Connectomics is gaining increasing interest in the scientific and clinical communities. It consists in deriving models of structural or functional brain connections based on some local measures. Here we focus on structural connectivity as detected by diffusion MRI. Connectivity matrices are derived from microstructural indices obtained by the 3D-SHORE. Typically, graphs are derived from connectivity matrices and used for inferring node properties that allow identifying those nodes that play a prominent role in the network. This information can then be used to detect network modulations induced by diseases. In this paper we take a complementary approach and focus on link as opposed to node properties. We hypothesize that network modulation can be better described by measuring the connectivity alteration directly in the form of modulation of the properties of white matter fiber bundles constituting the network communication backbone. The goal of this paper is to detect the paths that are most altered by the pathology by exploiting a feature selection paradigm. Temporal changes on connection weights are treated as features and those playing a leading role in a patient versus healthy controls classification task are detected by the Infinite Feature Selection (Inf-FS) method. Results show that connection paths with high discriminative power can be identified that are shared by the considered microstructural descriptors allowing a classification accuracy ranging between 83% and 89%

Granziera, C.

Menegaz, G.

Obertino, S.

Roffo, G.

English

Enlighten

     Obertino, S., Roffo, G., Granziera, C. and Menegaz, G. (2016) Infinite Feature Selection on Shore-Based Biomarkers Reveals Connectivity Modulation after Stroke. In: 2016 International Workshop on Pattern Recognition in Neuroimaging (PRNI), Trento, Italy, 22-24 June 2016, pp. 1-4. ISBN 9781467365307 (doi:10.1109/PRNI.2016.7552347)   This is the author’s final accepted version.  There may be differences between this version and the published version. You are advised to consult the publisher’s version if you wish to cite from it.  http://eprints.gla.ac.uk/149663/                                                                         Deposited on: 11 October 2017              Enlighten – Research publications by members of the University of Glasgow http://eprints.gla.ac.uk  INFINITE FEATURE SELECTION ON SHORE-BASED BIOMARKERS REVEALSCONNECTIVITY MODULATION AFTER STROKES. Obertino1, G.Roffo1, C. Granziera2, G. Menegaz11 Dept. of Computer Science, University of Verona, Italy2 Martinos Center for Biomedical Imaging, Massachusetts General Hospital and Harvard Medical School,Chalestown, MA, United StatesABSTRACTConnectomics is gaining increasing interest in the scientificand clinical communities. It consists in deriving models ofstructural or functional brain connections based on some lo-cal measures. Here we focus on structural connectivity asdetected by diffusion MRI. Connectivity matrices are derivedfrom microstructural indices obtained by the 3D-SHORE.Typically, graphs are derived from connectivity matrices andused for inferring node properties that allow identifying thosenodes that play a prominent role in the network. This in-formation can then be used to detect network modulationsinduced by diseases. In this paper we take a complementaryapproach and focus on link as opposed to node properties. Wehypothesize that network modulation can be better describedby measuring the connectivity alteration directly in the formof modulation of the properties of white matter fiber bundlesconstituting the network communication backbone. The goalof this paper is to detect the paths that are most altered by thepathology by exploiting a feature selection paradigm. Tem-poral changes on connection weights are treated as featuresand those playing a leading role in a patient versus healthycontrols classification task are detected by the Infinite Fea-ture Selection (Inf-FS) method. Results show that connectionpaths with high discriminative power can be identified thatare shared by the considered microstructural descriptors al-lowing a classification accuracy ranging between 83% and89%.Index Terms— Feature Selection, Stroke, 3D-SHORE1. INTRODUCTIONRecent advances in diffusion MRI led to the definition ofnumerical parameters describing microstructural properties.The so called Ensemble Average Propagator (EAP) derivedmodels approximate the diffusion signal by series expan-sion over basis functions providing an analytical solutionfrom which indices can be derived in closed form. Amongthe most promising ones is the 3D-SHORE [1] model formwhich, under some ideal conditions, geometrical