3660-discriminative-network-models-of-schizophrenia.txt

Discriminative Network Models of Schizophrenia

Guillermo A. Cecchi, Irina Rish
IBM T. J. Watson Research Center

Yorktown Heights, NY, USA

Benjamin Thyreau

Neurospin

CEA, Saclay, France

Bertrand Thirion

INRIA

Saclay, France

Marion Plaze

INSERM - CEA - Univ. Paris Sud

Research Unit U.797

Neuroimaging & Psychiatry

SHFJ & Neurospin, Orsay, France

Marie-Laure Paillere-Martinot

AP-HP, Adolescent Psychopathology
and Medicine Dept., Maison de Solenn,

Cochin Hospital, University Paris Descartes

F-75014 Paris, France

Catherine Martelli

Departement de Psychiatrie

et dAddictologie

Centre Hospitalier Paul Brousse

Villejuif, France

Jean-Luc Martinot

INSERM - CEA - Univ. Paris Sud

Research Unit U.797

Neuroimaging & Psychiatry

SHFJ & Neurospin, Orsay, France

Jean-Baptiste Poline

Neurospin

CEA, Saclay, France

Abstract

Schizophrenia is a complex psychiatric disorder that has eluded a characterization
in terms of local abnormalities of brain activity, and is hypothesized to affect the
collective, emergent working of the brain. We propose a novel data-driven ap-
proach to capture emergent features using functional brain networks [4] extracted
from fMRI data, and demonstrate its advantage over traditional region-of-interest
(ROI) and local, task-specific linear activation analyzes. Our results suggest that
schizophrenia is indeed associated with disruption of global brain properties re-
lated to its functioning as a network, which cannot be explained by alteration of
local activation patterns. Moreover, further exploitation of interactions by sparse
Markov Random Field classifiers shows clear gain over linear methods, such as
Gaussian Naive Bayes and SVM, allowing to reach 86% accuracy (over 50% base-
line - random guess), which is quite remarkable given that it is based on a single
fMRI experiment using a simple auditory task.

1 Introduction

It has been long recognized that extracting an informative set of application-specific features from
the raw data is essential in practical applications of machine learning, and often contributes even
more to the success of learning than the choice of a particular classifier. In biological applications,
such as brain image analysis, proper feature extraction is particularly important since the primary
objective of such studies is to gain a scientific insight rather than to learn a black-box predictor;
thus, the focus shifts towards the discovery of predictive patterns, or biomarkers, forming a basis
for interpretable predictive models. Conversely, biological knowledge can drive the definition of
features and lead to more powerful classification.
The objective of this work is to identify biomarkers predictive of schizophrenia based on fMRI
data collected for both schizophrenic and non-schizophrenic subjects performing a simple auditory
task in the scanner [14]. Unlike some other brain disorders (e.g., stroke or Parkinsons disease),
schizophrenia appears to be delocalized, i.e. difficult to attribute to a dysfunction of some par-

1

ticular brain areas1. The failure to identify specific areas, as well as the controversy over which
localized mechanisms are responsible for the symptoms associated with schizophrenia, have led us
amongst others [7, 1, 10] to hypothesize that this disease may be better understood as a disruption of
the emergent, collective properties of normal brain states, which can be better captured by functional
networks [4], based on inter-voxel correlation strength, as opposed (or limited) to activation failures
localized to specific, task-dependent areas.
To test this hypothesis, we measured diverse topological features of the functional networks and
compared them across the normal subjects and schizophrenic patients groups. Specifically, we
decided to ask the following questions: (1) What specific effects does schizophrenia have on the
functional connectivity of brain networks? (2) Does schizophrenia affect functional connectivity
in ways that are congruent with the effect it has on area-specific, task-dependent activations? (3)
Is it possible to use functional connectivity to improve the classification accuracy of schizophrenic
patients?
In answer to these questions, we will show that degree maps, which assign to each voxel the number
of its neighbors in a network, identify spatially clustered groups of voxels with statistically signif-
icant group (i.e. normal vs. schizophrenic) differences; moreover, these highly significant voxel
subsets are quite stable over different data subsets. In contrast, standard linear activation maps com-
monly used in fMRI analysis show much weaker group differences as well as stability. Moreover,
degree maps yield very informative features, allowing for up to 86% classification accuracy (with
50% baseline), as opposed to standard local voxel activations. The best accuracy is achieved by fur-
ther exploiting non-local interactions with probabilistic graphical models such as Markov Random
Fields, as opposed to linear classifiers.
Finally, we demonstrate that traditional approaches based on a direct comparison of the correlation
at the level of relevant regions of interest (ROIs) or using a functional parcellation technique [17],
do not reveal any statistically significant differences between the groups. Indeed, a more data-driven
approach that exploits properties of voxel-level networks appears to be necessary in order to achieve
high discriminative power.
2 Background and Related Work

