ARTICLE
Received 13 Aug 2015 | Accepted 8 Mar 2016 | Published 14 Apr 2016

DOI: 10.1038/ncomms11254

OPEN

A small number of abnormal brain connections
predicts adult autism spectrum disorder
Noriaki Yahata1,2,3,*, Jun Morimoto4,*, Ryuichiro Hashimoto3,5,6,*, Giuseppe Lisi4,*, Kazuhisa Shibata3,7,
Yuki Kawakubo8, Hitoshi Kuwabara9, Miho Kuroda8,10, Takashi Yamada3,5, Fukuda Megumi3,11,
Hiroshi Imamizu3,12, José E. Náñez Sr13, Hidehiko Takahashi14, Yasumasa Okamoto15, Kiyoto Kasai16,
Nobumasa Kato5, Yuka Sasaki3,7, Takeo Watanabe3,7 & Mitsuo Kawato3

Although autism spectrum disorder (ASD) is a serious lifelong condition, its underlying neuralmechanism remains unclear. Recently, neuroimaging-based classiﬁers for ASD and typicallydeveloped (TD) individuals were developed to identify the abnormality of functional
connections (FCs). Due to over-ﬁtting and interferential effects of varying measurement
conditions and demographic distributions, no classiﬁers have been strictly validated forindependent cohorts. Here we overcome these difﬁculties by developing a novel machinelearning algorithm that identiﬁes a small number of FCs that separates ASD versus TD. The
classiﬁer achieves high accuracy for a Japanese discovery cohort and demonstrates aremarkable degree of generalization for two independent validation cohorts in the USA andJapan. The developed ASD classiﬁer does not distinguish individuals with major depressive
disorder and attention-deﬁcit hyperactivity disorder from their controls but moderately
distinguishes patients with schizophrenia from their controls. The results leave open
the viable possibility of exploring neuroimaging-based dimensions quantifying themultiple-disorder spectrum.

1 Department of Youth Mental Health, Graduate School of Medicine, The University of Tokyo, Tokyo 113-0033, Japan. 2 Diagnostic Imaging Program,
Molecular Imaging Center, National Institute of Radiological Sciences, Chiba 263-8555, Japan. 3 Department of Decoded Neurofeedback, ATR Brain
Information Communication Research Laboratory Group, Kyoto 619-0288, Japan. 4 Department of Brain Robot Interface, ATR Brain Information
Communication Research Laboratory Group, Kyoto 619-0288, Japan. 5 Medical Institute of Developmental Disabilities Research, Showa University
Karasuyama Hospital, Tokyo 157-8577, Japan. 6 Department of Language Sciences, Tokyo Metropolitan University, Tokyo 192-0397, Japan. 7 Department of
Cognitive, Linguistic and Psychological Sciences, Brown University, Rhode Island 02912, USA. 8 Department of Child Neuropsychiatry, Graduate School of
Medicine, The University of Tokyo, Tokyo 113-0033, Japan. 9 Disability Services Ofﬁce, The University of Tokyo, Tokyo 113-0033, Japan. 10 Child Mental
Health-Care Center, Fukushima University, Fukushima 960-1296, Japan. 11 Institute of Cognitive Neuroscience, University College London, London WC1N
3AZ, UK. 12 Department of Psychology, Graduate School of Humanities and Sociology, The University of Tokyo, Tokyo 113-0033, Japan. 13 School ofSocial and Behavioral Sciences, Arizona State University, Phoenix, Arizona 85306, USA. 14 Department of Psychiatry, Kyoto University Graduate School of
Medicine, Kyoto 606-8507, Japan. 15 Department of Psychiatry and Neurosciences, Graduate School of Biomedical Sciences, Hiroshima University, Hiroshima734-8553, Japan. 16 Department of Neuropsychiatry, Graduate School of Medicine, The University of Tokyo, Tokyo 113-0033, Japan. * These authors
contributed equally to this work. Correspondence and requests for materials should be addressed to Y.S. (email: yuka_sasaki@brown.edu) or to M.K.
(email: kawato@atr.jp).

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NATURE COMMUNICATIONS | DOI: 10.1038/ncomms11254

utism spectrum disorder (ASD) is a major developmental
disorder characterized by repetitive, restricted behaviour
as well as deﬁcits in communication and reciprocal social
interactions1. ASD has attracted a great deal of attention of basic
and clinical scientists in the hope that clariﬁcation of its
underlying mechanisms will lead to the development ofremedies for ASD as well as a better understanding of theneural substrates of important cognitive functions, including
social behaviour2. Despite the signiﬁcance of the disorder, noeffective biomarker has been developed. The medical diagnosis
for ASD has been made largely based on narrative interactions
between individuals and clinical professionals. With the exceptionof ‘clear and typical’ cases, such diagnostic methods without
any biological grounds could run the risk of producing
a high variance in diagnosis3 and delaying the detection ofabnormalities4.
Magnetic resonance imaging (MRI)-based characterization of
ASD has been explored as a complement to the current
behaviour-based diagnoses. While previous studies have identiﬁed a multitude of ASD-speciﬁc structural and functional
abnormalities, none of them were actually implemented as areliable biomarker. The most crucial reason for this disappointing
situation5,6 may be the lack of its generalizability—the validity ofthe previously developed classiﬁers has not been established interms of the diversity of population demographics and the variety
of data attributes7–13. These demographics and data attributes
include different ethnicities, ages14, sex15, medication proﬁles16,
scanner speciﬁcations17, imaging parameters18 and instructions
to participants19. All of these aspects are known to affect the
MRI data. Without proof of generalization, the classiﬁer canneither be regarded as practical in clinical applications, nor canneuroimaging features selected by the classiﬁer be regarded as thecandidate neural substrates of ASD.
The issue surrounding the generalization of neuroimagingbased biomarkers for psychiatric disorders has attracted little
attention in neuropsychiatry until recently20,21. The majority ofthe previous developments of ASD biomarkers were made basedon a single-site data, leaving the generalizability issue out ofreach7–13. This situation has held true in more recent
investigations that incorporated multiple-site data22–25, forwhich the generalizability issue was not examined for an
independent validation cohort. There is one unsuccessfulattempt in which the generalizability of a classiﬁer was tested
on an independent validation cohort26. This study applied aclassiﬁer, that was previously developed based on measures ofstructural MRI for the population of the UK7,8, to Japanese ASD
individuals26. The classiﬁer exhibited more than 80% sensitivity
and speciﬁcity for the UK training data. However, its
performance was no better than chance level for the Japanese
test cohort. The results indicate that the development of a reliable
neuroimaging-based biomarker is extremely challenging.
To develop a generalizable classiﬁer, we must overcome thefollowing two major difﬁculties: over-ﬁtting and nuisancevariables (NVs). First, particular conditions in data and model
properties can cause the over-ﬁtting problem20 in which modelﬁtting to the training data can be so accurate that the associatederrors become artiﬁcially smaller compared with the inherent
data variance. This inﬂated prediction performance typically fails
when the model is applied to independent data that are not used
for determination of the model. Among other possibilities,
determining a large number of model parameters using a
relatively small data sample almost inevitably leads to the stateof over-ﬁtting, which makes the generalization capability of themodel extremely poor. For example, the identiﬁcation of ASDspeciﬁc features in magnetic resonance images must necessarily
entail a search over a few 104 to 105 voxels (or its squared number2

