The ICC s bounded on 7 (,] wth greater values ndatng greater relablty. We ompute ICC statsts between Page 3 of 34

17 7 73 vsts and for omponent magntudes, denoted ICC g, and for eah voxel of the subjet- spef SMs, denoted ICC S Results Smulatons Fgure dsplays the average TCs and SMs for the smulated dataset, along wth the M average magntudes ( g M g ) for eah omponent. For the purposes of ths study we fous on the three task-related omponents (S, S, and S6), whh have large (S, mean ± SD; g =. ±.4), ntermedate (S6, g 6 =.5 ±.), and small (S, g =.3 ±.) magntudes relatve to other soures n the dataset Component Auray The effets of normalzaton (NN, IN or NN) and bak-reonstruton (GICA3 or DR) on ICA deompostons were evaluated at three dfferent model orders: 6 (under-estmate), 8 (true number of soures) and (over-estmate). Table dsplays the auray of the deompostons 85 based on the R statst between the estmated aggregate SMs ( R ( S, S )), sngle-subjet SMs ˆ ( R ( S, S ) ) and sngle-subjet TCs ( R ( R, R ) ). We note two general trends n auray that appear regardless of normalzaton or bak-reonstruton hoes. Frst, auray of snglesubjet TCs s onsstently hgher than that of sngle-subjet SMs. Seond, auray of all features mproves as model order nreases from 6 to 8 (the true number of soures) and does not suffer as model order further nreases to, suggestng that for datasets wth dstnt soures t Page 4 of 34

18 s preferable to overestmate (rather than underestmate) model order. Wth regard to normalzaton and bak-reonstruton, we fnd the followng: ) for the aggregate SMs, auray of VN s redued ompared to NN and IN, whh are nearly dental to one another. Ths s true over almost all omponents and model orders. ) Sngle-subjet SMs are also less aurate for VN, though ths dfferene s muh more pronouned wth GICA3 than wth DR bak-reonstruton, where the type of normalzaton has a mnmal effet. 3) Sngle-subjet TC auray s farly onsstent aross all methods, wth the notable exepton at model order 6 98 where VN R statsts are lower for both GICA3 and DR, partularly for S and S6. 4) Generally, the auray of GICA3 and DR methods are qute smlar. However, at model order 6, sngle-subjet SMs bak-reonstruted wth DR are less aurate than those obtaned wth GICA3, a dfferene whh has been noted n prevous work (Erhardt et al., ). To smplfy the presentaton of results, we fous on ICA deompostons at model order 8 for the remander of ths study and note fndngs spef to other model orders when they appear. The estmated aggregate spatal maps of soures S, S, and S6 are dsplayed n Fgure A. Dstntons n omponent auray are evdent from the dfferene maps ( S ˆ S, Fg. A mddle row) and satter plots of the true versus estmated voxel ntenstes ( S ˆ versus S, Fg. A bottom row). NN and IN both show roughly lnear relatonshps wth the true voxel ntenstes whle the VN method alters omponent shape, overestmatng the ntenstes of some voxels and underestmatng those of others. Ths s partularly evdent for S (the omponent wth the largest magntude), where the ntenstes of the most atve voxels have been underestmated and the relatve ntenstes of less atve voxels have been overestmated. Examples of randomly seleted sngle-subjet SMs are dsplayed n Fgure B. Here, the dfferene between bak-reonstruton methods beomes apparent. For GICA3 (Fgure B, top Page 5 of 34

19 row), whh projets the aggregate map bak nto subjet-spef spae, effets of normalzaton on sngle-subjet SMs resemble those found n the aggregate maps: VN voxel ntenstes are not aurately estmated, partularly for regons wth the largest ampltude. However for DR (Fgure B, bottom row), whh regresses the aggregate SM onto the orgnal (un-normalzed) data, the approprate voxel ntenstes are essentally reaptured, leadng to SMs and very smlar to those aheved wth NN and IN. R statsts that are Fgure C shows the analogous nformaton for randomly seleted examples of sngle- subjet TCs. Here, some modest mxng between the omponents s evdent, partularly n the dfferene tme ourses (Fg. C, bottom row). For example, the estmates of the S and S6 TCs are ontamnated by the spke n the TC of S8 (refer to Fg. ). However, as suggested by quanttatve omparsons n Table, ths mxng s present aross all normalzaton and bak- reonstruton ombnatons and estmated TCs are farly smlar to eah other and to the true TCs Component Magntude In addton to omparng the auray of omponent features wthn subjets, we also examned the ablty of dfferent methods to apture dfferenes n omponent magntude between subjets. Fgure 3A-B dsplays the satter plots of the true versus estmated omponent magntudes for the three normalzaton methods n ombnaton wth GICA3 and DR. For GICA3 (Fg. 3A), both NN and IN show roughly lnear roughly relatonshps wth the true 333 omponent magntudes, however NN s noser wth nreased pont spread and lower R ( g, g ) 334 statsts for all omponents. The R ( g, g ) statsts for VN are n some ases greater than 335 those for NN and IN, though nspeton of the satter plots shows a nonlnear relatonshp Page 6 of 34

20 between the true and estmated magntudes where the largest magntudes are underestmated and appear to saturate. Ths s most obvous for S and s dereasngly apparent n S6 and S, suggestng that the degree of saturaton s related to the relatve magntude of the omponent n the dataset (see Fg. ). In Fgure 3C, we re-plot the true and estmated magntudes for all omponents on the same axs. For NN and IN, we see that the relatve magntude salng aross omponents s onsstent, thus t s vald to ompare magntudes not only between subjets but also between omponents. For VN, ths does not appear to be the ase; the slopes between the true and estmated magntudes are dfferent for eah omponent, leadng to a substantal 344 reduton n the R statst for the saled omponents taken together ( R ( gg, ) =.77 versus and.97 for NN and IN, respetvely). For DR (Fg. 3B,D), normalzaton has very lttle effet on the estmaton of omponent magntude, whh s antpated gven that n all ases the sngle-subjet omponents are dependent on sale nformaton n the orgnal data. In fat, the magntude estmates of DR omponents are extremely smlar to those seen wth the NN-GICA3 omponents, both n terms of the overall pattern (ompare Fg. 3B to Fg. 3A, left olumn, and Fg. 3D to Fg. 3C, red 35 symbols) and R ( g, g ) statsts. We note, however, that dfferenes n magntude auray 35 between DR and GICA3 were more apparent at model order 6. For example, R ( g, g ) statsts for S estmated wth DR are.6,.59 and.8 (for NN, IN, and VN, respetvely), whle bak-reonstruton wth GICA3 yelds auray values of.78,.93, and.64. Results at model order are essentally dental to those shown n Fgure 3. These fndngs ndate that when ICA model order under-estmates the true number of soures, DR not only ompromses the auray of omponent estmaton wthn subjets (see Table ), but also estmates dfferenes between subjets wth less fdelty than GICA3 bak-reonstruton. Page 7 of 34