In Functional Magnetic Resonance Imaging (fMRI), a MR scanner non-invasively records a sub-
jects blood-oxygenation-level dependent (BOLD) signal, known to be correlated with neural activ-
ity, as a subject performs a task of interest (e.g., viewing a picture or reading a sentence). Such scans
produce a sequence of 3D images, where each image typically has on the order of 10,000-100,000
subvolumes, or voxels, and the sequence typically contains a few hundreds of time points, or TRs
(time repetitions). Standard fMRI analysis approaches, such as the General Linear Model (GLM)
[9], examine mass-univariate relationships between each voxel and the stimulus in order to build
so-called statistical parametric maps that associate each voxel with some statistics that reflects its
relationship to the stimulus. Commonly used activation maps depict the activity level of each
voxel determined by the linear correlation of its time course with the stimulus (see Supplemental
Material for details).
Clearly, such univariate analysis can miss important information contained in the interactions among
voxels. Indeed, as it was shown in [8], highly predictive models of mental states can be built from
voxels with sub-maximal activation. Recently, applying multivariate predictive methods to fMRI
became an active area of research, focused on predicting mental states from fMRI data [11, 13, 2].
However, our focus herein is not just predictive modeling, but rather discovery of interpretable
features with high discriminative power. Also, our problem is much more high-dimensional, since
each sample (e.g., schizophrenic vs. non-schizophrenic) corresponds to a sequence of 3D images
over about 400 time points, rather than to a single 3D image as in [11, 13, 2].
While the importance of modeling brain connectivity and interactions became widely recognized in
the current fMRI-analysis literature [6, 19, 16], practical applications of the proposed approaches
such as dynamic causal modeling [6], dynamic Bays nets [19], or structural equations [16] were

1This is often referred to as the disconnectionhypothesis[5, 15], and can be traced back to the early research
on schizophrenia: in 1906, Wernicke [18] was the first one to postulate that anatomical disruption of association
fiber tracts is at the roots of psychosis; in fact, the term schizophrenia was introduced by Bleuler [3] in 1911,
and was meant to describe the separation (splitting) of different mental functions.

2

ROI name

Temporal mid L

Temporal mid et sup L

Frontal inf L

cuneus L

Temporal sup et mid L

Angular L

Temporal sup R

Angular R

Cingulum post R

ACC

(x,y,z) position

-44,-48,4
-56,-36,0
-40,28,0
-12,-72,24
-52,-16,-8
-44,-48,32
40,-64,24
40,-64,24
4,-32,24
0,20,30

1
2
3
4
5
6
7
8
9
10

Middle and superior left temporal

Anatomical position

Left temporal

Left Inferior frontal

Left cuneus

Middle and superior left temporal

Left angular gyrus

Right superior temporal

Right angular gyrus

Right posterior cingulum
Anterior cingulated cortex

Figure 1: Regions of Interest and their location on standard brain.