for voxel-to-voxel functional connections (FCs)) using a data set
that typically consists of not more than B103 individuals. In thiscase, the derived classiﬁcation scheme falls almost inevitably to astate of over-ﬁtting, resulting in catastrophic generalization to theexternal data20. In essence, an excessive number of freeparameters in the model introduces undesirable ﬁtting to aunique structure of the data, including inherent noise.
Second, any machine-learning algorithm used for classiﬁcation
is doomed to exploit NVs unique to a given sample data, and toerroneously select neuroimaging features that are correlated with
the NVs. NVs include both site-speciﬁc conditions in image
acquisition and properties in the sample population such as
demographic attributes, medication status, and onset andduration of illness. However, the neuroimaging features
correlated with these NVs are irrelevant to ASD itself in an
independent validation cohort, and naturally for the general ASD
population. To avoid biased extraction of ASD irrelevant features,
it is thus essential that classiﬁer development proceed with a large
population that is recruited at multiple sites and that all thepossible NVs be identiﬁed, controlled and removed appropriately
in the feature selection (FS) process.
Here, for the ﬁrst time we have developed an ASD classiﬁer
using a multiple-site data set in Japan, and conﬁrmed its
generalization capability in two independent validation cohorts
in the USA and Japan. We focus on abnormal functional
connectivity (FC) in ASD as revealed by resting-state fcMRI(rs-fcMRI)6,27–29. To suppress the over-ﬁtting and the effects ofNVs, a unique combination of machine-learning algorithms
automatically and objectively identiﬁes a small number of FCs
related to the ASD-speciﬁc abnormality. The resulting ASD
classiﬁer, based only on the identiﬁed FCs, achieves generalization
capability across multiple imaging sites (site generalization).
We also examine a different type of generalizability of theclassiﬁer towards other disorders (disorder generalization).
It is generally believed that ASD shares aetiological andpathophysiological backgrounds with schizophrenia (SCZ) to agreater degree than with attention-deﬁcit hyperactivity disorder(ADHD) and major depressive disorder (MDD)30–33. Recent
genome-level studies reported that ASD shares a signiﬁcantdegree of polygenic risk with SCZ, but not with ADHD or
MDD30,31. An accumulating body of evidence by clinical,
behavioural and neuronal phenotypes studies has shown a close
relationship between ASD and SCZ32,33. To our knowledge, nostudy has quantiﬁed spectral relationships among multiple
psychiatric disorders with respect to biological dimensions
deﬁned by intrinsic FCs. Here we examine the spectral
relationships among four disorders, ASD, SCZ, ADHD and
MDD, by means of a measure provided by the ASD classiﬁer.
More concretely, we examine the extent to which the ASD
classiﬁer is speciﬁc to ASD or extendable (generalizable) to otherpsychiatric disorders. This question can be rephrased as follows.
Does the ASD classiﬁer discriminate only ASD individuals from
TD control (that is, speciﬁc to ASD), or does it discriminate
patients with general psychiatric disorder from their healthy
controls (that is, generalized to other disorders)? At the individuallevel, the output of the ASD classiﬁer might provide a quantitative
measure of ‘ASD-ness’ along one of biological dimensions in
psychiatric disorders (Supplementary Fig. 1). If the ASD classiﬁershows speciﬁcity and/or generalizability only for a certain rangeof disorders, the ASD-ness may provide a useful biologicaldimension across the multiple-disorder spectrum34,35.
Results
Highly accurate Japanese-population-based classiﬁer for ASD.
We constructed a classiﬁer based on the FCs of each individual to

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Generalization of the classiﬁer for independent cohorts. We
tested the generalizability of the classiﬁer using two independentvalidation cohorts obtained from the US ABIDE Project40 andfrom site B in Japan (see Methods). In the ABIDE data pool,
we selected a subset of individuals that contained 44 highfunctioning adults with ASD and demographically matched 44
TD adults, who were recruited from seven sites in this data pool(see Methods). For this US-independent validation cohort locatedacross the Paciﬁc from Japan, the present classiﬁer, trained onlywith Japanese labelled samples, achieved a high performance withan accuracy of 75% (AUC ¼ 0.76) and a DOR of 9.0. The
probability of obtaining this high performance by chance isextremely small as P ¼ 1.4  10  6 (one-sided binomial test) anda

Classification based on WLS
TD
40

ASD
Japan
TD
ASD

30

20

10

b

Number of individuals

distinguish ASD from TD adults. The whole brain images werecollected from three different sites in Japan (74 high-functioning
adult ASDs and 107 adult TDs; see Methods for details). Age andsex were matched between ASD and TD for sites A and B. Site C
collected only TD data (Supplementary Table 1). This unbalanced
ASD/TD composition among the three sites was taken care of bya machine-learning algorithm as explained below. Each individual
image was divided into 140 regions using a sulci-based
anatomical atlas (extended Brainvisa Sulci Atlas)36. To obtain
interregional FCs through rs-fcMRI, Pearson correlation
coefﬁcients were computed for all possible 9,730 pairs of these
140 regions from their mean fMRI time-series data. A machinelearning technique was then applied to the whole set ofcorrelation matrices to optimally select a subset of FCs so thatthe best classiﬁcation performance would be obtained.
Speciﬁcally, we applied the L1-norm regularized sparsecanonical correlation analysis (L1-SCCA)37 to the data set to
identify a subset of FCs relevant only to the neural substrates of
ASD while factoring out the effects of noise and NVs associatedwith the data. In particular, the unbalanced ASD/TD composition
was addressed appropriately by incorporating the site label as NV(see Methods subsection ‘Selecting FCs as the ASD classiﬁer’).
We then employed the sparse logistic regression (SLR)38 tofurther perform dimension reduction to mitigate the over-ﬁtting
and thereby to extract the essential FCs representing the coreabnormal connectivity in ASD (see Methods and Supplementary
Fig. 2).
The classiﬁcation accuracy was evaluated by the leaveone-participant-out cross validation procedure (LOOCV, see
Methods). At each iteration, the classiﬁer incorporated only
15.3±0.7 out of 9,730 FCs (0.2% of the entire FCs).
Supplementary Note 1 and Supplementary Fig. 3 show therobustness and stability of the identiﬁed FCs across the
cross-validation procedure. The classiﬁer separated ASD- from
TD-populations with an accuracy of 85% (Permutation test,
P ¼ 0.001; see Supplementary Fig. 4)39. The corresponding area
under the curve (AUC) was 0.93, indicating high discriminatory
ability. For this classiﬁer, the weighted linear summation (WLS orlinear discriminant function) of the correlation values of theidentiﬁed FCs predicted the diagnostic label of each individual.
An individual with a positive and negative WLS was classiﬁed as
ASD and TD, respectively. Figure 1a shows that the two WLS
distributions of the ASD and TD populations from the Japanesedata set were clearly separated by the threshold of WLS ¼ 0, to theright (ASD) and to the left (TD). The sensitivity was 80% andspeciﬁcity was 89%. This leads to a high diagnostic odds ratio(DOR) of 31.1, which indicates that the effect size is very large.
We found that high classiﬁcation accuracy was not only achieved
for the entire data set, but also distributed equally among thethree imaging sites in Japan (85% accuracy for all the sites A–C;
see Supplementary Fig. 5 and Supplementary Table 2).

