Structural Connectome Validation Using Pairwise Classification

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by  Dmitry Petrov

STRUCTURALCONNECTOMEVALIDATIONUSINGPAIRWISECLASSIFICATION
DmitryPetrov⋆† BorisGutman† AlexanderIvanov⋆ JoshuaFaskowitz†
NedaJahanshad† MikhailBelyaev‡⋆ PaulThompson†
⋆KharkevichInstituteforInformationTransmissionProblems,Moscow,Russia
†ImagingGeneticsCenter,UniversityofSouthernCalifornia,LosAngeles,USA
‡SkolkovoInstituteofScienceandTechnology,Moscow,Russia
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ABSTRACT ICCisgenerallylow,whichcomplicatesmethodcomparison.

n Also, theparametricconstraintsofclassicICC[10]maynot
In this work, we study the extent to which structural
a bevalid. Non-parametricapproachesfreeofdatadistribution
J connectomesandtopologicalderivativemeasuresareunique
assumptionsmaybemoresuitable.
0 to individual changes within human brains. To do so, we
To address this issue, we propose a pairwise classifica-
3 classify structural connectome pairs from two large longi-
tudinal datasets as either belonging to the same individual tionapproachtointrinsicallyassessconnectomeutilityacross
] time, somewhat in line with a recent method for functional
C or not. Our data is comprised of 227 individuals from the connectomes as well [11]. For each set of connectomes Ci
AlzheimersDiseaseNeuroimagingInitiative(ADNI)and226 j
N and features f(Ci) in question, we construct all possible
fromtheParkinson’sProgressionMarkersInitiative(PPMI). j
o. Weachieve0.99areaundertheROCcurvescoreforfeatures pairs (Ci1,Ci2), where i-indices correspond to images and
j1 j2
bi which represent either weights or network structure of the j-indices correspond to subjects. We then conduct a linear
q- cOounrnaepcptoromaecsh(mnoadyebdeeugsreefeusl,fPoargeelRimaninkatainndglnoociaslyeffefiactuiernecsya)s. colfasthsiefisceatpiaoinrsonwtihtherpeasiprwecitsetoditfhfeeretanrcgeest∥vfa(rCiajib11l)e−y:f(yCji=22)1∥
[
apreprocessingstepinbrainagingstudiesandearlydiagnosis ifj1=j2,0else.

2 classificationproblems. We test this pipeline on structural connectomes derived
v from two publicly available neuroimaging datasets: ADNI
7 Index Terms— machine learning, DWI, structural con-
and PPMI. These datasets have scanned subjects multi-
4 nectomes
ple times, with at least a one year interval between scans.
8
7 Weachieve0.99ROCAUCbothfordirectconnectomemea-
0 1. INTRODUCTION sures(bagofedges)andforfeaturesrepresentingconnectome
1. structure (PageRank), suggesting that the tested data is reli-
0 Predictivemodelingofneurodegenerativediseasesusingdif- ableenoughtodistinguishsubjectsbytheproposedapproach.
7 fusionMR-basedstructuralconnectomeshasbecomeapop- Similar research was conducted by Yeh et al. [12]. Though
1 ularsub-genreofneuroimaging[1]. Thegreatvarietyofpos- theauthorsusedalocalstructuralconnectome,differentfea-
:
v siblepre-processingapproachesneededforconnectomecon- tures, datasets and connectome construction pipelines, they
i structionleadstopotentialchallengesindownstreamapplica- arrivedatsimilarconclusions.
X
tionoftheconnectomes,forexample,inaclassificationtask.
r
a Choices of e.g, non-linear registration, parcellation, or trac-
2. PAIRWISECLASSIFICATION
tography, may all have a substantial impact ([2], [3]). This
stateofaffairspresentsachallengebothintermsofintrinsic
We propose the following pipeline for pairwise connectome
connectomereliability,andthedegreetowhichtherecovered
classification: normalization, building connectome features,
connectomes are valid, if summary, representations of true
building pairwise features based on connectome features.
brainconnectivity([4],[5],[6],[7]).