usually limited to interactions analysis among just a few (e.g., less than 15) known brain regions
believed to be relevant to the task or phenomenon of interest. In this paper, we demonstrate that such
model-based region-of-interest (ROI) analysis may fail to reveal informative interactions which,
nevertheless, become visible at the finer-grain voxel level when using a purely data-driven, network-
based approach [4]. Moreover, while recent publications have already indicated that functional
networks in the schizophrenic brain display disrupted topological properties, we demonstrate, for
the first time, that (1) specific topological properties (e.g. voxel degrees) of functional networks can
help to construct highly-predictive schizophrenia classifiers that generalize well and (2) functional
network differences cannot be attributed to alteration of local activation patterns, a hypothesis that
was not ruled out by the results of [1, 10] and similar work.
3 Experimental Setup
The present study is a reanalysis of image datasets previously acquired according to the method-
ology described in [14]. Two groups of 12 subjects each were submitted to the same experimental
paradigm involving language: schizophrenic patients and age-matched normal controls (same ex-
periment was performed with a third group of alcoholic patients, yielding similar results - see Suppl.
Materials for details). The studies had been performed after approval of the local ethics committee
and all subjects were studied after they gave written informed consent. The task is based on au-
ditory stimuli; subjects listen to emotionally neutral sentences either in native (French) or foreign
language. Average length (3.5 sec mean) or pitch of both kinds of sentences is normalized. In order
to catch attention of subjects, each trial begins with a short (200 ms) auditory tone, followed by
the actual sentence. The subjects attention is asserted through a simple validation task: after each
played sentences, a short pause of 750 ms is followed by a 500 ms two-syllable auditory cue, which
belongs to the previous sentence or not, to which the subject must answer to by yes (the cue is part
of the previous sentence) or no with push-buttons, when the language of the sentence was his own.
For each subject, two fMRI acquisition runs are acquired, each of which consisted of 420-scans
(from which the first 4 are discarded to eliminate T1 effect). A full fMRI run contains 96 trials, with
32 sentences in French (native), 32 sentences in foreign languages, and 32 silence interval controls.
Data were spatially realigned and warped into the MNI template and smoothed (FWHM of 5mm)
using SPM5 (www.fil.ucl.ac.uk); also, standard SPM5 motion correction was performed. Several
subjects were excluded from the consideration due to excessive head motion in the scanner, leav-
ing us with 11 schizophrenic and 11 healthy subjects, i.e. the total of 44 samples (there were two
samples per subject, corresponding to the two runs of the experiment). Each sample associated with
roughly 53,000 voxels (after removing out-of-brain voxels from the original 53  63  46 image),
over 420 time points (TRs), i.e. with more than 22,000,000 voxels/variables. Thus, some kind of
dimensionality reduction and/or feature extraction is necessary prior to learning a predictive model.
4 Methods
We explored two different data analysis approaches aimed at discovery of discriminative patterns:
(1) model-driven approaches based on prior knowledge about the regions of interest (ROI) that are
believed to be relevant to schizophrenia, or model-based functional clustering, and (2) data-driven
approaches based on various features extracted from the fMRI data, such as standard activation maps
and a set of topological features derived from functional networks.
4.1 Model-Driven Approach using ROI
First, we decided to test whether the interactions between several known regions of interest (ROIs)
would contain enough discriminative information about schizophrenic versus normal subjects. Ten