descrip-tors of the diffusion compartments can be inferred [2, 3].Combined with quantitative tractography, such indices allowmodeling structural connectivity through the construction ofthe connectivity matrix from which a representation of thenetwork in the form of a graph is derived. Typically, cor-tical/subcortical regions represent the nodes and the matrixelements represent the weight of the link between pairs ofregions. Then, graph theory is exploited for deriving nodeproperties and thus identifying those playing a leading role inthe network. This information can be exploited for detectingnetwork modulations due to some pathological conditions.In this paper we take a complementary approach focusingon connections instead than on nodes, with the aim of iden-tifying the paths that are more prominent in the networkmodulation. The reason behind this choice is the observa-tion that pathologies compromise the communication amongregions by disrupting the white matter fibers that constitutethe backbone for communication. In consequence, we hy-pothesize that network modulation can be better described bymeasuring the connectivity alteration directly in the form ofmodulations of the properties of white matter fiber bundles.The objective is to check this hypothesis by detecting thepaths that are most altered by the pathology in a feature se-lection paradigm. Temporal changes on connection weightsare treated as features and those playing a leading role ina patients versus healthy controls classification task are de-tected by the Infinite Feature Selection (Inf-FS) method. Thenovelty of this approach is twofold. First, the focus is onlinks instead than on nodes, as previously stated. Second,the set of connections that are altered by the pathology re-sults from a feature selection task. Previous works exploitingmicrostructural indices for assessing neuronal plasticity afterstroke have been focusing on a predefined set of manuallyselected cortical and subcortical regions as the end-points ofthe considered links [4, 5, 6]. The proposed approach relaxesthe constraint on the choice of the regions and connectionssuch that the relevant links naturally emerge by feature selec-tion. This has the potential of providing new insights on thechanges induced by pathologies both locally and globally.2. METHODSFour microstructural indices are derived from the 3D-SHOREmodel. Connectivity matrices are derived from each indexby quantitative tractography. Each entry of the connectivitymatrix represents the absolute percent temporal variation ofthe mean value of each index along the connection linking thecorresponding cortical/subcortical regions and plays the roleof feature in the classification task. Feature selection by Inf-FS is performed for detecting the set of connections playing adominant role in group discrimination.2.1. DatasetA total of 18 subjects (9 patients and 9 age and gendermatched controls) were imaged following Diffusion Spec-trum Imaging (DSI) scans [TR/TE = 6600/138 msec, FoV =212× 212 mm2, 34 slices, 2.2× 2.2× 3 mm3 resolution, 258diffusion directions, b-value = 8000 s/mm2, ∼ 25 min scantime] within one week (tp1) and one month (± one week,tp2) after stroke for patients and one month apart for controls.Pre-processing was performed as in [4]. All subjects pro-vided written informed consent and the Lausanne UniversityHospital review board approved the study protocol.2.2. 3D-SHORE modelThe SHORE model decomposes the signal E(q) as a linearcombination of basis functions that are the solutions of the3D harmonic oscillator. The orthonormal formulation of the3D-SHORE model is expressed asE(qu) =Nmax∑l=0,even(Nmax+l)/2∑n=ll∑m=−lcnlmΦnlm(qu) (1)whereNmax is the maximal order of the functions in the trun-cated series and Φnlm(q) is the orthonormal 3D-SHORE ba-sis, defined asΦnlm(qu) =[2(n− l)!ζ3/2Γ(n+ 3/2)]1/2(q2ζ)l/2(2)× exp(−q22ζ)× Ll+1/2n−l(q2ζ)Y ml (u)where Γ is the Gamma function and ζ is a scaling parameterdependent on the diffusion time τ and the diffusivity D. Allthese models provide close approximations of the diffusionsignal and allow deriving important EAP features such as theOrientation Distribution Function (ODF) in a reliable manner.From EAP models, it is also possible to derived microstruc-ture related indices, namely the Return To the Origin Prob-ability (RTOP), the Return To the Axis Probability (RTAP),and the Return To the Plane Probability (RTPP). RTOP, RTAPand RTPP represent the zero net displacement probabilities inthe three, two and mono-dimensional cases, respectively. Un-der some ideal conditions regarding the acquisition protocolthey provide an estimation of the mean pore geometry