0
−30

−20

−10

0

10

20

30

25
USA
20

TD
ASD

15
10
5
0
−30

−20 −100
1020Weighted linear summation

30

Figure 1 | Distribution of weighted linear summations (WLS) of
functional connections used for the classiﬁcation of ASD and TD.
(a) The number of TD (white) and ASD (black) individuals in the Japanesedata included in a speciﬁc WLS interval of width 5 is shown as a histogram(see also Supplementary Fig. 5). (b) WLS for the US ABIDE dataset in thesame formats as a.

P ¼ 0.001 (permutation test, see Supplementary Fig. 4). We
emphasize that this performance was achieved when the classiﬁer
was applied to the US ABIDE data set for the ﬁrst time without
any retuning of the machine-learning procedure. Thus, this USA
data set was a true and ﬁnal validation set. One of the reasons forthe true validation test is that our algorithm does not allow any
parameter tuning based on the validation cohort (see also
Methods). As can be seen in the WLS distribution for the USA
data shown in Fig. 1b, the degree of separation between the ASD
and TD populations was almost comparable to that of theJapanese data set shown in Fig. 1a. This indicates that the present
classiﬁer was successfully generalized across the Paciﬁc to anindependent validation cohort of more diverse races/ethnicities
that were acquired under various imaging settings and conditions.
These results indicate that although we developed a highly
reliable classiﬁer by only using the training data obtained fromJapan, it is sufﬁciently universal to classify ASD/TD in the USA
validation cohort.
Given the possibility that the identiﬁcation of ASD-speciﬁc FCs
in the classiﬁer could have been inﬂuenced by ASD individuals’
factors irrelevant to the core ASD pathology, including secondary
symptoms and the medication status, the next challenge was to
examine how the ASD classiﬁer is resistant to such complications.
By relaxing the selection criteria for ASD, we identiﬁed 19
additional individuals with ASD and demographically matched
19 additional TDs in the ABIDE data pool (see Methods andSupplementary Note 2). We appended these individuals into themain USA data set to form the extended ABIDE data set thatconsisted of 63 individuals with ASDs and 63 TDs. Repeating the

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same analysis for this broadened data set, we found the results to
be: AUC ¼ 0.74, accuracy ¼ 71% and DOR ¼ 6.4, which wereslightly worse than the original narrower data set.
We further conﬁrmed the generalizability of the classiﬁer
using the Japanese-independent validation cohort (AUC ¼ 0.77,
accuracy ¼ 70%). This cohort incorporated 27 individuals with
ASD and 27 demographically matched TDs. These participants
were scanned more recently using a newer and different 3 T MR
scanner at site B in Japan, compared to the original Japanese
discovery cohort.

inter-hemispheric (69%) and right intra-hemispheric (31%) FCs
dominated, whereas the left intra-hemispheric FCs were absent(one-sided binomial test, P ¼ 0.01). Second, regarding thehemispheric distribution of the brain regions involved in the 16
FCs, there were signiﬁcantly more regions in the right hemispherethan in the left (one-sided binomial test, P ¼ 0.05). Third,
regarding the functional network attributes of the 32 brain
regions comprising these 16 FCs (allowing for duplicates in the
count), 41% (13 regions) belonged to the cingulo-opercular
network14,42. This percentage was signiﬁcantly higher than 24%,
the anatomically expected percentage, given 33 cingulo-opercularregions among a total of 140 regions ( ¼ 33/140  100) (one-sided
binomial test, P ¼ 0.02; see also Table 1).
The state of FC exhibiting the smaller (that is, more negative)
and greater (more positive) mean correlation index in the
ASD population than the TD control is termed under- andover-connectivity, respectively. In the 16 FCs incorporated in
the classiﬁer, ASD exhibited under-connectivity in nine FCs(rASDorTD) and over-connectivity in seven FCs (rASD4rTD)
compared with TD. See Table 1 for the mean correlation values
for the ASD and TD populations and Supplementary Fig. 6 fortheir distributions. A w2-test indicated that there was no
signiﬁcant difference between the number of FCs exhibiting
under- and over-connectivity (P ¼ 0.62). These results suggestthat neither the under- or over-connectivity hypothesis43–45 alone
can successfully describe the overall aberrancy in the FCs
exhibited by the ASD population. One previous study observed

Characteristics of the 16 identiﬁed FCs in the classiﬁer. Figure 2
shows the spatial distribution of the 16 FCs that were automatically and objectively identiﬁed from the data for reliableclassiﬁcation of ASD and TD by the machine-learning algorithm.
A detailed list of FC properties is provided in Table 1. Because thereliability of classiﬁcation was generalized to the two independentcohorts, these FCs are thought to be much more trustworthy incharacterizing neural substrates of ASD than the FCs that were
simply selected in many previous studies by conventional
statistical thresholding of ASD/TD differences within a limited
data set41.
We identiﬁed the following three major characteristics ofthe 16 FCs in terms of their hemispheric distributions andattributions to known intrinsic functional networks (Fig. 3 andTable 1). First, regarding the hemispheric distribution of the FCs,a

Anterior

Anterior
1
3

26

Left

PosteriorSuperior

Superior

11
13

10

Anterior

19
18

9

All 9,730 FCs
considered

Posterior

29
17

15

Right

14

28
22

Right

23

6 4
2 5

24 12

21

27

Left

7

Left

8

Right

20
25

16

Inferior

Posteriorb

InferiorcSuperior

Superior
14

14

12

Inferior

22

2

15
23

Anterior

20 5
1
3

1018
17

21
4 26
28
6
25 27
9
8

7

24

19
13
11

16

Posterior

3

2
20
15
21
23
5
10
1 17
18
4
28 26
6
19
9
16 27
7
25
8 24 13
29
11

Right

Left

22

29

12

Inferior

Figure 2 | The 16 FCs identiﬁed for the ASD/TD classiﬁer. (a–c) The 16 FCs viewed from (a) top, (b) posterior and (c) left. The inset displays all
9,730 FCs. The 29 terminal regions connected by the 16 FCs were numbered as follows: in the frontal lobe, the superior (1), middle (2), inferior (3, left;
4–7, right) gyri and rectus (8); in the temporal lobe, the superior (9), middle (10), inferior (11), parahippocampal (12) and fusiform (13) gyri; in theparietal lobe, the superior parietal lobule (14) and the postcentral gyrus (15); in the occipital lobe, the middle occipital gyrus (16), cuneus (17, left; 18, right)
and the calcarine ﬁssure (19); in the limbic system, the anterior (20), middle (21–22), posterior (23) cingulate gyri and amygdala (24); in the basal ganglia,
the caudate (25, left; 26, right), pallidum (27), thalamus (28); and cerebellum (29). See also Table 1 and Supplementary Movie 1.
4

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Table 1 | Properties of the 16 interregional FCs used in the classiﬁcation of the ASD and TD populations.
ID
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16

Terminal regions
Lat.
R
R
R
R
R
L
R
L
R
R
R
L
R
R
R
L
L
R
R
L
R
L
L
R
M
R
L
R
R
R
L
R

Name
Diagonal ramus of the lateral f.
Ascending ramus of the lateral f.
Subcallosal s.
Calloso-marginal posterior f.
ThalamusSubcallosal s.
Amygdala
Accumbens
Rhinal s.
Olfactory s.
Median occipito-temporal lateral s.
Anterior inferior frontal s.
Posterior terminal ascending branch of the superior temporal s.
Internal occipito-temporal lateral s.
Intermediate precentral s.
Lobe occipital
Polar frontal s.
Retro central transverse ramus of the lateral f.
CaudateCalloso-marginal anterior f.
Olfactory s.
Parieto-occipital f.
Pallidum
Superior temporal s.
VermisSuperior temporal s.
Superior parietal s.
Anterior lateral f.
Inferior precentral s.
Parieto-occipital f.
Anterior inferior frontal s.
Calcarine f.