3

regions of interests (ROI) were defined using previous literature on schizophrenia and language
studies, including inferior, middle and superior left temporal cortex, left inferior temporal cortex,
left cuneus, left angular gyrus, right superior temporal, right angular gyrus, right posterior cingu-
lum, and anterior cingular cortex (Figure 1). Each region was defined as a sphere of 12mm diameter
centered on the x,y,z coordinates of the corresponding ROI. Because predefined regions of inter-
est may be based on too much a priori knowledge and miss important areas, we also ran a more
exploratory analysis. A second set of 600 ROIs was defined automatically using a parcellation al-
gorithm [17] that estimates, for each subject, a collection of regions based on task-based functional
signal similarity and position in the MNI space.
Time series were extracted as the spatial mean over each ROI, leading to 10 time series per subject
for the predefined ROIs and 600 for the parcellation technique. The connectivity measures were
of two kinds. First, the correlation coefficient was computed along time between ROIs blindly with
respect to the experimental paradigm. Additionally, we computed a psycho-physiological interaction
(PPI), by contrasting the correlation coefficient weighted by experimental conditions (i.e. correlation
weighted by the Language French condition versus correlation weighted by Control condition
after convolution with a standard hemodynamic response function). Those connectivity measures
were then tested for significance using standards non parametric tests between groups (Wilcoxon
signed-rank test) with corrected p-values for multiple comparisons.
4.2 Data-driven Approach: Feature Extraction
Topological Features and Degree Maps. In order to continue investigating possible disruptions
of global brain functioning associated with schizophrenia, we decided to explore lower-level (as
compared to ROI-level) functional brain networks [4] constructed at the voxel level: (1) pair-wise
Pearson correlation coefficients are computed among all pairs of time-series (vi(t), vj(t)) where
vi(i) corresponds to the BOLD signal of i-th voxel; (2) an edge between a pair of voxels (i, j) is
included in the network if the correlation between vi and vj exceeds a specified threshold (herein,
we used the same threshold of c(Pearson)=0.7 for all voxel pairs).
For each subject, and each run, a separate functional network was constructed. Next, we measured
a number of its topological features, including the degree distribution, mean degree, the size of the
largest connected subgraph (giant component), and so on (see the supplemental material for the full
list). Besides global topological features, we also computed a series of degree maps based on the
individual voxel degree in functional network: (1) full degree maps, where the value assigned to
each voxel is the total number of links in the corresponding network node, (2) long-distance degree
maps, where the value is the number of links making non-local connections (5 voxels apart or more),
and (3) inter-hemispheric degree maps, where only links reaching across the brain hemispheres are
considered when computing each voxels degree.
Activation maps. To find out whether local task-dependent linear activations alone could possibly
explain the differences between the schizophrenic and normal brains, we used as a baseline set of
features based on the standard voxel activation maps. For each subject, and for each run, activation
maps, as well as their differences, or activation contrast maps, were obtained using several regressors
based on the language task, as described in the supplemental material (for simplicity, we will refer
to all such maps as activation maps). The activation values of each voxel were subsequently used
as features in the classification task. Similarly to degree maps, we also computed a global feature,
mean-activation (mean-t-val)), by taking the mean absolute value of the voxels t-statistics. Both
activation and degree maps for each sample were also normalized, i.e. divided by their maximal
value for the given sample.
4.3 Classification Approaches
First, off-the-shelf methods such Gaussian Naive Bayes (GNB) and Support Vector Machines (SVM)
were used in order to compare the discriminative power of different sets of features described above.
Moreover, we decided to further investigate our hypothesis that interactions among voxels contain
highly discriminative information, and compare those linear classifiers against probabilistic graph-
ical models that explicitly model such interactions. Specifically, we learn a classifier based on a
sparse Gaussian Markov Random Field (MRF) model [12], which leads to a convex problem with
unique optimal solution, and can be solved efficiently; herein, we used the COVSEL procedure [12].
The weight on the l1-regularization penalty serves as a tuning parameter of the classifier, allowing
to control the sparsity of the model, as described below.

4

2 e 1

(cid:80)n

Sparse Gaussian MRF classifier. Let X = {X1, ..., Xp} be a set of p random variables (e.g.,
voxels), and let G = (V, E) be an undirected graphical model (Markov Network, or MRF) rep-
resenting conditional independence structure of the joint distribution P (X). The set of vertices
V = {1, ..., p} is in the one-to-one correspondence with the set X. There is no edge between Xi
and Xj if and only if the two variables are conditionally independent given all remaining variables.
Let x = (x1, ..., xp) denote a random assignment to X. We will assume a multivariate Gaussian
2 xT Cx, where C = 1 is the inverse covari-
probability density p(x) = (2)p/2 det(C) 1
ance matrix, and the variables are normalized to have zero mean. Let x1, ..., xn be a set of n i.i.d.
samples from this distribution, and let S = 1
i xi denote the empirical covariance matrix.
n
Missing edges in the above graphical model correspond to zero entries in the inverse covariance ma-
trix C, and thus the problem of learning the structure for the above probabilistic graphical model is
equivalent to the problem of learning the zero-pattern of the inverse-covariance matrix 2. A popular
approach is to use l1-norm regularization that is known to promote sparse solutions, while still al-
lowing (unlike non-convex lq-norm regularization with 0 < q < 1) for efficient optimization. From
the Bayesian point of view, this is equivalent to assuming that the parameters of the inverse covari-
(cid:80)
ance matrix C = 1 are independent random variables Cij following the Laplace distributions
2 eij|Cijij| with zero location parameters (means) ij and equal scale parameters
p(Cij) = ij
ij |Cij| is the
ij = . Then p(C) =
(vector) l1-norm of C. Assume a fixed parameter , our objective is to find arg maxC(cid:194)0 p(C|X),
where X is the n  p data matrix, or equivalently, since p(C|X) = P (X, C)/p(X) and p(X) does
not include C, to find arg maxC(cid:194)0 P (X, C), over positive definite matrices C. This yields the
following optimization problem considered, for example, in [12]