21 Component Deteton Although the VN method appears to ompromse estmaton of SM shape, we wondered f t mght mprove omponent deteton n terms of orretly dentfyng atve and natve voxels. Voxels were lassfed based on the t-statsts omputed aross the true subjet-spef SMs ( S ), where statsts exeedng the Bonferron-orreted threshold at P.5 were onsdered atve. Analogous t-statst maps were then omputed from the estmated subjet- spef SMs ( S ), and the threshold was vared to reate reever operatng haraterst (ROC) urves as dsplayed n Fgure 4A. In general, all ombnatons of bak-reonstruton and normalzaton methods show farly smlar ROC urves. No substantal dfferenes were onsstent aross omponents, however we dd note slghtly redued deteton performane for omponents S and S6 usng DR bak-reonstruton. Ths dfferene was present for all model orders and was very promnent at model order 6 (data not shown), onsstent wth the auray results presented n Table. Examples of voxel lassfaton for S6 (whh had the poorest dsrmnaton) are shown n Fgure 4B at a t-statst threshold of P.5. All methods orretly dentfy the two dsks of atvaton (though mslassfy the edges of the dsks where atvaton s weaker) and falsely dentfy voxels n the lower rght porton of the SM as atve due to mperfet separaton of S6 and S3. Overall, we onlude that nether ampltude normalzaton nor bak-reonstruton methods strongly affet omponent deteton, though n the ase of VN-GICA3, the spatal profle of the deteted omponent may be dstorted. Page 8 of 34

22 Restng-state data Component Comparsons For restng-state data we lmt omparsons to sx manually dentfed omponents that are well desrbed as restng-state networks (RSNs) and appear onsstently n ICA-based deompostons over a large range of model orders and analyss types (e.g. (Abou-Elseoud et al., ; Calhoun et al., 8; Damoseaux et al., 6; Smth et al., 9)). These nlude a medal vsual network (RSN ), lateral vsual network (RSN ), sensormotor network (RSN 3), posteror seton of the default-mode network (RSN 4), rght frontoparetal network (RSN 5), and left frontoparetal network (RSN 6). 388 The aggregate SMs of these RSNs are dsplayed n Fgure 5A, and the R statsts 389 omparng the smlarty between ampltude normalzaton methods are lsted n Table. 39 Components are farly omparable aross methods, though the mages and R statsts ndate that NN and IN aggregate SMs are more smlar to eah other than to VN, as was the ase for smulatons (see Fg. and Table ). Another feature resemblng the fndngs for smulated data s the more unform appearane of some VN omponent maps. Ths an be seen learly n the jont hstograms of the voxel ntenstes between dfferent methods, as shown n Fgure 5B for RSN (prmary vsual network), a robust and promnent network n fmri data and the omponent wth the largest magntude ( g 5.4 ). Though the relatonshp between NN and IN s roughly lnear, the NN versus VN jont hstogram shows a sub-lnear relatonshp omparable to the plateau shape observed between the true and estmated VN ntenstes for S of the smulatons (see Fg. A). Page 9 of 34

23 4 Table also lsts the R statsts between sngle-subjet SMs and TCs obtaned wth 4 dfferent normalzaton methods for both bak-reonstruton types. The pattern of R statsts between normalzaton methods s qute smlar for DR and GICA3 and parallels the results for aggregrate SMs: NN and IN and more smlar to eah other than to VN. However, the dfferenes between normalzaton tehnques are muh smaller for omponents bak-reonstruted wth DR as ompared to GICA3, partularly wth regard to VN sngle-subjet SMs. The underlyng ause of ths dsparty an be seen n Fgure 5C, where we dsplay the jont hstogram of voxel ntenstes between the NN aggregate SM (dental to Fg. 5B) and the mean of the VN snglesubjet SMs obtaned wth DR for RSN. Note that beause the mean of the sngle-subjet SMs obtaned wth GICA3 s a saled verson of the aggregate SM (see Seton.5) we are essentally omparng the average maps obtaned wth eah bak-reonstruton method. Contrastng panels B and C of Fgure 5, we see that DR has to some degree unsaturated the voxel ntenstes of the VN SMs as ompared to the VN aggregate map from the ICA deomposton. These fndngs orrespond wth those observed n smulated data (see Fg. B). As a fnal omment on the smlarty between omponents estmated wth the dfferent methods, we address the relatve mpats of varous ampltude normalzaton methods versus 46 bak-reonstruton approahes. Table 3 lsts the R statsts between SMs and TCs obtaned wth dfferent bak-reonstruton types for a gven normalzaton method. For all RSNs, the average SMs are very smlar between GICA3 and DR. For example, R statsts between NN- GICA3 and NN-DR are lustered at extremely hgh values, rangng between.93 and.97. Note 4 that these R statsts (mean ± SD:.9 ±.6) whh ompare bak-reonstruton methods 4 4 are more onsstent and on average onsderably larger than the analogous statsts omparng normalzaton methods n Table (.73 ±.3), ndatng that normalzaton pror to ICA has a Page of 34