beingrespectively proportional to the reciprocal of the mean vol-ume, cross-sectional area and length of the pore [1]. In thiswork, only RTAP was usedRTAP =∫R2E(q⊥)d2q⊥ =∫RP (~r‖)dr (3)Additionally, Generalized Fractional Anysotropy (GFA) andPropagator Anysotropy (PA), expressing the distance betweenthe EAP and its isotropic component, were calculated. Theseindices reflect the degree of restriction of the water moleculesin the voxel, which is directly linked to the underlying poreshape.Fig. 1: Image of RTAP in presence of a stroke lesion.2.3. Feature extraction by tract-based analysisThe ODFs were reconstructed and fiber-tracking was per-formed via a streamline algorithm (www.cmtk.org). Brainsegmentation was performed using the Desikan-Killany atlasprovided by Freesurfer (www.surfer.nmr.mgh.harvard.edu)resulting in as a set of 32 cortical and 7 subcortical regions.The mean value of the microstructural indices along the fiberswere calculated and the absolute percentage changes acrosstime points were used for generating one connectivity matrixof size 39× 39 per subject per index as∆tp12,i =|Fi,tp1 − Fi,tp2|Fi,tp1(4)where Fi denotes the index in use.2.4. Feature SelectionLet Gn = (V,E) be an undirected graph where V is the setof vertices corresponding to ROIs, and E codifies weightededges among connections. We represent the graph Gn by theadjacency matrix Dn, where each element dnij , 1 ≤ i, j ≤ N ,N = 39 is the corresponding entry of the connectivity matrixof subject n, n = 1, . . . , 18. In order to measure how welleach connection separates the two classes of patients (P ) andcontrols (C), we define a discriminant matrix M by using asimple heuristic for measuring class separation. The heuristicis based on the separation of the class means. In the two-class problem at hand there are Nc = 9 adjacency matrices ofclass C and Np = 9 adjacency matrices of class P for eachmicrostructural index RTAP, R, GFA and PA. For each entry,that is for each feature, the mean and variance are estimatedacross subjects to generate the matrix M whose entries areMi,j =µCi,j − µPi,j(σCi,j)2 + (σPi,j)2(5)whereµki,j =1Nk∑n∈Nkdni,j , k ∈ {C,P}.In the same way, we calculate the standard deviation vectorsσki,j for each feature dki,j of class k.Our approach proposes to rank the features by importanceregarding the patients versus controls classification task. Tothis end, we use the matrix M as input of the infinite featureselection (Inf-FS) [7] algorithm, where the percent absolutechanges of the microstructural values along the connectionsare seen as features. By construction, the Inf-FS method al-lows to use convergence properties of the power series of ma-trices, and evaluate the relevance of a feature with respect toall the other ones taken together. In the Inf-FS formulation,each path of a certain length l over the graph is seen as apossible selection of features. Letting these paths tend to aninfinite number permits the investigation of the importance ofeach feature. As a result, this method assigns a score of “im-portance” to each feature by taking into account all the pos-sible feature subsets, therefore the higher the final score, themost important the feature. In this work a simplified versionwhere only the Fisher distance of the features across classeswas used. The final rank was then used in our experimentalsection, where we proved that the selected connections turnout to be effective from the classification point of view. In or-der to obtain some measure of relevance of the subset of fea-tures (connections), a classification approach was followed.Performance was defined in terms of accuracy, precision andrecall. Moreover, the ROC curve was obtained as well as thecorresponding the area under the curve (AUC). Training andtesting pools were created using a cross-validation leave-1-out method, while a SVM was used for classification.3. RESULTS & DISCUSSIONFigure 3 illustrates the performance of the classifier as a func-tion of the number of features that are retained after the Inf-FSbased selection in terms of accuracy, precision, recall and areaunder the curve (AUC). Good performance was obtained us-ing a relatively low number of features, suggesting that fewkey connections could be the key for discriminating patientsfrom controls. Among the set of the first 20 features, six werecommon to the four indices. These correspond to connectionsbetween the pairs of regions illustrated in Figure 2.Fig. 2: A) lateral occipital (Ol) - para central (PCG) (as sup-plementary motor area); B) lateral orbito frontal (Fol) - Cau-date (Cau); C) isthmus cingulate (Ci) - medial orbito frontal(F02); D) pre cuneus (PCN) - Caudate (Cau); E) lateral