e||C||1, where ||C||1 =

j=1 p(Cij) = (/2)p2

i=1 xT

(cid:81)p

(cid:81)p

i=1

ln det(C)  tr(SC)  ||C||1

max
C(cid:194)0

where det(A) and tr(A) denote the determinant and the trace (the sum of the diagonal elements) of
a matrix A, respectively. For the classification task, we estimate on the training data the Gaus-
sian conditional density p(x|y) (i.e.
the (inverse) covariance matrix parameter) for each class
Y = {0, 1} (schizophrenic vs non-schizophrenic), and then choose the most-likely class label
arg maxc p(x|c)P (c) for each unlabeled test sample x.
Variable Selection: We used variable selection as a preprocessing step before applying a partic-
ular classifier, in order to (1) reduce the computational complexity of classification (especially for
sparse MRF, which, unlike GNB and SVM, could not be directly applied to over 50,000 variables),
(2) reduce noise and (3) identify relatively small predictive subsets of voxels. We applied a sim-
ple filter-based approach, selecting a subset of top-ranked voxels, where the ranking criterion used
p-values resulting from the paired t-test, with the null-hypothesis being that the voxel values cor-
responding to schizophrenic and non-schizophrenic subjects came from distributions with equal
means. The variables were ranked in the ascending order of their p-values (lower p = higher confi-
dence in between-group differences), and classification results on top k voxels will be presented for
a range of k values.
Evaluation via Cross-validation. We used leave-one-subject-out rather than leave-one-sample-out
cross-validation, since the two runs (two samples) for each subject are clearly not i.i.d. and must be
handled together to avoid biases towards overly-optimistic results.
5 Results
Model-driven ROI analysis. First, we observed that correlations (blind to experimental paradigm)
between regions and within subjects were very strong and significant (p-value of 0.05, corrected
for the number of comparisons) when tested against 0 for all subjects (mean correlation > 0.8 for
every group). However, these inter-region correlations do not seem to differ significantly between
the groups. The parcellation technique led to some smaller p-values, but also to a stricter correction
for multiple comparison and no correlation was close to the corrected threshold. Concerning the
psycho-physiological interaction, results were closer to significance, but did not survive multiple
comparisons. In conclusion, we could not detect significant differences between the schizophrenic
patient data and normal subjects in either the BOLD signal correlation or the interaction between
the signal and the main experimental contrast (native language versus silence).

2Note that the inverse of the empirical covariance matrix, even if it exists, does not typically contain exact

zeros. Therefore, an explicit sparsity constraint is usually added to the estimation process.

5

(a)

(b)

Figure 2: (a) FDR-corrected 2-sample t-test results for (normalized) degree maps, where the null hypothesis at
each voxel assumes no difference between the schizophrenic vs normal groups. Red/yellow denotes the areas
of low p-values passing FDR correction at  = 0.05 level (i.e., 5% false-positive rate). Note that the mean
(normalized) degree at those voxels was always (significantly) higher for normals than for schizophrenics. (b)
Direct comparison of voxel p-values and FDR threshold: p-values sorted in ascending order; FDR test select
voxels with p <   k/N ( - false-positive rate, k - the index of a p-value in the sorted sequence, N - the total
number of voxels). Degree maps yield a large number (1033, 924 and 508 voxels in full, long-distance and
inter-hemispheric degree maps, respectively) of highly-significant (very low) p-values, staying far below the
FDR cut-off line, while only a few voxels survive FDR in case of activation maps: 7 and 2 voxels in activation
maps 1 (contrast FrenchNative - Silence) and 6 (FrenchNative), respectively (the rest of the activation maps
do not survive the FDR correction at all).