24 43 44 muh greater effet on the resultng SMs than the hosen method of sngle-subjet bak- reonstruton Component Relablty Beause the true SMs and TCs are unknown n real data, we ompare normalzaton and bak-reonstruton methods by examnng the test-retest relablty of omponents aross vsts (Zuo et al., 9). Maps of voxelwse relablty statsts, ICC S, for the sx RSNs are dsplayed n Fgure 6A. For GICA3, both NN and IN demonstrate moderate to hgh relablty throughout regons wth promnent atvaton n all omponents (ompare to Fg. 5A). VN shows strkngly redued relablty n the same regons, as do omponents bak-reonstruted wth DR (note that beause ICC S statsts were extremely smlar aross the normalzaton methods for DR bakreonstruton we dsplay full maps for only the NN data). To better understand patterns of testretest relablty we examne the jont-hstograms between voxel ntensty and relablty, as shown n Fgure 6B for RSN. For NN and IN omponents bak-reonstruted wth GICA3 (Fg. 6B, left), ICC S statsts are broadly dstrbuted at low ntenstes but show a onsstent nrease wth postve voxel atvaton (.e., the regons representng hgh onnetvty wthn the network are the most relable between vsts). Ths pattern of relablty parallels fndngs from seed-based analyses showng that sgnfant, postve orrelatons between voxels are the most onsstent between sans (Shehzad et al., 9). ICC S values for VN omponents are less varable at low ntenstes but do not show the same degree of mprovement wth nreasng atvaton and atually show a subtle derease n relablty at very hgh ntenstes. Note that the derease n ICC S at voxels wth maxmal atvaton lkely reflets a derease n between-subjet varablty, rather than an nrease n wthn-subjet varablty (see Seton.6.3), sne VN wll Page of 34

25 445 sale the tme seres of peak voxels to have smlar ampltudes aross all subjets. For DR (Fg B, rght), all three normalzaton methods show a smlar pattern where the dstrbuton of ICC S statsts s very broad at low ntenstes but narrows somewhat symmetrally as atvaton nreases. 449 We an quantfy the dfferenes n these dstrbutons by alulatng the medan ICC S statst for voxels exeedng a gven ntensty threshold. In Fgure 6C we plot the medan ICC S (averaged over all sx RSNs) for eah method as a funton of ntensty threshold, whh spans the full range of average voxel ntenstes. The medan ICC S statsts are hghest for NN- GICA3 and IN-GICA3 at all thresholds, though the enhanement grows substantally as ntensty threshold nreases. VN-GICA3 shows slghtly greater relablty than the DR bak-reonstruted omponents at lower thresholds, though ths dstnton fades at hgher thresholds largely due to the VN derease n relablty (see Fg. 6B). We note that very smlar results were observed when usng other measures of entralty suh as the mean and mode of the ICC S dstrbuton. Overall, these results suggest that ) SMs bak-reonstruted wth DR are substantally less relable than those obtaned wth GICA3 regardless of normalzaton method, and ) NN and IN omponents bak-reonstruted wth GICA3 exhbt the greatest relablty, partularly n regons wth strong atvaton where one would desre relablty to be hgh. We also examned the mpat of ampltude normalzaton and bak-reonstruton on the relablty of omponent magntudes estmated from subjet-spef SMs and TCs (see Seton.6.). Lne plots of the ICC g relablty statsts averaged over RSNs are shown n Fgure 7A. For GICA3 (Fg. 7A, left), IN shows the greatest test-retest relablty (mean ± SD: ICC g =.59 ±.8) whle NN and VN magntudes are less onsstent between vsts ( ICC g =.4 ±.8 and Page of 34

26 ±.6, respetvely). For DR (Fg. 7A, rght), relablty statsts are roughly the same aross normalzaton methods ( ICC g =.44 ±.9 and.4 ±.4, and.36 ±., for NN, IN and VN, respetvely). These results suggest that whle all methods an yeld magntude estmates that are at least moderately relable between vsts, IN-GICA3 provdes a dstnt enhanement n test-retest relablty. Furthermore, lose nspeton of satter plots dsplayng vst versus vst magntudes, as shown n Fgure 7B for RSN, ndated that relablty statsts mght be dsproportonately nfluened by outlyng subjets wth extreme magntudes. Applyng a threshold of twe the nterquartle range, omponent magntudes of subjets 6 and 3 were dentfed as outlers for all RSNs bak-reonstruted wth DR and all NN-GICA3 omponents. To determne the effet of these outlyng values, we reomputed ICC g statsts of eah dataset followng the removal of subjets 6 and 3. As shown n Fgure 7A, outler removal dramatally redues relablty statsts for all normalzaton methods wth DR and NN-GICA3, but has a relatvely lttle mpat on the relablty of IN or VN omponent bakreonstruted wth GICA3. For example, followng outler removal, test-retest relablty of omponent magntudes for IN wth DR drops to. ±.4, whle ICC g statsts for IN wth GICA3 are stll moderate at.49 ±.9. These fndngs suggest that magntudes estmated from data whh have not been normalzed (.e., va an NN ICA deomposton or regresson onto orgnal data) are senstve only to extreme dfferenes and fal to apture more subtle dstntons between subjets. In addton to the dfferenes n magntude relablty between methods, we also note substantal dfferenes n subjet orderng between methods (see Fg. 7B). For example, VN wth GICA3 bak-reonstruton estmates that subjet 6 has one of the smallest magntudes relatve to other subjets, whle all other methods suggest the opposte. Analogous dsrepanes were Page 3 of 34

27 present n other RSNs and were also observed whether examnng the ombned magntude estmates (from TCs and SMs, as n Fgure 7) or lookng at the magntudes from the omponent TCs and SMs ndependently (not shown). These results have serous mplatons for analyses determnng the effets of ategoral and ontnuous varables, where nferenes may be based on omponent magntudes and demonstrate the onsderable mpat of ampltude normalzng transformatons Dsusson In the present study, we examned the effets of dfferent ampltude normalzaton methods (NN, IN and VN) n the ontext of multvarate deompostons of fmri data wth group ICA. Our omparsons yelded two man results. Frst, VN redues the auray of estmated aggregate SMs as ompared to NN and IN (Table ) and dstorts omponent shape suh that the ntenstes of the most atve voxels an be underestmated (Fg. and Fg. 5). Seond, IN mproves the estmaton of relatve omponent magntudes between subjets for smulated data (Fg. 3) and mproves test-retest relablty of SM ntensty and omponent magntude n real data (Fg. 6 and Fg. 7). Importantly, these benefts were only seen wth GICA3 bak-reonstruton; DR bak-reonstruton yelded substantally redued relablty statsts regardless of the type of ampltude normalzaton. Eah of these fndngs s dsussed n greater detal below Effets on Component Auray and Shape The hghly varable and somewhat arbtrary sale of the BOLD sgnal advoates the use of ampltude standardzaton or normalzaton pror to analyss. Ths preproessng step may be of even greater prudene n omplex multvarate analyses, suh as mult-subjet ICA, whh Page 4 of 34