Let’s denote a set of connectomes as {Ci}, where j is an
At the same time, the performance of a particular case- j
indexofasubjectandiisanindexofanimage.
control classifier may not suffice as a means of data verifi-
cation due to small samples and high dimensionality. Al-
ternative, more objective validation may be needed, such as 2.1. Normalizations
the frequently used Intra-class Correlation Coefficient (ICC)
Topological normalization of connectivity matrices may be
ontest-retestdata([8],[9]). However,structuralconnectome
useful prior to any analysis, because the number of detected
[email protected] streamlines is known to vary from individual to individual
and can also be affected by fiber tract length, volume of 3. EXPERIMENTS
cortical regions and other factors ([13], [14]). There is no
consensusonthebestnormalizationapproach,soweusethe 3.1. Basedata
three following topological normalization schemes along-
We used two datasets for our experiments. Our first dataset,
side with pure weights (no normalization at all) – by mean,
theAlzheimersDiseaseNeuroimagingInitiative(ADNI2),is
by maximum and binary normalization with zero threshold:
comprisedof227individuals(675scans),meanageatbase-
ab = 1ifa >0,0elsewherea isaconnectomeedge.
kl kl kl linevisit73.1±7.4,99females. Eachindividualhadatleast
1 brain scan and at most 6 scans. The data include 46 peo-
2.2. Networkfeatures
plewithAD(111ADscans),80individualswithEMCI(247
MCI scans), 40 people with LMCI (120 LMCI scans) and
For each connectome and each normalization we build “bag
61 healthy participants (160 scans). Second, we used imag-
of edges” vectors from the upper triangle of the symmetric
ing data from the Parkinsons Progression Markers Initiative
connectivity matrix. In addition, we calculate eight net-
(PPMI)database. FromitweselectedsubjectswithPD(159
work metrics for each node: weighted degrees, or strength;
subjects)andhealthycontrols(67subjects). Theseincludeda
closeness, betweenness and eigenvector centralities; local
totalof226individuals(456scans),meanageatthebaseline
efficiency; clustering coefficient; weighted number of trian-
61.0±9.8 years, 79 females. Each individual had at least 1
gles around node. We choose these features because they
brainscanandatmost4scans.
are well-described and reflect different structural properties
of connectomes [15]. We also calculate PageRank for each
node. Introduced in 1998 by Brin and Page [16] this metric 3.2. Networkconstruction
roughlyestimatesprobabilitythatapersonrandomlyclicking
InhomogeneitycorrectedT1-weightedimagesforADNIand
onlinksinthenetworkwillarriveatparticularnode.
PPMI data were processed with FreeSufer’s [17] recon-all
pipeline to obtain a triangular mesh of the gray-white mat-
2.3. Pairwisefeatures
ter boundary registered to a shared spherical space, as well
Each normalization and set of features described above de- as corresponding vertex labels per subject for a cortical par-
finesamappingfromconnectomespacetofeaturespaceC → cellationbasedontheDesikan-Killiany(DK)atlas[18]. This
f(C).Sinceourgoalistocheckhowwellthismappingsepa- atlas includes 68 cortical brain regions; hence, our cortical
ratesconnectomesinit,weproposevariouspairwisefeatures. connectivitymatriceswere68×68.