Data-driven analysis: topological vs activation features. Empirical results are consistent with our
hypothesis that schizophrenia disrupts the normal structure of functional networks in a way that is
not derived from alterations in the activation; moreover, they demonstrate that topological properties
are highly predictive, consistently outperforming predictions based on activations.
1. Voxel-wise statistical analysis. Degree maps show much stronger statistical differences be-
tween the schizophrenic vs. non-schizophrenic groups than the activation maps. Figure 2 show
the 2-sample t-test results for the full degree map and the activation maps, after False-Discovery
Rate (FDR) correction for multiple comparisons (standard in fMRI analysis), at  = 0.05 level
(i.e., 5% false-positive rate). While the degree map (Figure 2a) shows statistically significant differ-
ences bilaterally in auditory areas (specifically, normal group has higher degrees than schizophrenic
group), the activation maps show almost no significant differences at all: practically no voxels there
survived the FDR correction (Figure 2b. This suggests that (a) the differences in the collective be-
havior cannot be explained by differences in the linear task-related response, and that (b) topology
of voxel-interaction networks is more informative than task-related activations, suggesting an ab-
normal degree distribution for schizophrenic patients that appear to lack hubs in auditory cortex,
i.e., have significantly lower (normalized) voxel degrees in that area than the normal group (possibly
due to a more even spread of degrees in schizophrenic vs. normal networks). Moreover, degree
maps demonstrate much higher stability than activation maps with respect to selecting a subset of
top ranked voxels over different subsets of data. Figure 3a shows that degree maps have up to
almost 70% top-ranked voxels in common over different training data sets when using the leave-
one-subject out cross-validation, while activation maps have below 50% voxels in common between
different selected subsets. This property of degree vs activation features is particularly important for
interpretability of predictive modeling.
2. Inter-hemispheric degree distributions. A closer look at the degree distributions reveals that a
large percentage of the differential connectivity appears to be due to long-distance, inter-hemispheric
links. Figure 3a compares (normalized) histograms, for schizophrenic (red) versus normal (blue)
groups, of the fraction of inter-hemispheric connections over the total number of connections, com-
puted for each subject within the group. The schizophrenic group shows a significant bias towards
low relative inter-hemispheric connectivity. A t-test analysis of the distributions indicates that dif-
ferences are statistically significant (p=2.5x10-2). Moreover, it is evident that a major contributor to
the high degree difference discussed before is the presence of a large number of inter-hemispheric
connections in the normal group, which is lacking in schizophrenic group. Furthermore, we selected
a bilateral regions of interest (ROIs) corresponding to left and right Brodmann Area 22 (roughly, the
clusters in Figure 2a), suchthatthelinearactivationfortheseROIswasnotsignificantlydifferent
betweenthegroups, even in the uncorrected case. For each subject, the link between the left and

6

100101102103104105109108107106105104103102101100k/Np value  P values  and FDR correction0.05* k/Nactivation 1 FrenchNativeSilence  activation 6 FrenchNativedegree (full)degree (longdistance)degree (interhemispheric)(a)

(b)

(c)

Figure 3: (a) Stability of feature subset selection over CV folds, i.e. the percent of voxels in common among
the subsets of k top variables selected at all CV folds. (b) Disruption of global inter-hemispheric connectivity.
For each subject, we compute the fraction of inter-hemispheric connections over the total number of connec-
tions, and plot a normalized histogram over all subjects in a particular group (normal - blue, schizophrenic -
red). (c) Disruption of task-dependent inter-hemispheric connectivity between specific ROIs (Brodmann Area
22 selected bilaterally). The ROIs were defined by a 9 mm radius ball centered at [x=-42, y=-24, z=3] and
[x=42, y=-24, z=3].