28 smultaneously onsders spatotemporal patterns among a group of ndvduals. One proposed transformaton s VN (Bekmann and Smth, 3, 4), whh z-sores eah voxel s tme seres to have zero mean and unt standard devaton. A hypotheszed beneft of VN s that equal ontrbutons of voxels to the varane of the normalzed dataset wll enhane retenton of mportant features followng varane-based data reduton (.e., PCA). However, a possble detrment of ths method s the loss of mportant ampltude nformaton between dfferent voxels and subjets. In our experments wth smulated data, we found no evdene that VN enhanes the auray of aggregate or sngle-subjet omponents (Table ), nor does t appear to mprove deteton of omponent SMs at the group level usng ether GICA3 or DR bak-reonstruton (Fg. 4). In ontrast, we found onsderable evdene that, as a onsequene of removng some ampltude nformaton, VN dstorts the spatal dstrbuton of ampltudes. Ths was apparent for smulated data n whh we found sublnear relatonshps between true aggregate SM ntenstes and ther estmated values (Fg. A), and was also suggested by evaluatons of restng-state data whh showed smlar trends between NN and VN SM ntenstes (Fg. 5B). A seond proposed method of ampltude normalzaton s IN, whh has long been used n mass-unvarate analyss of fmri data (Glover, 999; Handwerker et al., 4). IN dvdes eah voxel s tme seres by the mean over tme, thus mpltly assumng that hanges n a voxel s BOLD sgnal should be proportonal to the average level of ntensty. Note that ths assumpton s n lne wth the bophysal model of BOLD ontrast. For a gven voxel, the hange n BOLD 53 sgnal s modeled (usng the notaton of (Ogawa et al., 993)) as * S S( te R), where S s 533 the baselne ntensty, t e s the expermental eho tme, and * R s the hange n the transverse 534 relaxaton rate onstant, * R, whh s related to loal alteratons n deoxyhemoglobn levels Page 5 of 34

29 (Ogawa et al., 993). Ths relatonshp mples that the hanges n BOLD sgnal over tme should ndeed be proportonal to the baselne, whh we estmate as the mean sgnal wth IN, and that for fxed feld strength and expermental parameters, the quantty S / S should be most senstve to hanges n blood oxygenaton. As wth VN, IN has the potental to alter both the varane struture of normalzed data and thus feature retenton n ompressed data, as well as the relatve ampltudes of sgnals between voxels and subjets. Somewhat surprsngly, we found essentally no effet of IN (as ompared to NN) on the auray of group or sngle-subjet SMs or TCs for smulated data (Table, Fg. and Fg. 4) and relatvely lttle effet on the omponents of restng-state data (Table, Fg. 5 and Fg. 6). In terms of omponent auray and shape, we onlude that the deompostons of NN and IN datasets are qute smlar, and that these normalzaton methods are preferred over VN whh may dstort the relatve ontrbutons of voxels to omponent SMs. Whle not seen n our smulatons, we do note that VN, or smlar approahes amed to equalze varane, ould outperform NN or IN n terms of omponent deteton when the range of varane between dfferent omponents s extremely hgh Effets on Component Magntude In addton to bas dfferenes n omponent auray and shape, our experments also demonstrated that ampltude normalzaton affets the estmaton of relatve omponent magntudes between subjets. In smulatons, IN mproved the estmaton of omponent magntudes as ompared to NN and dd not suffer from nonlnear and nonsstent salng that was present n VN deompostons (Fg. 3). A smlar dstnton was noted for restng-state data: omponent magntudes were most relable between vsts when IN was appled pror to group ICA (Fg. 7), an effet that was partularly evdent when test-retest relablty statsts were Page 6 of 34

30 alulated after the removal of outlyng data ponts. Whle nreased test-retest relablty ertanly does not mply nreased auray, t stands that magntude relablty s a hghly desrable property of ICA deompostons that should be dsernble gven the overall stablty and relablty of other aspets of RSNs, as seen n Fgure 6 and prevous studes (Damoseaux et al., 6; Zuo et al., 9). A rual larfaton regardng the observed enhanements wth IN s that they only our wth the use of GICA3 bak-reonstruton to estmate sngle-subjets SMs and TCs. For the estmatons of omponent magntudes n smulated data (Fg. 3), the test-retest relablty of RSN SMs (Fg. 6), and the test-retest relablty of omponent magntudes (Fg. 7), results wth DR bak-reonstruton were very smlar aross normalzaton methods and were roughly equvalent or nferor to results of NN-GICA3 deompostons (Fg. 3, Fg 6, and Fg. 7). These fndngs have mportant mplatons for the use of DR, as they demonstrate that no matter how data s normalzed or transformed pror to ICA, regresson bak onto to the orgnal data rentrodues the ampltude nformaton from the un-normalzed dataset. Note that n some ases, ths may be benefal. For example, nformaton of voxel ampltudes that s lost wth VN an be reaptured va DR to mprove estmates of omponent shape (Fg. B, Fg. 5B-C). However, regresson onto the orgnal data wll also reapture the arbtrary salng and nose present n the BOLD sgnals. Ths step an redue the ablty to aurately estmate omponent magntude between subjets (Fg. 3 and Fg. 7) and substantally derease the test-retest relablty of omponent SMs n restng-state data (Fg. 6). Addtonally, we fnd that DR redues the auray of sngle-subjet SMs as ompared to GICA3 at model orders less than the true dmenson for some omponents (Table and (Erhardt et al., )). For these reasons, we reommend the use Page 7 of 34