Mean FC
Gyral region(4) Inferior frontal g.
(6) Inferior frontal g.
(21) Middle cingulum(22) Middle cingulum(28) Thalamus(23) Posterior cingulum(24) Amygdala(25) Caudate(12) Parahippocampal g.
(8) Rectus(11) Inferior temporal g.
(3) Inferior frontal g.
(10) Middle temporal g.
(13) Fusiform(2) Middle frontal g.
(16) Middle occipital g.
(1) Superior frontal g.
(15) Postcentral g.
(26) Caudate(20) Anterior cingulum(8) Rectus(17) Cuneus(27) Pallidum(9) Superior temporal g.
(29) Vermis(9) Superior temporal g.
(14) Superior parietal g.
(7) Inferior frontal g.
(5) Inferior frontal g.
(18) Cuneus(3) Inferior frontal g.
(19) Calcarine

BA
44
45
23
23
—
29
34
—
30
11
20
45
21
37
46
19
9
3
—
32
11
18
—
22
—
22
7
47
44
18
45
17

Net.
SM
CO
DM
CO
CO
DM
CO
CO
CO
DM
CO
FP
DM
OC
FP
OC
DM
SM
CO
CO
DM
DM
CO
CO
CB
CO
FP
CO
SM
OC
FP
OC

Wt.

rTD
0.77

rASD
0.71

 0.880.39

0.22

 1.950.30

0.10

 2.620.16

0.05

 2.140.11

 0.04

 2.110.03

 0.01

 0.98

 0.09 0.21

 1.26

 0.10 0.19

 1.59

 0.16

 0.29

 1.52

0.17

0.22

0.76

 0.10 0.021.78

 0.140.04

1.90

 0.18

 0.041.85

 0.19

 0.060.99

 0.24

 0.131.00

 0.24

 0.16

1.74

CB, cerebellum; CO, cingulo-opercular; DM, default-mode; f., ﬁssure; FC, functional connection; FP, fronto-parietal; g., gyrus; Lat, laterality; L, left; M, medial; Net, network; OC, occipital; R, right;s., sulcus; SM, sensorimotor; Wt., weight.
Listed here are the laterality and anatomical identiﬁcation of the terminal regions (as deﬁned in the Brainvisa Sulci Atlas), the associated gyral regions (as identiﬁed by the Anatomical Automatic
Labeling), their Brodmann’s areas, and associated networks, for each connection. The number in parenthesis appended to each gyral region represents the region identiﬁcation in Fig. 2. Identiﬁcationof the network is after Dosenbach et al.14. In addition, the mean correlations of the TD and ASD populations and the weighting coefﬁcient in the SLR classiﬁer are shown. FCs 1–9 represent
under-connectivity (rASDorTD), whereas FCs 10–16 represent over-connectivity (rASD4rTD). See also Supplementary Fig. 6.

a similar trend for the FCs selected simply by using a statisticalthreshold for the difference in FC between the two populations41.
However, there is no guarantee that the FCs that survived should
represent the neural substrates of ASD. This is because any
statistical result using thresholds varies with a speciﬁc data set
and the thresholds. Our result is the ﬁrst demonstration thatneither the under- or over-connectivity hypothesis alone
sufﬁciently characterizes the FCs that can classify the ASD
population from the TD population in independent validation
cohorts (Supplementary Fig. 6 and Table 1). Furthermore, thepresent ﬁndings are at odds with the previous distance-dependent
abnormality hypothesis that proposed disrupted long-range andenhanced short-range connectivity in ASD46. Speciﬁcally, we
found that the mean distance of the FCs was not signiﬁcantly
correlated with enhancement in the FCs in ASD (that is,correlation between the distance of an FC and its rASD  rTD;
difference in correlations of FCs for ASD and TD, r ¼ 0.42,
P ¼ 0.10) or with the difference in their absolute strengths(|rASD|  |rTD|; r ¼ 0.24, P ¼ 0.36). Furthermore, there wasno signiﬁcant difference (t14 ¼ 1.3, P ¼ 0.23) between themean distance of nine FCs exhibiting under-connectivity(64.6±51.1 mm) and the mean distance of seven FCs exhibiting
over-connectivity (92.8±33.9 mm). Here the distance of each FC
was computed as a one-line distance between the central
coordinates of the two connected brain regions.

Prediction of diagnostic instrument scores using the 16 FCs.
Using the 16 FCs identiﬁed in the classiﬁer, we predicted themeasured domain scores of the two standard diagnostic
instruments, the Autism Diagnostic Observation Schedule(ADOS)47 and the Autism Diagnostic Interview-Revised(ADI-R)48. The number of available subjects was 58 for ADOS
and 27 for ADI-R. Each instrument contained four domains, assummarized in Supplementary Table 3. In each domain of each
instrument, a linear regression was individually employed todetermine the weights of 16 FCs so that their weighted linear
summation was used as a predictor for the corresponding
measured score. Among the total of eight domains of ADOS and
ADI-R, we found that the communication domain of the ADOS(ADOS A) was well predicted from the 16 FCs with statisticallysigniﬁcant correlation (r ¼ 0.44, uncorrected P ¼ 0.001o0.05/8, aBonferroni-corrected threshold for multiple comparisons; see
Fig. 4a and Supplementary Table 3). The bootstrapping analysis
demonstrated that the probability that this correlation r ¼ 0.44
would be derived from 16 FCs randomly selected from 9,688( ¼ 9,730  42) FCs, which were not identiﬁed in the LOOCV
procedure, was small (P ¼ 0.048, Fig. 4b, see also Methods). These
results demonstrate that the 16 FCs identiﬁed in the classiﬁer
speciﬁcally contain more useful information than the remaining
FCs in predicting the ADOS A score, which is the degree ofdeﬁcits in communicative behaviours.

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69%

31%

Inter-hemisphericconnections

Right intra-hemisphericconnections
Ascend ram of lat f
Ant lat f
Med occi-temp lat s
Calloso-marg post f

Calloso-marg ant f

Sup temp s

Pallidum

Rhinal s

Accumbens

Amygdala

Int occi-temp lat s
Parieto-occipital f
Calcarine f
Post term ascend branch of
sup temp sParieto-occipital f

Subcallosal s

Polar frontal s

Olfactory s

Sup parietal sIntmed precentral s

Ant inf frontal s

Diag ram of lat f
Inf precentral s
Retro central transverse
ram of lat f

OthersLeft

VermisRight

Figure 3 | The 16 FCs (solid lines) and their terminal regions (names inboxes). The left and right halves of the ﬁgure correspond to the left andright brain hemispheres, respectively. The FCs were classiﬁed into threehemispherical categories: left intra-hemispheric, right intra-hemisphericand inter-hemispheric. The terminal regions deﬁned by the Brainvisa
Sulci Atlas belong to either cingulo-opercular or other networks. The
red background indicates the cingulo-opercular network. ant, anterior;ascend, ascending; calloso-marg, calloso-marginal; diag, diagonal; f, ﬁssure;inf, inferior; int, internal; intmed, intermediate; lat, lateral; med, median;occi-temp, occipito-temporal; post, posterior; ram, ramus; s, sulcus;
sup, superior; temp, temporal; term, terminal.