Foreachsetofconnectomefeaturesinquestionwemakeall Inparallel,T1wimageswerealigned(6-dof)tothe2mm
possible pairs of connectome features – (f(Ci1),f(Ci2)). isotropic MNI 152 template. These were used as the tem-
For each pair, we assign a binary target variablje1– 1 ifjc2on- plate to register the average b0 of the DWI images, in or-
nectomes are from the same subject (j = j ), 0 – if they der to account for EPI related susceptibility artifacts. DWI
1 2
are from different subjects (j ≠ j ). Finally, for each pair images were also corrected for eddy current and motion re-
1 2
webuildavectorofthreefeatures,describingtheirdifference lated distortions. Rotation of b-vectors was performed ac-
∥f(C )−f(C )∥accordingtol ,l andl norms. cordingly. Tractography for ADNI data was then conducted
1 2 1 2 ∞
usingthedistortioncorrectedDWIin2mmisotropicMNI152
space. Probabilistic streamline tractography was performed
2.4. Classifiersandvalidation
usingtheDipy[19]LocalTrackingmoduleandimplementa-
We use linear classifiers for pairwise classification: logistic tionofconstrainedsphericaldeconvolution(CSD)[20]witha
regression (LR), SVM with linear kernel and stochastic gra- sphericalharmonicsorderof6. Streamlineslongerthan5mm
dientdescent(SGD)withmodifiedHuberloss. Wescalefea- withbothendsintersectingthecorticalsurfacewereretained.
tures with standard scaling and apply elastic-net regulariza- Edgeweightsintheoriginalmatricesareproportionaltothe
tionforeachofclassifiers. numberofstreamlinesdetectedbythealgorithm.
Model performance we measure with area under ROC PPMI data were processed in a slightly different fashion
curve (ROC AUC) through a two-step validation proce- to account for variability in the acquisition protocols and to
dure. First, for each dataset, we perform hyperparameter show our method is not dependent on any single processing
grid search based on a 10-fold cross-validation with a fixed scheme. Imageswereinitiallydenoisedwithanadaptivede-
random state for reproducibility. For each model we varied noising algorithm [21] and two DWI acquisitions from each
overallregularizationparameter, l -ratioandnumberofiter- subject were merged. DWI images were corrected for eddy
1
ationsforSGD.Thenweevaluatethebestparameterson100 currentandmotionrelateddistortions,thennon-linearlyepi-
train/test splits with fixed different random states (test size corrected with ANTs SyN. Rotation of b-vectors was per-
wassetto20%ofdata).WereporttheROCAUCdistribution formed accordingly. Tractography for PPMI data was then
on these 100 test splits for each combination of normaliza- conductedin2mmisotropicMNI152space,againusingthe
tion/basefeatures/diagnosticgroupinresultssection. DipyLocalTrackingmodule. Ateachvoxel,theCSDwasfit-
tedrecursively[20]withasphericalharmonicorderof6. De-
terministicstreamlinetractographywasseededattworandom
locations in each white matter voxel. Similar to the ADNI
data,onlystreamlineslongerthan5mmwithbothendsinter-
sectingthecorticalsurfacewereretained.
3.3. Pairwisedata
Foreachsetofconnectomesdescribedabove(ADNI,PPMI)
wemadeallpossiblepairsofconnectomesasdescribedin2.3.
Usingthistechniqueweobtained227475pairs(764ofwhich
were labeled as 1) from ADNI2 data and 152031 pairs from Fig.2. ROCAUCdistributionsforpairwiseclassificationon
PPMI data (301 of which were labeled as 1). Due to huge all ADNI data depending on choice of connectome normal-
imbalanceofclassesingeneratedpairs, weusedallsamples izing scheme and base features. For betweenness centrality,
with label 1 and equally sized random subsample of 0. Our clustering coefficient, eigenvector centrality, PageRank and
result do not depend for different subsamples of 0s, so we triangles,wereportresultsonlyforthebinaryandmeannor-
reportthemforafixedrandomstate. malizations. Normalizing by the other norms affects these
featuresidenticallytothemeannormalization.
3.4. Pairwiseclassificationperformance
Figures 2 and 3 quantify this observation for ADNI and
PPMIdataintermsofROCAUCdistributionsdependingon
normalizationandbasefeatures. Weseethat0.99ROCAUC
can be achieved either for connectome weights themselves,
or for features that capture connectome structure. We also
seethatthechoiceofnormalizationgreatlyaffectstheaccu-
racyofpairwiseclassification. Normalizingbythemeanisa
winnerinmostcases,withtheexceptionofeigenvectorcen-
trality and clustering coefficient features. It is interesting to
notethatforclusteringcoefficientandeigenvectorcentrality,
binarynormalization performedbetter thanothernormaliza-
tionseventhoughitpreservessomewhatlessinformation.