31 58 58 of IN pror to group ICA n ombnaton wth GICA3 bak-reonstruton to estmate sngle- subjet omponent features Lmtatons and Future Work Whle we have provded a detaled evaluaton of ampltude normalzaton on several aspets of ICA deompostons, we must onsder these effets n ombnaton wth the many other methodologal hoes made n group ICA. As we outlne n a reent paper (see Fg. of (Erhardt et al., )), the mplementaton of mult-subjet ICA vares wdely aross studes, and one must make a number of desons regardng the data organzaton, data reduton wthn and aross subjets, feature spae over whh to maxmze ndependene (e.g. tme or spae) (Calhoun et al., 9), ICA algorthm used to determne maxmal ndependene (Correa et al., 7; Correa et al., 5), and ICA model order (Abou-Elseoud et al., ). These fators ertanly affet multvarate deompostons and ther possble nteraton wth dfferent strateges for ampltude normalzaton merts examnaton; however a omprehensve omparson of the many analyt permutatons s beyond the sope of the urrent study. Addtonally, we beleve that gven the fundamental mpat of ampltude transformatons, our urrent fndngs wll generalze to a broad range of group ICA approahes Conluson Despte ts fundamental and elementary role n fmri analyses, ampltude normalzaton has reeved lttle attenton n past work and ts effets on multvarate deompostons have not been evaluated. Here, we explored the effets of normalzaton strateges on numerous aspets of ICA deompostons whle onsderng dfferent bak-reonstruton tehnques. Based on ongruent evdene from smulated and real data, we reommend applyng IN pror to Page 8 of 34

32 performng ICA and advoate the use of GICA3 bak-reonstruton to estmate sngle-subjet SMs and TCs. The benefts of these analyss hoes may be most apparent n studes omparng omponent features between subjets, suh as nvestgatons nto the effets of ategoral or ontnuous varables on ntrns onnetvty networks. We note that all the ampltude normalzaton and bak-reonstruton methods desrbed n ths study are mplemented n the GIFT toolbox (v.d and later) Aknowledgments Ths work was supported by the Natonal Insttutes of Health (grant numbers R4- HD5836 and R-NS64464-A to A.M; grant numbers R-EB5846 and R- EB684 to V.D.C.) and the Natonal Center for Researh Resoures, Centers of Bomedal Researh Exellene (grant number P-RR938 to V.D.C.). TE was supported through a BILATGRUNN grant from the Researh ounl of Norway (RCN). We thank Nolle Correa for the use of her ode to generate smulatons and Eswar Damaraju for helpful dsussons and adve throughout the ompleton of ths work. 66 Page 9 of 34

33 67 7 Referenes Abou-Elseoud, A., Stark, T., Remes, J., Nkknen, J., Tervonen, O., Kvnem, V.,. The effet of model order seleton n group PICA. Hum Bran Mapp 3, 7-6. Agurre, G.K., Zarahn, E., D'Esposto, M., 998. The varablty of human, BOLD hemodynam responses. Neuromage 8, Bekmann, C.F., Makay, C.E., Flppn, N., Smth, S.M., 9. Group omparson of restngstate fmri data usng mult-subjet ICA and dual regresson. HBM, San Franso. Bekmann, C.F., Smth, S.M., 3. Probablst ICA for FMRI nose and nferene. Fourth Int. Symp. on Independent Component Analyss and Blnd Sgnal Separaton. Bekmann, C.F., Smth, S.M., 4. Probablst ndependent omponent analyss for funtonal magnet resonane magng. IEEE transatons on medal magng 3, Bell, A.J., Sejnowsk, T.J., 995. An nformaton-maxmzaton approah to blnd separaton and blnd deonvoluton. Neural Comput 7, Calhoun, V.D., 4. Group ICA of fmri toolbox (GIFT). Onlne at Calhoun, V.D., Adal, T., Pearlson, G.D., Pekar, J.J.,. A method for makng group nferenes from funtonal MRI data usng ndependent omponent analyss. Human Bran Mappng 4, 4-5. Calhoun, V.D., Adal, T., Pearlson, G.D., Pekar, J.J.,. Erratum: A method for makng group nferenes from funtonal MRI data usng ndependent omponent analyss. Human Bran Mappng 6, 3. Calhoun, V.D., Kehl, K.A., Pearlson, G.D., 8. Modulaton of temporally oherent bran networks estmated usng ICA at rest and durng ogntve tasks. Human Bran Mappng 9, 88. Calhoun, V.D., Lu, J., Adal, T., 9. A Revew of Group ICA for fmri Data and ICA for Jont Inferene of Imagng, Genet, and ERP data. NeuroImage 45, Calhoun, V.D., Pekar, J.J., Pearlson, G.D., 4. Alohol ntoxaton effets on smulated drvng: explorng alohol-dose effets on bran atvaton usng funtonal MRI. Neuropsyhopharmaology 9, Correa, N., Adal, T., Calhoun, V.D., 7. Performane of blnd soure separaton algorthms for fmri analyss usng a group ICA method. Magn Reson Imagng 5, Correa, N., Adal, T., L, Y.O., Calhoun, V.D., 5. Comparson of blnd soure separaton algorthms for fmri usng a new Matlab toolbox: GIFT. IEEE Internatonal Conferene on Aousts, Speeh, and Sgnal Proessng, 5. Proeedngs. (ICASSP'5), Phladelpha. Page 3 of 34