orbitofrontal (Fol) - rostral middle frontal (F2.r); F) superior frontal(F1) - Pallidum (Pall)Reducing the feature set to this ensemble the classificationperformance is slightly degraded especially for GFA andRTAP. However, the still good performance could be an indi-cation of the relevance of such connections in the consideredtask, pointing to a network modulation involving areas indifferent cortical and subcortical regions.For the sake of comparison, Table 2 provides the perfor-mance of the classification algorithm when using the 23 con-nections involving the cortical and subcortical motor loopsmanually selected as in [4, 6]. As it can be observed, the dis-criminative power of those features is lower than the that ob-tained using the same number of features that are first rankedby the Inf-FS algorithm that are reported in Table 1. Thiscould suggest that a more extended portion of the network isinvolved in the plasticity process and thus that a wider per-spective should be taken for its assessment.Finally, Table 4 shows the performance that is obtainedby gathering the six features common to all indices together.Accuracy is not significantly affected while precision, recalland AUC reach the maximum value.# connections0 200 400 600406080100accuracy# connections0 200 400 600406080100AUC# connections0 200 400 600406080100Precision0 200 400 600406080100RecallGFA PA R RTAPFig. 3: Performance of classification after Inf-FS from abso-lute delta adjancecy matrix.Table 1: Classification performance on the 23 first rankedfeatures following Inf-FS.Index Accuracy AUC Precision RecallGFA 88.89 97.53 100 77.78PA 83.33 92.59 87.50 77.78R 88.89 97.56 87.50 77.78RTAP 88.89 100 100 77.78Table 2: Classification performance on the 23 manually se-lected features as in [4, 5, 6].Index Accuracy AUC Precision RecallGFA 66.67 56.79 61.53 88.89PA 50 41.98 50 33.33R 55.56 50.62 55.56 55.56RTAP 50 54.32 50 22.22Table 3: Classification performance on the 6 features withinthe first 20 ranked by Inf-FS for each index.Index Accuracy AUC Precision RecallGFA 83.33 95.06 80 88.89PA 83.33 96.30 87.50 77.78R 83.33 97.53 87.50 77.78RTAP 77.78 95.06 77.78 77.78Table 4: Classification performance on the 6 features withinthe first 20 ranked by Inf-FS for all the indices.Accuracy AUC Precision Recall88.89 98.77 100 77.784. CONCLUSIONSIn this paper we proposed a novel approach for the charac-terization of the structural connectivity network after strokefocusing on link as opposed to node properties. The basichypothesis is that network modulation can be better describedby measuring the connectivity alterations directly in the formof modulation of the properties of white matter fiber bundlesconstituting the communication backbone. A feature selec-tion paradigm was exploited where features were representedby percent absolute changes of mean values of a predefinedset of microstructural indices across connections betweenpairs of regions. Results show that connection paths withhigh discriminative power can be identified that are sharedby the considered microstructural descriptors allowing a clas-sification accuracy ranging between 83% and 89% for thedifferent indices.5. REFERENCES[1] E. Ozarslan, C. Koay, T. Shepherd, S. Blackband, andP. Basser, “Simple harmonic oscillator based reconstruc-tion and estimation for three-dimensional q-space MRI,”in ISMRM, 2009.[2] E. Ozarslan, C. Koay, T. Shepherd, M. Komlosh, M. Ir-fanolu, C. Pierpaoli, and P. Basser, “Mean apparent prop-agator (map) mri: A novel diffusion imaging method formapping tissue microstructure,” Neuroimage, vol. 78, pp.16–32, 2013.[3] M. Zucchelli, E. Garyfallidis, M. Paquette, S. Merlet,G. Menegaz, and M. Deascoteaux, “Comparison betweendiscrete and continuous propagator indices from cartesianq-space dsi sampling,” in ISMRM, 2014.[4] C. Granziera, A. Daducci, D.E. Meskaldji, A. Roche,P. Maeder, P. Michel, N. Hadjikhani, A.G. Sorensen, R.S.Frackowiak, J.P. Thiran, R. Meuli, and G. Krueger, “Anew early and automated MRI-based predictor of motorimprovement after stroke,” Neurology, vol. 79, no. 1, pp.39–46, 2012.[5] Y. Lin, A. Daducci, D. Meskaldji, J. Thiran, P. Michel,R. Meuli, G. Krueger, G. Menegaz, and C. Granziera,“Quantitative Analysis of Myelin and Axonal Remodel-ing in the Uninjured Motor Network After Stroke,” BrainConnectivity, vol. 5, no. 7, pp. 401–412, 2015.[6] L. Brusini, S. Obertino, M. Zucchelli, I. Boscolo Galazzo,G. Krueger, C. Granziera, and G. Menegaz, “Assessmentof Mean Apparent Propagator-based indices as biomark-ers of axonal remodeling after stroke,” in MICCAI, 2015.[7] Giorgio Roffo, Simone Melzi, and Marco Cristani, “Infi-nite feature selection,” in ICCV, 2015.