Figures3-4showtheROCAUCdistributionsofpairwise
classification depending on the base features and diagnos-
tic group for connectomes normalized by the mean. We see
thatthereisalmostnodifferenceinpairwiseclassificationre-
sultsindifferentdiagnosticgroups. Wenotethatinterquartile
spreadishighfordiagnosticgroupswiththesmallestnumber
ofsubjects.
4. CONCLUSION
Fig. 1. Multidimensional scaling for ADNI data based on
l norm. Pointswithsamecolorsrepresentsamesubjects. To
2 We have presented a method for structural connectome fea-
avoid mess on the pictures we’ve decided to color only 17
ture validation through pairwise classification which is free
subjects. Othersubjectsrepresentedbysmallergreymarkers.
ofdistributionassumptions. WetestedthispipelineonADNI
Marker shape indicates diagnostic group: ◯ – controls, △ –
andPPMIdataandobtainedhighclassificationperformance
LMCI,▽–EMCI,◻–AD.
in terms of ROC AUC suggesting that there are mappings
fromconnectomestofeaturespacesthatatleastdifferentiate
Figure1showsmultidimensionalscaling(MDS)basedon subjectsfromeachother.
l -norm dissimilarity matrix of bag of edges for ADNI sub- Itisworthnotingthatpairwiseclassificationisnotafea-
2
jects (for PPMI data picture is essentially the same, so we tureselectiontechniqueforclassificationtasks. Itispossible
omittedit). Weseethatinmostcasesimagesfromsamesub- that a feature distinguish classes in the context of this work,
jectareneareachotherinthatfeaturespace. Wealsoseethat but fails to distinguish subjects, for example in a diagnostic
thereisnosuchclearpicturewithdiagnosticgroupslabels. classification task. Our results suggest that pairwise classi-
Fig.3. ROCAUCdistributionsforpairwiseclassificationon Fig.5. ROCAUCdistributionsforpairwiseclassificationon
all PPMI data depending on choice of connectome normal- PPMIdatafordifferentdiagnosticgroupsondifferent“base”
izing scheme and base features. For betweenness centrality, features. These results are reported for connectome normal-
clustering coefficient, eigenvector centrality, PageRank and izationbythemean.
triangles,wereportresultsonlyforthebinaryandmeannor-
malizations. Normalizing by the other norms affects these
featuresidenticallytothemeannormalization.
Finally, due to limitations of the data used here, same-
subjectpairswereconstructedfromdiffusionimagesacquired
at least one year apart. Such a time scale provides ample
opportunityforsubstantiallongitudinaleffects,suchasthose
duetoneurodegeneration, toaffectourfeatures. Aswecan-
not exclude such effects, any conclusions to be drawn about
optimalnetworkfeaturesandnormalizationsforfurtherstud-
iesmustbemadewiththeappropriatereservations.
5. ACKNOWLEDGMENTS
Theresultsofsections2and3arebasedonthescientificre-
searchconductedatIITPRASandsupportedbytheRussian
Fig.4. ROCAUCdistributionsforpairwiseclassificationon ScienceFoundation(project14-50-00150).
ADNIdatafordifferentdiagnosticgroupsondifferent“base” Someofdatausedinpreparationofthisarticlewereob-
features. These results are reported for connectome normal- tainedfromtheAlzheimersDiseaseNeuroimagingInitiative
izationbymean. (ADNI) database. A complete listing of ADNI investiga-
tors as well as data acquisition protocols can be found at
adni.loni.usc.edu. Additional data were obtained
from the Parkinsons Progression Markers Initiative (PPMI)
ficationmaybeusefulforvalidatingpreprocessingpipelines
database. For up-to-date information on the study, visit
andparticularfeaturesintermsofhowmuchsubject-related
www.ppmi-info.org.
signal they preserve. As such, it may be treated as a “first-
pass”forconnectomefeaturestobeusedinfurtherstudies.
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