34 Damaraju, E., Phllps, J.R., Lowe, J.R., Ohls, R., Calhoun, V.D., Caprhan, A.,. Restngstate funtonal onnetvty dfferenes n premature hldren. Front Syst Neuros 4. Damoseaux, J.S., Rombouts, S.A., Barkhof, F., Sheltens, P., Stam, C.J., Smth, S.M., Bekmann, C.F., 6. Consstent restng-state networks aross healthy subjets. Pro Natl Aad S U S A 3, Erhardt, E.B., Rahakonda, S., Bedrk, E., Allen, E.A., Adal, T., Calhoun, V.D.,. Comparson of mult-subjet ICA methods for analyss of fmri data. Human Bran Mappng. In Press. Flppn, N., MaIntosh, B.J., Hough, M.G., Goodwn, G.M., Frson, G.B., Smth, S.M., Matthews, P.M., Bekmann, C.F., Makay, C.E., 9. Dstnt patterns of bran atvty n young arrers of the APOE-epslon4 allele. Pro Natl Aad S U S A 6, Formsano, E., Esposto, F., D Salle, F., Goebel, R., 4. Cortex-based ndependent omponent analyss of fmri tme seres. Magn Reson Imagng, Glahn, D.C., Wnkler, A.M., Kohunov, P., Almasy, L., Duggrala, R., Carless, M.A., Curran, J.C., Olvera, R.L., Lard, A.R., Smth, S.M., Bekmann, C.F., Fox, P.T., Blangero, J.,. Genet ontrol over the restng bran. Pro Natl Aad S U S A 7, 3-8. Glover, G.H., 999. Deonvoluton of mpulse response n event-related BOLD fmri. Neuromage 9, Handwerker, D.A., Ollnger, J.M., D'Esposto, M., 4. Varaton of BOLD hemodynam responses aross subjets and bran regons and ther effets on statstal analyses. Neuromage, Hmberg, J., Hyvärnen, A., Esposto, F., 4. Valdatng the ndependent omponents of neuromagng tme seres va lusterng and vsualzaton. NeuroImage, 4-. L, Y.O., Adal, T., Calhoun, V.D., 7. Estmatng the number of ndependent omponents for funtonal magnet resonane magng data. Human Bran Mappng 8, Logothets, N.K., Pauls, J., Augath, M., Trnath, T., Oeltermann, A.,. Neurophysologal nvestgaton of the bass of the fmri sgnal. Nature 4, MKeown, M.J., Makeg, S., Brown, G.G., Jung, T.P., Kndermann, S.S., Bell, A.J., Sejnowsk, T.J., 998. Analyss of fmri data by blnd separaton nto ndependent spatal omponents. Hum Bran Mapp 6, Mezn, F.M., Maotta, L., Ollnger, J.M., Petersen, S.E., Bukner, R.L.,. Charaterzng the hemodynam response: effets of presentaton rate, samplng proedure, and the possblty of orderng bran atvty based on relatve tmng. Neuromage, Ogawa, S., Menon, R.S., Tank, D.W., Km, S.G., Merkle, H., Ellermann, J.M., Ugurbl, K., 993. Funtonal bran mappng by blood oxygenaton level-dependent ontrast magnet Page 3 of 34

35 resonane magng. A omparson of sgnal haratersts wth a bophysal model. Bophys J 64, Okada, T., Yamada, H., Ito, H., Yonekura, Y., Sadato, N., 5. Magnet feld strength nrease yelds sgnfantly greater ontrast-to-nose rato nrease: measured usng BOLD ontrast n the prmary vsual area. Aadem radology, Shehzad, Z., Kelly, A.M., Ress, P.T., Gee, D.G., Gotmer, K., Uddn, L.Q., Lee, S.H., Margules, D.S., Roy, A.K., Bswal, B.B., Petkova, E., Castellanos, F.X., Mlham, M.P., 9. The restng bran: unonstraned yet relable. Cereb Cortex 9, 9-9. Shrout, P.E., Fless, J.L., 979. Intralass orrelatons: uses n assessng rater relablty. Psyhol Bull 86, Smth, S.M., Fox, P.T., Mller, K.L., Glahn, D.C., Fox, P.M., Makay, C.E., Flppn, N., Watkns, K.E., Toro, R., Lard, A.R., Bekmann, C.F., 9. Correspondene of the bran's funtonal arhteture durng atvaton and rest. Pro Natl Aad S U S A 6, Varoquaux, G., Sadaghan, S., Pnel, P., Klenshmdt, A., Polne, J.B., Thron, B.,. A group model for stable mult-subjet ICA on fmri datasets. Neuromage 5, Zuo, X.N., Kelly, C., Adelsten, J.S., Klen, D.F., Castellanos, F.X., Mlham, M.P., 9. Relable ntrns onnetvty networks: test-retest evaluaton usng ICA and dual regresson approah. Neuromage 49, Page 3 of 34

36 Fgure Legends Fgure. Smulated data. Average SMs (left) and TCs (rght) of the smulated mult-subjet dataset. Soures S, S, and S6 have task-related TCs and subjet-spef ampltudes are onsdered throughout the text. Average omponent magntudes ( g ) are lsted adjaent to eah soure. Fgure. Comparson of SMs and TCs for smulated data. A) Aggregate SMs of soures S, S, and S6 for NN (left olumn), IN (enter olumn) and VN (rght olumn) methods. Eah panel dsplays the true group SMs ( S ) above the estmated SMs ( S ˆ, top row), dfferene maps ( S ˆ S, mddle row), and satter plots of the true versus estmated ntenstes ( S versus S ˆ, bottom row). Dfferene maps are omputed from the z-sored true and estmated SMs. B) Examples of sngle-subjet SMs for randomly seleted subjets. True sngle-subjet SMs ( S ) are dsplayed above the estmates ( S ) for GICA3 (top row) and DR (bottom row) bakreonstruton. C) Estmated sngle-subjet TCs for randomly-seleted subjets. Top row shows the z-sored estmated TCs for NN (red), IN (green) and VN (blue) methods bak-reonstruted wth GICA3 (sold lnes) and DR (dotted lnes) overlad on the true TC (thk gray). Bottom row shows the dfferene TCs n the same format. If lnes are not vsble, they have been obsured by TCs estmated wth other methods. R statsts lst auray of the TCs for NN, IN and VN methods, respetvely. Fgure 3. Comparson of omponent magntudes for smulated data. A-B) Satter plots of true versus estmated magntudes for NN (left), IN (mddle) and VN (rght) methods for soures S (top row), S (mddle row) and S6 (bottom row). Estmates from GICA3 (A) and DR (B) bak-reonstruton are dsplayed. R ( g, g ) statsts are provded on eah axs. C-D) Same data n (A, B) on a sngle axs shows true magntudes versus estmated NN (red), IN (green) and VN (blue) magntudes for soures S (damonds), S (rles) and S6 (squares). Results from GICA3 (C) and DR (D) bak-reonstruton are dsplayed. True and estmated magntudes for eah method are normalzed to range from to. Dotted lnes show the least-squares lnear ft to the data ponts. R ( gg, ) statsts for eah method are provded n the legend. If symbols are not vsble, they have been obsured by other magntudes estmated wth other methods. Fgure 4. Comparson of omponent deteton for smulated data. A) Comparson of ROC urves between NN (red), IN (green), and VN (blue) normalzaton methods and GICA3 (sold lnes, flled squares) and DR (dotted lnes, open squares) bak-reonstruton methods for omponents S (left), S (mddle) and S6 (rght). Curves were generated by varyng the t- statst threshold from to n steps of.. Squares ndate the pont on the urve orrespondng to a t-statst threshold of P.5 (Bonferron orreted). B) Examples of voxel lassfaton for S6 at the threshold denoted by squares n (A). Page 33 of 34