Infinite Feature Selection on Shore-Based Biomarkers Reveals Connectivity Modulation after Stroke

S. Obertino

G. Roffo

C. Granziera

G. Menegaz

Crossref

Infinite feature selection on shore-based biomarkers reveals connectivity modulation after stroke

Enlighten: Publications

 
 
 
 
 
Obertino, S., Roffo, G., Granziera, C. and Menegaz, G. (2016) Infinite 
Feature Selection on Shore-Based Biomarkers Reveals Connectivity 
Modulation after Stroke. In: 2016 International Workshop on Pattern 
Recognition in Neuroimaging (PRNI), Trento, Italy, 22-24 June 2016, pp. 
1-4. ISBN 9781467365307 (doi:10.1109/PRNI.2016.7552347) 
 
 
This is the author’s final accepted version. 
 
There may be differences between this version and the published version. 
You are advised to consult the publisher’s version if you wish to cite from 
it. 
 
http://eprints.gla.ac.uk/149663/                                                                   
 
 
 
 
 
 
Deposited on: 11 October 2017 
 
 
 
 
 
 
 
 
 
 
 
 
 
Enlighten – Research publications by members of the University of Glasgow 
http://eprints.gla.ac.uk  
INFINITE FEATURE SELECTION ON SHORE-BASED BIOMARKERS REVEALS
CONNECTIVITY MODULATION AFTER STROKE
S. Obertino1, G.Roffo1, C. Granziera2, G. Menegaz1
1 Dept. of Computer Science, University of Verona, Italy
2 Martinos Center for Biomedical Imaging, Massachusetts General Hospital and Harvard Medical School,
Chalestown, MA, United States
ABSTRACT
Connectomics is gaining increasing interest in the scientific
and clinical communities. It consists in deriving models of
structural or functional brain connections based on some lo-
cal measures. Here we focus on structural connectivity as
detected by diffusion MRI. Connectivity matrices are derived
from microstructural indices obtained by the 3D-SHORE.
Typically, graphs are derived from connectivity matrices and
used for inferring node properties that allow identifying those
nodes that play a prominent role in the network. This in-
formation can then be used to detect network modulations
induced by diseases. In this paper we take a complementary
approach and focus on link as opposed to node properties. We
hypothesize that network modulation can be better described
by measuring the connectivity alteration directly in the form
of modulation of the properties of white matter fiber bundles
constituting the network communication backbone. The goal
of this paper is to detect the paths that are most altered by the
pathology by exploiting a feature selection paradigm. Tem-
poral changes on connection weights are treated as features
and those playing a leading role in a patient versus healthy
controls classification task are detected by the Infinite Fea-
ture Selection (Inf-FS) method. Results show that connection
paths with high discriminative power can be identified that
are shared by the considered microstructural descriptors al-
lowing a classification accuracy ranging between 83% and
89%.
Index Terms— Feature Selection, Stroke, 3D-SHORE
1. INTRODUCTION
Recent advances in diffusion MRI led to the definition of
numerical parameters describing microstructural properties.
The so called Ensemble Average Propagator (EAP) derived
models approximate the diffusion signal by series expan-
sion over basis functions providing an analytical solution
from which indices can be derived in closed form. Among
the most promising ones is the 3D-SHORE [1] model form
which, under some ideal conditions, geometrical descrip-
tors of the diffusion compartments can be inferred [2, 3].
Combined with quantitative tractography, such indices allow
modeling structural connectivity through the construction of
the connectivity matrix from which a representation of the
network in the form of a graph is derived. Typically, cor-
tical/subcortical regions represent the nodes and the matrix
elements represent the weight of the link between pairs of
regions. Then, graph theory is exploited for deriving node
properties and thus identifying those playing a leading role in
the network. This information can be exploited for detecting
network modulations due to some pathological conditions.
In this paper we take a complementary approach focusing
on connections instead than on nodes, with the aim of iden-
tifying the paths that are more prominent in the network
modulation. The reason behind this choice is the observa-
tion that pathologies compromise the communication among
regions by disrupting the white matter fibers that constitute
the backbone for communication. In consequence, we hy-