Application of the ASD classiﬁer to other disorders. Here we
examine the speciﬁcity to ASD of the ASD classiﬁer, and/or its
generalizability to psychiatric disorders other than ASD. If the
ASD classiﬁer predicts patients with a different disorder as
healthy control individuals, then AUC by the ASD classiﬁer forthe classiﬁcation of patients with that disorder from their control
should be close to 0.5. In this case, we may as well say that thepatients possess so little ASD-ness and that the disorder is not
related to ASD from the viewpoint of the imaging biologicaldimension. In contrast, if the ASD classiﬁer perfectly discriminates patients with a different disorder from its control, theclassiﬁcation AUC should be close to 1. In this case, we may as
well say that the patients possess a large degree of ASD-ness inthem and that this disorder is closely related to ASD according to
the biological dimension.
To test this, we applied the ASD classiﬁer to two additional
Japanese cohorts of SCZ and MDD (each containing a healthy
control population) and one European cohort of ADHD
(containing a TD population) (see Methods). We computed the
WLS of the identiﬁed FCs in the ASD classiﬁer, that is, theASD-ness of each individual within the SCZ, MDD and ADHD
data sets, and their corresponding healthy or TD control
populations. We then compared the WLS distributions between
each disorder group and its corresponding healthy or TD control(Fig. 5). As expected and already demonstrated in Fig. 1, theseparation of WLS distributions was the largest between ASD and
TD (Fig. 5a), meaning that the developed ASD classiﬁer has a
6

6
4
2

r = 0.44
P < 0.001

0CaudateSubcallocal s

b

8

0

ThalamusLobe occipital

Measured score

Cingulo-opercular network

a

2
4
6
Predicted score

8

Frequency

0%
Left intra-hemisphericconnections(r = 0.44)

450
300
150
P = 0.048

0−1−0.5 00.5
1Correlation coefficient

Figure 4 | Prediction of ADOS A domain score (communication) using
the 16 FCs identiﬁed in the classiﬁer. (a) Scatter plot of the measured
ADOS A domain versus the predicted score, which was computed as alinear weighted summation of the 16 FCs identiﬁed by the ASD/TD
classiﬁer. Each dot represents individual data (n ¼ 58, see Methods,
Participants). The line indicates the linear regression of the measured scorefrom the predicted score, and correlation coefﬁcient and statisticalsigniﬁcance are shown (see Supplementary Table 3 for results of the otherthree domains of ADOS and all four domains of the ADI-R instrument).
(b) The frequency of the different correlation coefﬁcient values is plotted ina bootstrap analysis in which 16 FCs were randomly selected from all 9,730
FCs, with the exception of those 42 FCs selected in the LOOCV procedure.
The correlation coefﬁcient between the measured and predicted scores wascomputed as in a. This analysis indicates that the probability of obtaining
the correlation coefﬁcient r ¼ 0.44 was small (P ¼ 0.048), anddemonstrates that the 16 FCs identiﬁed in the classiﬁer speciﬁcally contain
information useful to predict the ADOS A score.

good ability to discriminate ASD from TD individuals, and the
ASD-ness is able to successfully separate the two populations. The
separation between SCZ individuals and their healthy controls
was poorer than that of ASD but statistically signiﬁcant (Fig. 5b;
AUC ¼ 0.65, Kolmogorov–Smirnov test, P ¼ 0.012 corrected for
multiple comparisons). In contrast to SCZ, the WLS distributionsof ADHD and MDD, and their corresponding TD and healthy
controls were not distinguishable (Fig. 5c,d; AUC ¼ 0.57,
Kolmogorov–Smirnov test, P ¼ 0.65 for ADHD; AUC ¼ 0.48,
Kolmogorov–Smirnov test, P ¼ 0.83 for MDD). In other words,
the ASD-ness of individuals with ADHD or MDD is not different
from that of their controls. Note that MDD was more completely
indistinguishable from its control compared with ADHD
according to the ASD-ness. It can be said that the ASD classiﬁer
was speciﬁc to ASD regarding ADHD and MDD, but wasmodestly generalized to SCZ (compare AUC ¼ 0.93 for the ASD
discovery cohort and AUC ¼ 0.65 for the SCZ data set). These
results demonstrate that the WLS of the ASD classiﬁer, in otherwords the ASD-ness, quantiﬁed the spectrum of the four
disorders as follows; SCZ was close to ASD, ADHD was distantfrom ASD, and MDD was farthest from ASD.
Discussion
In the present study, we established a reliable neuroimagingbased classiﬁer for ASD by investigating the whole-brain patternsof FCs using the rs-fcMRI data of 74 adults with ASD and 107 TD
individuals collected at multiple sites in Japan. This classiﬁer
incorporated as small as 16 FCs (only 0.2% of the entire FCs)
distributed across the brain but not contained in the left
hemisphere, and allowed a diagnosis prediction accuracy of
85% for each individual with balanced sensitivity and speciﬁcityof 80% and 89%, respectively. Most importantly, the highperformance of the classiﬁer was generalized across the Paciﬁcto the independent, ethnically more diverse, validation cohort
in the USA (75% accuracy) with only 10% decrease inaccuracy compared with the Japanese discovery cohort. Although

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a ASD

Densityb SCZ

c ADHD

AUC = 0.93
P = 6.7×10–20

AUC = 0.65
P = 0.012

AUC = 0.57
P = 0.65= 0.48d MDD AUC
P = 0.83

–2

–1

0

1
2
WLS

3

4

5

Figure 5 | Application of the ASD classiﬁer to other psychiatricdisorders. The density distributions of the weighted linear sum (WLS)
obtained by applying the ASD classiﬁer to (a) ASD, (b) SCZ, (c) ADHD
and (d) MDD data sets. In each panel, the patient distribution and theTD/healthy control distribution are plotted separately, with coloured andgrey areas, respectively. For reference, the WLS distribution of the ASD
patients (red area) in a is duplicated across the panels (b–d). For eachpatient–control pair in a–d, the signiﬁcance of the Benjamini–Hochbergcorrected Kolmogorov–Smirnov test and AUC values are shown. In thisﬁgure, for the visualization purposes, the WLS of each data set isstandardized to match median and s.d. of TD controls across the panels.
Note that this WLS standardization is not performed in any quantitative
analysis.