37 Fgure 5. Comparson of aggregate SMs for restng-state data. A) Aggregrate SMs of RSNs for NN (left olumn), IN (enter olumn), and VN (rght olumn) methods. Maps are thresholded at an ntensty value of 3 (arbtrary unts from the ICA deomposton) to hghlght areas wth strong atvaton. Dsplay sles were seleted by averagng the oordnates wth maxmal varane aross the three methods and are ndated at the top of eah panel n MNI oordnates (x,y,z). B) Jont-dstrbuton of voxel ntenstes between NN and IN preproessng methods (left) and NN and VN (rght) for RSN. Gray lnes denote unty. C) Jont-dstrbuton of voxel ntenstes between the NN aggregate and average VN map bak-reonstruted wth DR. Note that the NN aggregate s a saled verson of the average NN map bak-reonstruted wth GICA3. Also note logarthm olorbar sale, refletng the large number of ponts wth low atvaton. Fgure 6. Comparson of sngle-subjet SM relablty for restng-state data. A) Maps of SM relablty statsts ( ICC S ) at the same sles shown n Fgure 5A for NN (left olumn), IN (enter olumn) and VN (rght olumn) SMs bak-reonstruted wth GICA3 and NN (rght sde of dashed lne) SMs bak-reonstruted wth DR. ICC S statsts are thresholded at.5 to hghlght areas wth moderate to hgh relablty. B) Jont hstograms between RSN average voxel ntenstes and ICC S statsts for NN (top row), IN (mddle row), and VN (bottow row) wth GICA3 (left) and DR (rght) bak-reonstruton. Note the dfferent sales of voxel ntenstes for GICA3 and DR. Gray shaded regons denote voxels wth magntude greater than. for GICA3 and 3 for DR; horzontal dashed lnes sgnfy the medan ICC S for voxels exeedng ths threshold. C) Medan ICC S values at ntensty thresholds spannng the range of dstrbuton (GICA3: to. n steps of.; DR: to 7 n steps of ). Colored lnes represent the mean aross all sx RSNs for NN (red), IN (green), and VN (blue) methods wth GICA3 (sold lnes) and DR (dotted lnes) bak-reonstruton; shaded areas ndate ± standard error. Fgure 7. Comparson of omponent magntude relablty for restng-state data. A) Lne plots of magntude relablty statsts ( ICC g ) averaged over RSNs for eah normalzaton method wth GICA3 (left) and DR (rght) bak-reonstruton. ICC g statsts are alulated usng all subjets (squares, sold lnes) and wth outlers removed (rles, dotted lnes). Error bars ndate ± standard error. B) Satter plots between vst and vst omponent magntudes (RSN ) for NN (top row), IN (mddle row) and VN (bottom row) wth GICA3 (left) and DR (rght) bak-reonstruton. Labels on eah pont ndate the subjet number. Outlers (subjets 6 and 3) are ndated wth blak outlned boxes. Gray lnes denote perfet orrespondene between vsts and. ICC g statsts for all subjets (blak) and wth outlers removed (gray) are provded n the lower rght orner of eah plot. Page 34 of 34

38 4. Table Table. Auray of omponents for smulated data Soure R aggregate SM R sngle-subjet SM, mean (SD) R sngle-subjet TC, mean (SD) Model Order NN IN VN NN IN VN NN IN VN S GICA3.9 (.8).9 (.8).7 (.5).99 (.).99 (.).95 (.3) DR.9 (.9).9 (.9).9 (.9).99 (.).99 (.).98 (.) GICA3.9 (.8).9 (.8).7 (.5).99 (.).99 (.).97 (.) DR.9 (.9).9 (.9).9 (.9).99 (.).99 (.).99 (.) GICA3.9 (.8).9 (.8).7 (.5).99 (.).99 (.).96 (.3) DR.9 (.9).9 (.9).9 (.9).99 (.).99 (.).98 (.) S GICA3.53 (.7).54 (.7).39 (.3).7 (.4).73 (.5).36 (.5) DR.3 (.).3 (.).3 (.9).73 (.5).74 (.5).37 (.7) GICA3.57 (.8).57 (.8).46 (.5).9 (.3).9 (.4).9 (.4) DR.57 (.9).57 (.9).56 (.9).89 (.8).89 (.8).9 (.7) GICA3.57 (.8).57 (.8).46 (.5).9 (.4).89 (.5).9 (.5) DR.56 (.9).56 (.9).55 (.9).89 (.9).89 (.9).9 (.8) S GICA3.68 (.6).68 (.6).66 (.5).89 (.).9 (.).84 (.5) DR.6 (.9).6 (.9).58 (.7).9 (.9).9 (.8).84 (.3) GICA3.7 (.6).69 (.6).65 (.5).96 (.5).96 (.5).96 (.5) DR.69 (.7).69 (.7).69 (.7).97 (.3).97 (.3).97 (.4) GICA3.7 (.6).69 (.6).66 (.5).95 (.6).96 (.5).95 (.5) DR.68 (.8).68 (.8).68 (.7).97 (.4).97 (.4).96 (.5)