pothesize that network modulation can be better described by
measuring the connectivity alteration directly in the form of
modulations of the properties of white matter fiber bundles.
The objective is to check this hypothesis by detecting the
paths that are most altered by the pathology in a feature se-
lection paradigm. Temporal changes on connection weights
are treated as features and those playing a leading role in
a patients versus healthy controls classification task are de-
tected by the Infinite Feature Selection (Inf-FS) method. The
novelty of this approach is twofold. First, the focus is on
links instead than on nodes, as previously stated. Second,
the set of connections that are altered by the pathology re-
sults from a feature selection task. Previous works exploiting
microstructural indices for assessing neuronal plasticity after
stroke have been focusing on a predefined set of manually
selected cortical and subcortical regions as the end-points of
the considered links [4, 5, 6]. The proposed approach relaxes
the constraint on the choice of the regions and connections
such that the relevant links naturally emerge by feature selec-
tion. This has the potential of providing new insights on the
changes induced by pathologies both locally and globally.
2. METHODS
Four microstructural indices are derived from the 3D-SHORE
model. Connectivity matrices are derived from each index
by quantitative tractography. Each entry of the connectivity
matrix represents the absolute percent temporal variation of
the mean value of each index along the connection linking the
corresponding cortical/subcortical regions and plays the role
of feature in the classification task. Feature selection by Inf-
FS is performed for detecting the set of connections playing a
dominant role in group discrimination.
2.1. Dataset
A total of 18 subjects (9 patients and 9 age and gender
matched controls) were imaged following Diffusion Spec-
trum Imaging (DSI) scans [TR/TE = 6600/138 msec, FoV =
212× 212 mm2, 34 slices, 2.2× 2.2× 3 mm3 resolution, 258
diffusion directions, b-value = 8000 s/mm2, ∼ 25 min scan
time] within one week (tp1) and one month (± one week,
tp2) after stroke for patients and one month apart for controls.
Pre-processing was performed as in [4]. All subjects pro-
vided written informed consent and the Lausanne University
Hospital review board approved the study protocol.
2.2. 3D-SHORE model
The SHORE model decomposes the signal E(q) as a linear
combination of basis functions that are the solutions of the
3D harmonic oscillator. The orthonormal formulation of the
3D-SHORE model is expressed as
E(qu) =
Nmax∑
l=0,even
(Nmax+l)/2∑
n=l
l∑
m=−l
cnlmΦnlm(qu) (1)
whereNmax is the maximal order of the functions in the trun-
cated series and Φnlm(q) is the orthonormal 3D-SHORE ba-
sis, defined as
Φnlm(qu) =
[
2(n− l)!
ζ3/2Γ(n+ 3/2)
]1/2(
q2
ζ
)l/2
(2)
× exp
(
−q2
2ζ
)
× Ll+1/2n−l
(
q2
ζ
)
Y ml (u)
where Γ is the Gamma function and ζ is a scaling parameter
dependent on the diffusion time τ and the diffusivity D. All
these models provide close approximations of the diffusion
signal and allow deriving important EAP features such as the
Orientation Distribution Function (ODF) in a reliable manner.
From EAP models, it is also possible to derived microstruc-
ture related indices, namely the Return To the Origin Prob-
ability (RTOP), the Return To the Axis Probability (RTAP),
and the Return To the Plane Probability (RTPP). RTOP, RTAP
and RTPP represent the zero net displacement probabilities in
the three, two and mono-dimensional cases, respectively. Un-
der some ideal conditions regarding the acquisition protocol
they provide an estimation of the mean pore geometry being
respectively proportional to the reciprocal of the mean vol-
ume, cross-sectional area and length of the pore [1]. In this
work, only RTAP was used
RTAP =
∫
R2
E(q⊥)d
2q⊥ =
∫
R
P (~r‖)dr (3)
Additionally, Generalized Fractional Anysotropy (GFA) and
Propagator Anysotropy (PA), expressing the distance between
the EAP and its isotropic component, were calculated. These
indices reflect the degree of restriction of the water molecules
in the voxel, which is directly linked to the underlying pore
shape.
Fig. 1: Image of RTAP in presence of a stroke lesion.
2.3. Feature extraction by tract-based analysis
The ODFs were reconstructed and fiber-tracking was per-
formed via a streamline algorithm (www.cmtk.org). Brain
segmentation was performed using the Desikan-Killany atlas
provided by Freesurfer (www.surfer.nmr.mgh.harvard.edu)