Feature

degree (D)

clustering coeff. (C)
geodesic dist. (G)
mean activation (A)

D + A
C + A
G + A

G +D +C
G+D+C+A

SVM
27.5%
42.5%
45.0%
45%
27.5%
45.0%
45.0%
27.5%
27.5%

(GNB
27.5%
30.0%
67.5%
40.0%
27.5%
27.5%
45.0%
37.5%
30.0%

(a)

MRF(0.01)

27.5%
45.0%
45.0%
72.5%
32.5%
55.0%
72.5%
27.5%
32.5%

Feature

degree (full)

degree (long-distance)
degree (inter-hemis)
activation 1 (and 3)
activation 2 (and 4)

activation 5
activation 6
activation 7
activation 8

False Pos

27%
32%
46%
29%
55%
18%
27%
18%
23%

False Neg

5%
9%
18%
82%
45%
68%
46%
46%
37%

Error
16%
21%
32%
54%
50%
43%
36%
32%
30%

(b)

Table 1: Classification errors using (a) global features and (b) activation and degree maps (using SVM on the
complete set of voxels (i.e., without voxel subset selection).

right ROIs was computed as the fraction of ROI-to-ROI connections over all connections; Figure
3c shows the normalized histograms. Clearly, the normal group displays a high density of inter-
hemispheric connections, which are significantly disrupted in the schizophrenic group (p=3.7x10-
7). This provides a strong indication that the group differences in connectivity cannot be explained
by differences in local activation.
3. Global features. For each global feature (full list in Suppl. Mat.) we computed its mean for
each group and p-value produced by the t-test, as well as the classification accuracies using our
classifiers. While more details are presented in the supplemental material, we outline here the main
observations: while mean activation (we used map 8, the best performer for SVM on the full set of
voxels - see Table1b) had an relatively low p-value of 5.5  104, as compared to less significant
p = 5.3  102 for mean-degree, the predictive power of the latter, alone or in combination with
some other features, was the best among global features reaching 27.5% in schizophrenic vs normal
classification (Table 1a), while mean activation yielded more than 40% error with all classifiers.
4. Classification results using degree vs. activation maps. While mean-degree indicates the
presence of discriminative information in voxel degrees, its generalization ability, though the best
among global features and their combinations, is relatively poor. However, voxel-level degree maps
turned out to be excellent predictive features, often outperforming activation features by far. Table
1b compares prediction made by SVM on complete maps (without voxel subset selection): both
full and long-distance degree maps greatly outperform all activation maps, achieving 16% error
vs. above 30% for even the best-performing activation map 8. Next, in Figure 4, we compare the
predictive power of different maps when using all three classifiers: Support Vector Machines (SVM),
Gaussian Naive Bayes (GNB) and sparse Gaussian Markov Random Field (MRF), on the subsets
of k top-ranked voxels, for a variety of k values. We used the best-performing activation map 8
from the Table above, as well as maps 1 and 6 (that survived FDR); map 6 was also outperforming
other activation maps in low-voxel regime. To avoid clutter, we only plot the two best-performing
degree maps out of three (i.e., full and long-distance ones). For sparse MRF, we experimented with
a variety of  values, ranging from 0.0001 to 10, and present the best results. We can see that: (a)
Degree maps frequently outperform activation maps, for all classifiers we used; the differences are

7

01000200030004000500000.10.20.30.40.50.60.7% voxels in common# of topranked voxels selectedStability of topranked voxel subset  degree(full)degree (long distance)degree(interhemispheric)activation  1 (and 3)activation 2 (and 4)activation 5activation 6activation 7activation 800.10.200.20.40.6Relative link densityHistograms over samples051015x 10400.20.40.60.81Relative link densityHistogram over samples(a)

(b)

(c)

(d)