successful construction of a FC-based ASD classiﬁer has beenreported previously49, our work presents the ﬁrst achievement of
successful classiﬁcation for ASD across discovery as well as
validation cohorts. Our approach may lay a foundation fordeveloping classiﬁers for other psychiatric disorders. This isbecause, to the best of our knowledge, there exists noneuroimaging-based classiﬁer for any psychiatric disorder ofwhich the generalization capability is demonstrated for an
independent validation cohort. We have further applied the
ASD classiﬁer for classiﬁcation of SCZ, MDD and ADHD
patients from their healthy controls. The results indicate that,while the ASD classiﬁer exhibited hardly any generalizability as
applicable to ADHD and MDD, it can be to a modest degree
generalizable to SCZ.
In the present study, both sophisticated machine-learningalgorithms and a variety of data from the Japanese three sites
were essential for successful generalization of the classiﬁer acrossmultiple sites. First, the unique combination of the two machinelearning algorithms, L1-SCCA and SLR, worked to achieve
optimal extraction of a small number of FCs that were relevant
only to the core ASD characteristics. This optimal extraction
avoids over-ﬁtting and eliminates the effects of NVs such as age,sex and site-dependent characteristics in the data composition
and imaging protocols. In fact, when we applied to our data
sets a state-of-the-art machine-learning algorithm of nested
cross-validation of the elastic net50, this algorithm selected

10 times more FCs and performed 14% worse on the USA
cohort (percent correct of 61%; see Supplementary Note 3 formore detail). This algorithm did not explicitly exclude theinterfering effects of NVs. This fact indicates that thegeneralization capability of our ASD classiﬁer across imaging
sites most probably stemmed from reduced inﬂuences of FCs
related to NVs owing to the unique combination of L1-SCCA and
SLR. By utilizing synthetic data sets and by comparing with elastic
net, we demonstrated that the unique combination of L1-SCCA
and SLR can be useful to reduce the inﬂuence of FCs related toNVs (see Supplementary Note 4). Second, we examined theconditions for which data sets can derive reliable ASD classiﬁers.
More concretely, we selected one or two of the three sites
within the Japanese discovery cohort for training data sets
(Supplementary Table 4) and constructed classiﬁers. In addition,
we trained a classiﬁer with the ABIDE data set and examined its
generalization capability for the Japanese cohort (Supplementary
Note 5). The resulting performances were generally poorer thanthat of the current ASD classiﬁer. Especially, the performance of
the ASD classiﬁer, which was developed using the ABIDE dataset, was very poor. It is suggested that having a sufﬁcient numberof participants in total as well as in each site is a necessary
condition to construct a reliable ASD classiﬁer (see also
Methods). We conclude that both a sophisticated machinelearning algorithm and a large training data set are essential fordeveloping a reliable and generalizable classiﬁer.
It is worth noting that the performance of the classiﬁer may be
upper-limited by the aetiological and phenotypic heterogeneity of
ASD, which is likely to be accompanied by differential biologicalunderpinnings. This limitation may be ameliorated and theoverall diagnostic precision may be improved by identifying
subgroups that are biologically more uniform within a given
population and by extracting a set of features that characterizeeach subgroup.
What do the results of the applications of the ASD classiﬁer tothe other psychiatric disorders suggest? Figure 5 shows thedensity distributions of the WLS that resulted from theapplication of the ASD classiﬁer to data sets for other disorders,
SCZ, MDD and ADHD. The results raise the intriguing
possibility that the degree of generalizability and speciﬁcity of
the ASD classiﬁer to these other disorders reﬂect their spectral
structure on the scale of whole-brain intrinsic functional
networks. From this perspective, Fig. 5 suggests that ASD shares
more intrinsic-functional networks with SCZ than with ADHD or
MDD. This is consistent with the results of the previous clinicalworks as described in the opening paragraphs30,32. These results
raise the possibility that a neuropsychiatric disorder can be
redeﬁned and represented as a location in a multi-dimensional
space deﬁned by FC-based biological ‘dimensions’, each of whichtakes the form of WLS consisting of a small number of FCs34,35.
In this case, the ‘ASD-ness’ could make a dimension along which
ASD and SCZ are located and might be orthogonal to anotherdimension along which ADHD and MDD are located.
Interestingly, to aim at building a biomarker for ASD, westarted with a categorical approach by which a supervisedmachine-learning algorithm was utilized and a diagnostic label
was adopted as its teaching signal. However, the results ofapplying the classiﬁer built for that original purpose to otherneuropsychiatric diseases have raised the exciting possibility thatthe classiﬁer allowed us to go beyond the category regime and toembark on the exploration for new biological dimensions34,35.
How would the current research results contribute to the future
diagnoses and therapy for neuropsychiatric disorders? Recently,
an increasing number of researchers have had the perspective thata biomarker can be used to stratify a broad illness phenotype
into a ﬁnite number of treatment-relevant subgroups, thereby