resulting in as a set of 32 cortical and 7 subcortical regions.
The mean value of the microstructural indices along the fibers
were calculated and the absolute percentage changes across
time points were used for generating one connectivity matrix
of size 39× 39 per subject per index as
∆tp12,i =
|Fi,tp1 − Fi,tp2|
Fi,tp1
(4)
where Fi denotes the index in use.
2.4. Feature Selection
Let Gn = (V,E) be an undirected graph where V is the set
of vertices corresponding to ROIs, and E codifies weighted
edges among connections. We represent the graph Gn by the
adjacency matrix Dn, where each element dnij , 1 ≤ i, j ≤ N ,
N = 39 is the corresponding entry of the connectivity matrix
of subject n, n = 1, . . . , 18. In order to measure how well
each connection separates the two classes of patients (P ) and
controls (C), we define a discriminant matrix M by using a
simple heuristic for measuring class separation. The heuristic
is based on the separation of the class means. In the two-
class problem at hand there are Nc = 9 adjacency matrices of
class C and Np = 9 adjacency matrices of class P for each
microstructural index RTAP, R, GFA and PA. For each entry,
that is for each feature, the mean and variance are estimated
across subjects to generate the matrix M whose entries are
Mi,j =
µCi,j − µPi,j
(σCi,j)
2 + (σPi,j)
2
(5)
where
µki,j =
1
Nk
∑
n∈Nk
dni,j , k ∈ {C,P}.
In the same way, we calculate the standard deviation vectors
σki,j for each feature d
k
i,j of class k.
Our approach proposes to rank the features by importance
regarding the patients versus controls classification task. To
this end, we use the matrix M as input of the infinite feature
selection (Inf-FS) [7] algorithm, where the percent absolute
changes of the microstructural values along the connections
are seen as features. By construction, the Inf-FS method al-
lows to use convergence properties of the power series of ma-
trices, and evaluate the relevance of a feature with respect to
all the other ones taken together. In the Inf-FS formulation,
each path of a certain length l over the graph is seen as a
possible selection of features. Letting these paths tend to an
infinite number permits the investigation of the importance of
each feature. As a result, this method assigns a score of “im-
portance” to each feature by taking into account all the pos-
sible feature subsets, therefore the higher the final score, the
most important the feature. In this work a simplified version
where only the Fisher distance of the features across classes
was used. The final rank was then used in our experimental
section, where we proved that the selected connections turn
out to be effective from the classification point of view. In or-
der to obtain some measure of relevance of the subset of fea-
tures (connections), a classification approach was followed.
Performance was defined in terms of accuracy, precision and
recall. Moreover, the ROC curve was obtained as well as the
corresponding the area under the curve (AUC). Training and
testing pools were created using a cross-validation leave-1-
out method, while a SVM was used for classification.
3. RESULTS & DISCUSSION
Figure 3 illustrates the performance of the classifier as a func-
tion of the number of features that are retained after the Inf-FS
based selection in terms of accuracy, precision, recall and area
under the curve (AUC). Good performance was obtained us-
ing a relatively low number of features, suggesting that few
key connections could be the key for discriminating patients
from controls. Among the set of the first 20 features, six were
common to the four indices. These correspond to connections
between the pairs of regions illustrated in Figure 2.
Fig. 2: A) lateral occipital (Ol) - para central (PCG) (as sup-
plementary motor area); B) lateral orbito frontal (Fol) - Cau-
date (Cau); C) isthmus cingulate (Ci) - medial orbito frontal
(F02); D) pre cuneus (PCN) - Caudate (Cau); E) lateral orbito
frontal (Fol) - rostral middle frontal (F2.r); F) superior frontal
(F1) - Pallidum (Pall)
Reducing the feature set to this ensemble the classification
performance is slightly degraded especially for GFA and
RTAP. However, the still good performance could be an indi-
cation of the relevance of such connections in the considered
task, pointing to a network modulation involving areas in
different cortical and subcortical regions.
For the sake of comparison, Table 2 provides the perfor-
mance of the classification algorithm when using the 23 con-
nections involving the cortical and subcortical motor loops