Figure 4: Classification results comparing (a) GNB, (b) SVM and (c) sparse MRF on degree versus activation
contrast maps; (d) all three classifiers compared on long-distance degree maps (best-performing for MRF).
particularly noticeable when the number of selected voxels is relatively low. The most significant
differences are observed for SVM in low-voxel (approx. < 500) and full-map regimes, as well as
for MRF classifiers: it is remarkable that degree maps can achieve an impressively low error of
14% with only 100 most significant voxels, while even the best activation map 6 requires more than
200-300 to get just below 30% error; the other activation maps perform much worse, often above
30-40% error, or even just at the chance level. (b) Full and long-distance degree maps perform quite
similarly, with long-distance map achieving the best result (14% error) using MRFs. (c) Among the
activation maps only, while the map 8 (Silence) outperforms others on the full set of voxels using
SVM, its behavior in low-voxel regime is quite poor (always above 30-35% error); instead, map
6 (FrenchNative) achieves best performance among activation maps in this regime3. (d) MRF
classifiers clearly outperform SVM and GNB, possibly due to their ability to capture inter-voxel
relationships that are highly discriminative between the two classes (see Figure 4d).
6 Summary
The contributions of this paper are two-fold. From a machine-learning and fMRI analysis perspec-
tive, we (a) introduced a novel feature-construction approach based on topological properties of
functional networks, that is generally applicable to any multivariate-timeseries classification prob-
lems, and can outperform standard linear activation approaches in fMRI analysis field, (b) demon-
strated advantages of this data-driven approach over prior-knowledge-based (ROI) approaches, and
(c) demonstrated advantages of network-based classifiers (Markov Random Fields) over linear mod-
els (SVM, Naive Bayes) on fMRI data, suggesting to exploit voxel interactions in fMRI analyzes
(i.e., treat brain as a network). From neuroscience perspective, we provided strong support for the
hypothesis that schizophrenia is associated with the disruption of global, emergent brain properties
which cannot be explained just by alteration of local activation patterns. Moreover, while prior art
is mainly focused on exploring the differences between the functional and anatomical networks of
schizophrenic patients versus healthy subjects [10, 1], this work, to our knowledge, is the first at-
tempt to explore the generalization ability of predictive models of schizophrenia built on network
features.
Finally, a word of caution. Note that the schizophrenia patients studied here have been selected for
their prominent, persistent, and pharmaco-resistant auditory hallucinations [14], which might have
increased their clinical homogeneity. However, the patient group is not representative of the full
spectrum of the disease, and thus our conclusions may not necessarily apply to all schizophrenia
patients, due to the clinical characteristics and size of the studied samples.
Acknowledgements
We would like to thank Rahul Garg for his help with the data preprocessing and many stimulating
discussions that contributed to the ideas of this paper, and Drs. Andr e Galinowski, Thierry Gallarda,
and Frank Bellivier who recruited and clinically rated the patients. We also would like to thank
INSERM as promotor of the MR data acquired (project RBM 01  26).

3We also observed that performing normalization really helped activation maps, since otherwise their per-

formance could get much worse, especially with MRFs - we provide those results in supplemental material.

8

1011021030.10.20.30.40.50.60.70.8classification errorGaussian Naive Bayes  schizophrenic vs normal    K top voxels (ttest)activation 1 FrenchNative  Silence  activation 6 FrenchNative  activation 8 Silence  degree (longdistance)degree (full)1011021031041050.10.20.30.40.50.60.70.8K top voxels (ttest)  Support Vector Machine:schizophrenic vs normal  activation 1 FrenchNative  Silence activation 6 FrenchNative  activation 8 Silence  degree (longdistance)degree (full)  501001502002503000.10.20.30.40.50.60.70.8  Markov Random Field:schizophrenic vs normal   K top voxels (ttest)activation 1 FrenchNative  Silenceactivation 6 FrenchNative activation 8 Silence  degree (longdistance)degree (full)501001502002503000.10.20.30.40.50.60.70.8  MRF vs GNB vs SVM:schizophrenic vs normal  K top voxels (ttest)MRF (0.1): degree (longdistance)GNB: degree (longdistance)SVM:degree (longdistance)References
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