39 Table. Smlarty of omponents between ampltude normalzaton methods for restng-state data Restng-State Network R aggregate SM R sngle-subjet SM, mean (SD) R sngle-subjet TC, mean (SD) (NN,IN) (NN, VN) (IN, VN) (NN,IN) (NN, VN) (IN, VN) (NN,IN) (NN, VN) (IN, VN) Medal vsual GICA3.96 (.).73 (.4).7 (.4).96 (.6).8 (.3).7 (.9) DR.94 (.6).8 (.).78 (.3).99 (.).77 (.3).75 (.5) Lateral vsual GICA3.75 (.3).45 (.4).5 (.4).86 (.8).56 (.9).7 (.9) DR.8 (.6).5 (.).6 (.).88 (.8).37 (.).49 (.) 3 Sensormotor GICA3.75 (.3).45 (.5).43 (.6).8 (.).47 (.7).3 (.) DR.75 (.7).5 (.8).53 (.).8 (.9).38 (.3).33 (.3) 4 Posteror DMN GICA3.88 (.).58 (.5).5 (.5).93 (.6).7 (.).66 (.3) DR.8 (.).68 (.).59 (.4).94 (.4).75 (.).7 (.4) 5 R Frontoparetal GICA3.8 (.).6 (.4).45 (.5).87 (.7).6 (.9).48 (.) DR.78 (.7).76 (.8).56 (.).89 (.6).6 (.4).5 (.3) 6 L Frontoparetal GICA3.74 (.).6 (.4).57 (.5).8 (.).58 (.).49 (.) DR.68 (.6).7 (.8).67 (.).84 (.).64 (.3).63 (.)

40 Table 3. Smlarty of omponents between GICA3 and DR bak-reonstruton methods for restng-state data Restng-State Network R average SM R sngle-subjet SM, mean (SD) R sngle-subjet TC, mean (SD) (NN,NN) (IN,IN) (VN, VN) (NN,NN) (IN,IN) (VN, VN) (NN,NN) (IN,IN) (VN, VN) Medal vsual (.).77 (.9).64 (.8).97 (.4).96 (.6).89 (.7) Lateral vsual (.6).7 (.7).54 (.9).97 (.6).94 (.8).8 (.) 3 Sensormotor (.8).66 (.7).5 (.7).97 (.3).95 (.4).86 (.) 4 Posteror DMN (.9).7 (.8).58 (.9).97 (.).96 (.3).9 (.) 5 R Frontoparetal (.9).73 (.7).55 (.8).97 (.3).97 (.3).88 (.8) 6 L Frontoparetal (.).74 (.9).57 (.9).98 (.).98 (.).89 (.8)

41 5. Fgure Clk here to download 5. Fgure:.eps S g =. S g =.3 S3 g =.9 S4 g = S5 g = S6 g = S7 g =.5.5 S8 g = tme ponts

42 5. Fgure Clk here to download 5. Fgure:.eps A S S S S6 +max NN IN VN NN IN VN NN IN VN -max Ŝ Ŝ S Ŝ B 3 R =.99 R =.99 R =.9 R =.97 R =.97 R =.89 R =.96 R =.96 R = S Subjet Subjet 7.5 Subjet +3.3 z-sore -3.3 S NN IN VN NN IN VN NN IN R =.95 R =.95 R =.7 R =.5 R =.5 R =.4 R =.8 R =.8 R =.77 VN GICA3 S ɶ R =.95 R =.95 R =.96 R =.5 R =.5 R =.5 R =.8 R =.8 R =.8 DR S ɶ C R ɶ z sore (std) Subjet 7 Subjet Subjet 4 true GICA3 DR NN IN VN R R ɶ z sore (std).5.5 GICA3: R = [.98,.97,.95] DR: R = [.98,.98,.97] tme ponts.5.5 GICA3: R = [.93,.93,.93] DR: R = [.93,.93,.94] tme ponts.5.5 GICA3: R = [.99,.99,.98] DR: R = [.99,.99,.99] tme ponts

43 5. Fgure 3 Clk here to download 5. Fgure: 3.eps S A NN.3 R = R =.94.4 GICA3 IN. R =.83.5 VN B NN.5 R =.86. DR IN.5 R =.86. VN.5 R = S.8 R = R =.95. R = R = R = R = S6 estmated magntude C..4.5 R = true magntude..4.3 R = GICA3..4. R = estmated magntude D R = true magntude R = DR R = estmated magntude (normalzed) S S S6 NN (R =.93) IN (R =.97) VN (R =.73) estmated magntude (normalzed) S S S6 NN (R =.89) IN (R =.89) VN (R =.9) true magntude (normalzed) true magntude (normalzed)

44 5. Fgure 4 Clk here to download 5. Fgure: 4.eps A True Postve Rate B S GICA3 DR NN IN VN S..4.6 S6 S6 False Postve Rate NN IN VN true GICA3 DR

45 A5. Fgure RSN 5 (+4, -8, +7), g = 5.4 Clk NN here to download IN 5. Fgure: VN 5.eps RSN (+3, -79, -), g =.9 NN IN VN L R RSN 3 (+6, -, +), g = 3.8 NN IN VN RSN 4 (+4, -65, -37), g = 3.3 NN IN VN RSN 5 (+4, -54, +45), g =. NN IN VN RSN 6 (-43, -66, +44), g =. NN IN VN ntensty (a.u.) B aggregate voxel ntensty -max RSN R =.98 R =.87 IN VN NN NN max ount 5 R = aggregate voxel ntensty aggregate voxel ntensty C average voxel ntensty VN-DR NN

46 5. Fgure 6 Clk here to download 5. Fgure: 6.eps A RSN (+4, -8, +7) NN IN VN NN RSN (+3, -79, -) NN IN VN NN B GICA3 RSN DR NN NN L R ICCS RSN 3 (+6, -, +) NN IN VN NN RSN 4 (+4, -65, -37) NN IN VN NN IN IN VN VN average voxel ntensty ount RSN 5 (+4, -54, +45) NN IN VN NN RSN 6 (-43, -66, +44) NN IN VN NN C GICA3 ntensty threshold...8 GICA3 DR ICC S.5. medan ICCS.6.4. GICA3 DR NN IN VN 3 6 DR ntensty threshold