manually selected as in [4, 6]. As it can be observed, the dis-
criminative power of those features is lower than the that ob-
tained using the same number of features that are first ranked
by the Inf-FS algorithm that are reported in Table 1. This
could suggest that a more extended portion of the network is
involved in the plasticity process and thus that a wider per-
spective should be taken for its assessment.
Finally, Table 4 shows the performance that is obtained
by gathering the six features common to all indices together.
Accuracy is not significantly affected while precision, recall
and AUC reach the maximum value.
# connections
0 200 400 600
40
60
80
100
accuracy
# connections
0 200 400 600
40
60
80
100
AUC
# connections
0 200 400 600
40
60
80
100
Precision
0 200 400 600
40
60
80
100
Recall
GFA PA R RTAP
Fig. 3: Performance of classification after Inf-FS from abso-
lute delta adjancecy matrix.
Table 1: Classification performance on the 23 first ranked
features following Inf-FS.
Index Accuracy AUC Precision Recall
GFA 88.89 97.53 100 77.78
PA 83.33 92.59 87.50 77.78
R 88.89 97.56 87.50 77.78
RTAP 88.89 100 100 77.78
Table 2: Classification performance on the 23 manually se-
lected features as in [4, 5, 6].
Index Accuracy AUC Precision Recall
GFA 66.67 56.79 61.53 88.89
PA 50 41.98 50 33.33
R 55.56 50.62 55.56 55.56
RTAP 50 54.32 50 22.22
Table 3: Classification performance on the 6 features within
the first 20 ranked by Inf-FS for each index.
Index Accuracy AUC Precision Recall
GFA 83.33 95.06 80 88.89
PA 83.33 96.30 87.50 77.78
R 83.33 97.53 87.50 77.78
RTAP 77.78 95.06 77.78 77.78
Table 4: Classification performance on the 6 features within
the first 20 ranked by Inf-FS for all the indices.
Accuracy AUC Precision Recall
88.89 98.77 100 77.78
4. CONCLUSIONS
In this paper we proposed a novel approach for the charac-
terization of the structural connectivity network after stroke
focusing on link as opposed to node properties. The basic
hypothesis is that network modulation can be better described
by measuring the connectivity alterations directly in the form
of modulation of the properties of white matter fiber bundles
constituting the communication backbone. A feature selec-
tion paradigm was exploited where features were represented
by percent absolute changes of mean values of a predefined
set of microstructural indices across connections between
pairs of regions. Results show that connection paths with
high discriminative power can be identified that are shared
by the considered microstructural descriptors allowing a clas-
sification accuracy ranging between 83% and 89% for the
different indices.
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Connectomics is gaining increasing interest in the scientificand clinical communities. It consists in deriving models ofstructural or functional brain connections based on some localmeasures. Here we focus on structural connectivity asdetected by diffusion MRI. Connectivity matrices are derivedfrom microstructural indices obtained by the 3D-SHORE.Typically, graphs are derived from connectivity matrices andused for inferring node properties that allow identifying thosenodes that play a prominent role in the network. This informationcan then be used to detect network modulationsinduced by diseases. In this paper we take a complementaryapproach and focus on link as opposed to node properties. Wehypothesize that network modulation can be better describedby measuring the connectivity alteration directly in the formof modulation of the properties of white matter fiber bundlesconstituting the network communication backbone. The goalof this paper is to detect the paths that are most altered by thepathology by exploiting a feature selection paradigm. Temporalchanges on connection weights are treated as featuresand those playing a leading role in a patient versus healthycontrols classification task are detected by the Infinite FeatureSelection (Inf-FS) method. Results show that connectionpaths with high discriminative power can be identified that areshared by the considered microstructural descriptor allowinga classification accuracy ranging between 83% and 98% forthe different indices

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Infinite Feature Selection on SHORE based biomarkers reveals connectivity modulation after stroke

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Infinite Feature Selection on Shore-Based Biomarkers Reveals Connectivity Modulation after Stroke

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