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bypassing nosological arguments over diagnostic boundaries5.
This perspective could lead to developments of multiple
neuroimaging-based biomarkers for multiple psychiatricdisorders. The generalization capability across imaging sites is abare minimal requirement for a classiﬁer towards its clinicalapplications. If reliable classiﬁers for ASD, SCZ, MDD, ADHD
and even other disorders are developed in the near future, theseclassiﬁers may be utilized as a new diagnostic tool as a set of
biomarkers that can quantify intrinsic FCs of individuals whoneed in-depth clinical examinations for various disorders. Suchquantiﬁcation is possible because multiple biomarkers can use thesame rs-fcMRI data from an individual. In this vein, the current
study could provide a foundation for such a future direction inneuropsychiatric diagnoses.
We formed a consortium with other researchers in 2013 aspart of the Japanese Strategic Research Program for Promotionof Brain Science (SRPBS)51 with the aim of applying big
data, machine-learning algorithms and sophisticated fMRI
neurofeedback methods52,53 to study diagnosis and therapy for
multiple psychiatric disorders. We have developed fMRI real-time
neurofeedback methods that can change FC between brain
regions with healthy and ASD individuals. First, in healthy
individuals, 4 days of fMRI real-time neurofeedback of FC
between two designated areas changed rs-fcMRI connectivity,
and the changes remained for more than 2 months53. Second,
for ASD individuals within the SRPBS consortium, a further
developed neurofeedback method of FC has been applied54,55.
The identiﬁed 16 FCs in the present research may contribute toimprovements in the fMRI real-time neurofeedback of FC to ASD
individuals as a possible therapeutic target. In one recent study
with ASD individuals, target FCs were selected by the ASD
classiﬁer developed in the present study54, and the WLS of the
ASD classiﬁer was estimated in a real-time fMRI neurofeedback
paradigm for an ASD individual. Then, a sign-inverted WLS
value was presented to the ASD individual as a neurofeedback
target to increase in a reinforcement learning paradigm54.
Increases in the neurofeedback score lead to reductions in the
WLS value. Researches within the SRPBS consortium havesuggested that the ASD classiﬁer we have developed in this study
could be a useful tool, with which connectivity neurofeedback
methods would make further progress to attain the goal of ASD
individuals obtaining normal rs-fcMRI dynamics51.
In summary, we have developed a generalizable rs-fcMRIbased classiﬁer for ASD28 for the ﬁrst time. Despite the fact that
this classiﬁer is based on a small number of identiﬁed FCs, itgreatly distinguishes ASD from TD with demonstrated
generalization in the independent validation cohorts, andaccounts for socio-communicative aspects of ASD. The resultsof applications of this ASD classiﬁer to other psychiatric disorders
have left open the interesting possibility of exploring newneuroimaging-based dimensions for multiple-disorder spectrum.
Methods
Participants. All participants in the present study provided written informed
consent as approved by the ethics committees of the recruiting institutions asfollows: the Ethics Committee of the Graduate School of Medicine and Faculty of
Medicine at the University of Tokyo, the Ethics Committee of the Faculty of
Medicine of Showa University, the Institutional Review Board of Advanced
Telecommunications Research Institute International, the Committee on Medical
Ethics of Kyoto University and the Ethics Committee of Hiroshima University.
A total of 74 adults with ASD and 107 age, sex, handedness and IQ-matched
TD individuals participated in the present study. The participants were recruited atthree different sites in Japan (sites A–C). Their demographic information issummarized in Supplementary Table 1.
At site A, participants with ASD were recruited through the Department ofChild Psychiatry and Neuropsychiatry at the University of Tokyo Hospital and via
an advertisement on the website of the University of Tokyo Hospital. All ASD
participants (n ¼ 35) were diagnosed with pervasive developmental disorder (PDD)
8based on the DSM-IV-TR criteria56. DSM-IV-TR diagnoses of autistic disorder,
Asperger’s disorder, or pervasive developmental disorder not otherwise speciﬁed(PDD-NOS) (n ¼ 24, n ¼ 3 and n ¼ 8, respectively) were supported by ADOS47(n ¼ 35) and ADI-R48 (n ¼ 27). The Japanese version of mini-international
neuropsychiatric interview M.I.N.I. was used to evaluate psychiatric comorbidity57.
No participant satisﬁed the diagnostic criteria for substance use disorder, bipolar
disorder or SCZ. The IQ scores of participants with ASD were obtained using theWechsler adult intelligence scale-revised (WAIS-R) or third edition (WAIS-III).
The full-scale IQs (FIQs) of all of the individuals with ASD were measured andfound to be 485. TD individuals were recruited from the local community and via
other on-going studies at site A. M.I.N.I. was used to conﬁrm that none of the
TD met the diagnostic criteria for any psychiatric disorder. The IQs of the TD
individuals were estimated using the Japanese version of the national adult reading
test (JART)58. All participants were right-handed according to the Edinburgh
Handedness Inventory59. Participants completed the Japanese version of theautism-spectrum quotient (AQ-J)60. At the time of scanning, 11 ASD individuals
were medication free, whereas the remaining 24 ASD individuals had been
administered the following psychotropic drugs: anxiolytics (n ¼ 18),
antidepressants (n ¼ 20), antipsychotics (n ¼ 15), antiepileptics (n ¼ 6) andsleep-inducing drugs (n ¼ 17), before the scanning. Some participants had been
administered multiple drugs (n ¼ 20).
At site B (Showa University Karasuyama Hospital), the diagnoses were made bya team of experienced psychiatrists and clinical psychologists based on detailed
interviews of individuals regarding their development and behaviour, from infancy
through adolescence and family history. At least one caregiver who knew theindividual in his/her childhood was usually present in the interview. At the end of
the clinical interview, the psychiatrist diagnosed the individuals according to the
DSM-IV-TR diagnostic criteria for PDD based on the consensus of thepsychiatrists and the clinical psychologists. These assessments resulted in all of theparticipants in the ASD group (n ¼ 39) receiving clinical diagnoses of autistic
disorder (n ¼ 19), Asperger’s disorder (n ¼ 16) and PDD-NOS (n ¼ 4). The
diagnoses for 23 individuals were supported by ADOS47. As performed at site A,
the IQ scores of participants with ASD were obtained using WAIS-R or WAIS-III.
FIQ for all individuals with ASD was 480. FIQ for all TD individuals wasestimated using JART. All participants, including ASD and TD, completed theJapanese version of the AQ test60. M.I.N.I. was used to conﬁrm that none of the
TD individuals met the diagnostic criteria for any psychiatric disorder. At the timeof scanning, 27 ASD individuals were medication free, whereas the remaining 12
ASD individuals were administered the following psychotropic drugs: anxiolytics(n ¼ 7), antidepressant (n ¼ 9), antipsychotics (n ¼ 3), antiepileptics (n ¼ 3) andsleep-inducing drugs (n ¼ 7). Some participants were administered multiple
drugs (n ¼ 8).
At site C (Advanced Telecommunications Research Institute International),
33 TDs participated in the present study after providing written informed consent.
None of the participants had a previous history of neurological disorders. All
participants were right-handed as conﬁrmed by the Edinburgh inventory. No ASD
individuals were recruited at site C as it was not a medical institution.

Training data set used for construction of the ASD classiﬁer. MRI data for the
training of the ASD/TD classiﬁer were acquired at three different sites in Japan. An
MRI system was used at the site where participants were recruited. Each imaging
site adopted its own imaging protocol (Supplementary Table 5), differing in both
imaging parameters and instructions provided to the participants during the scan.
These discrepancies were taken into account in subsequent classiﬁcation analysis(see the section below ‘L1-regularized sparse canonical correlation analysis’and Supplementary Note 6). At all sites, participants were subjected tohigh-resolution T1-weighted structural imaging as well as resting-state functional
imaging, which were preprocessed with SPM8 (Wellcome Trust Centre for
Neuroimaging, University College London, UK) software running on MATLAB(R2012b, Mathworks, USA) as follows. First, the raw functional images werecorrected for slice-timing and realigned to the mean image of that sequence tocompensate for head motion. Next, the structural image was co-registered to themean functional image and segmented into three tissue classes in the Montreal
Neurological Institute (MNI) space. Using associated parameters, the functional
images were then normalized and resampled in a 2  2  2 mm3 grid. Finally,
they were smoothed by Gaussian of full-width at half-maximum 6 mm. Because
subsequent analysis is based on the pattern of temporal correlations among thebrain regions and the evaluation has shown itself to be highly sensitive to abrupt
head motion during scanning, the pre-processed sequence of functional images was
examined as follows. First, we evaluated the mean relative displacement61 in eachof the six motion parameters (that is, translation along and rotation with respect tothe x, y and z axes) by calculating the mean of the absolute frame-to-frame relativechanges in each individual parameter through a given time series (namely, themean of Dp ðiÞ  jpi þ 1  pi jacross the time series, where p is one of the six
motion parameters and i speciﬁes the time point). In both the Japanese and the
USA data sets, there was no statistically signiﬁcant group difference in this measure
for any of the six motion parameters (Supplementary Table 6). Next, for eachparticipant, we calculated the frame displacement (FD) at each time point bysumming Dp ðiÞ for all six parameters. Using this FD, we employed the ‘scrubbing’procedure62 to identify and exclude any frame exhibiting excessive head motions.

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Speciﬁcally, a frame was ﬂagged and removed, along with the previous and two
subsequent frames, from the correlation analysis, if the associated FD exceeded
0.5 mm (ref. 62). On average (±s.d.), 93.4±11.2% and 95.7±7.5% of the originalframes passed this ‘scrubbing’ procedure in the TD and ASD populations,
respectively, and these fractions did not differ signiﬁcantly between the two
populations (two-sample t-test, P ¼ 0.13).
Generalization to USA data. The performance of the classiﬁer was further tested
using an independent data set available from the US ABIDE Project40. For
individuals with ASD, the criteria for data inclusion were that they must (1) beolder than 18 years of age, (2) be right-handed, (3) have a FIQ exceeding 80,(4) have no comorbidity and (5) have been diagnosed as autistic by either ADI-R or
ADOS. Individuals with an explicit medication record at the time of the scan were
excluded. A total of 54 autistic individuals satisﬁed these criteria. In addition,
52 age-, sex- and FIQ-matched TD individuals satisfying criteria (1)–(4) wereselected from the same pool of participants. Then, their MRI data were obtained
and the functional images were visually inspected to ascertain that the ﬁeld of view
covered the entire brain. We found that functional images for 18 participants
suffered from severe truncation at either the top (parietal lobe) or bottom(inferior temporal lobe to cerebellum) portion of the brain, and they were removed
from the further analysis accordingly. A total of 44 individuals with ASD and 44
demographically matched TD individuals comprised the ﬁnal list. Their properties
are summarized in Supplementary Table 7. The imaging protocols adopted at eachsite are summarized in Supplementary Table 8. We preprocessed the MRI data inthe same way as for the Japanese data and calculated the interregional FC for eachsubject. In addition, to test the performance of the classiﬁer on individuals withmore diverse proﬁles, we formed a Supplementary Dataset by removing theconditions for FIQ, comorbidity and medication status. The detail of the data
set and the result of the analysis are provided in Supplementary Note 2.
Further evaluation of the generalization capability. To further examine theclassiﬁer’s generalization capability, we formed an extra data set at site B (Showa
University Karasuyama Hospital) independently of the training data set. This data
set incorporated 27 individuals with ASD and 27 demographically matched TDs
who were recruited under the criteria of this site (see the Participants section).
The data acquisition was conducted using a new 3 T MR scanner of a different
manufacturer, replaced after the formation of the training data set. For more detailincluding the imaging protocol, see Supplementary Table 9.
Application of the ASD classiﬁer to other disorder. To further understandthe generalization property of the ASD classiﬁer, we evaluated its classiﬁcation
speciﬁcity to ASD. Speciﬁcally, we tested its classiﬁcation performance using thedata sets that incorporated individuals with SCZ, MDD and ADHD as follows.
We formed a data set that consisted of 66 patients with SCZ (34 females, age
38.2±9.1 year) and 107 age-matched healthy control participants (40 females, age
34.6±8.2 year). Their handedness was determined by the Edinburgh Handedness
Inventory59. The mean±s.d. of the SCZ was 75.0±40.9 and that of the healthy
control was 81.2±35.1. The patients were recruited at in- and out-patient facilities
in the Kansai region in Japan. They were diagnosed with the patient edition of theStructured Clinical Interview for DSM-IV Axis I Disorders (SCID). None of thepatients had comorbid psychiatric disorders. The controls were recruited from thelocal community at Kyoto University. None of them had any history of psychiatricillness, as indicated by screening results using the nonpatient edition of the SCID.
These screening results were conﬁrmed by the fact that none of their ﬁrst-degree
relatives had any history of psychotic disorders. The MR data of both patientsand healthy controls were acquired at the Kyoto University Hospital (seeSupplementary Table 9 for more details). All participants were physically healthy
when they were scanned. The details of this data set are stated elsewhere.
Next, we formed a data set that consisted of 105 patients with unipolar MDD(51 females; 42.8±11.5 year) and 145 age-matched healthy control participants(90 females; 39.5±12.7 year). Their handedness was determined by the Edinburgh
Handedness Inventory59. The mean±s.d. of the MDD were 84.8±30.1 and that of
the healthy control populations was 81.7±36.0. The patients were recruited from a
local clinic and the healthy controls in the community of the Hiroshima University.
The MR data of both patients and healthy controls were acquired at the Hiroshima
University Hospital and other local imaging facilities (see Supplementary Table 9
for the summary of the data). All the patients were screened with the DSM-IV
criteria for a unipolar MDD diagnosis using M.I.N.I. No patient had current or past
SCZ episodes. Healthy participants were interviewed with M.I.N.I. and none ofthem showed a history of psychiatric disorders according to DSM-IV criteria. The
details of this data set will be described elsewhere.
Next, we formed a data set that incorporated individuals with ADHD and
TDs acquired by the NeuroIMAGE project in the Netherlands (http://www.
neuroimage.nl/). They were a part of the ADHD-200 Sample and we obtained
their permission-free MR data and the associated demographic and phenotypic
information from the ADHD-200 Sample website (http://fcon_1000.projects.nitrc.
org/indi/adhd200/) under an unrestricted usage agreement for non-commercial
research purposes. Because the current study focuses on adult ASD, only
individuals with rounded ages 418 years were incorporated into the present

analysis. The ﬁnal data set consisted of 13 individuals with ADHD (2 females;19.0±1.1 year) and age-matched 13 TDs (7 females; 19.2±1.2 year). The subtype
identiﬁcation of the ADHD populations was three hyperactive-impulsive types, one
inattentive type and nine combined (hyperactive-impulsive and inattentive) types.
Among the ADHD individuals, 10 were right-handed, 3 were left-handed and noinformation was available for 1 individual. Among the TD individuals, 11 wereright-handed and 2 were left-handed. For more information on their demographic
and phenotypic properties, see the ADHD-200 Sample website.
To evaluate the extent to which each additional disorder tends to share traits
with ASD, we applied the ASD classiﬁer to these three data sets in the same manneras the US ABIDE data. The AUC of the classiﬁcation was computed to evaluate thedegree of separation of SCZ, MDD and ADHD from their corresponding control
population. Moreover, the Kolmogorov–Smirnov test was used to compare the
WLS distributions of each disorder with their corresponding healthy controls and
TD individuals. The WLS distributions of the patient and control populations wereﬁtted separately with a mixture of Gaussians distributions and illustrated in Fig. 5,
along with the respective AUC and Kolmogorov–Smirnov P value. The P value ofeach test was corrected for multiple comparisons by the Benjamini–Hochberg
procedure. For visualization purposes, the WLS in each data set was standardized
such that the median and s.d. of healthy controls and TD individuals were matched
across panels. It should be noted that this standardization was not used for any
statistical analyses.
Interregional correlation analysis. For each participant, a pair-wise, interregional
FC was evaluated among 140 regions of interest (ROIs) covering the entire brain.
The spatial extent of each region was deﬁned anatomically by the digital atlas of theBrainvisa Sulci Atlas (BSA)36. Because this atlas did not include the cerebellum, thesubregions of the cerebellum were appended to it by incorporating their boundary
deﬁnitions in the anatomical automatic labelling (AAL) package63. Although theoriginal AAL atlas deﬁned 26 subregions in the cerebellum, they were reorganized
into the following three subregions in this study: the left and right cerebellum, andthe vermis. This modiﬁcation was necessary because the scanned volume did notcover the entire cerebellar regions for some individuals, and this incomplete
coverage lead to missing elements in the correlation matrix. To surmount this,the mean time courses in the cerebellar regions were evaluated in three broader
subregions by masking, if any, unavailable voxels in each individual. This
BSA-AAL composite atlas was resampled in the 2  2  2 mm3 grid MNI space.
The representative time course in each region was extracted by averaging the timecourses of the voxels therein. A band-pass ﬁlter (transmission range, 0.008–0.1 Hz)
was applied to these sets of time courses prior to the following regression
procedure. The ﬁltered time courses were linearly regressed by the temporal
ﬂuctuations of the white matter, the cerebrospinal ﬂuid, and the entire brain as wellas six head motion parameters. Here, the ﬂuctuation in each tissue class wasdetermined from the average time course of the voxels within a mask created by thesegmentation procedure of the T1 image. The mask for the white matter was erodedby one voxel to consider a partial volume effect. These extracted times course werebandpass ﬁltered (transmission range, 0.008–0.1 Hz) before the linear regression, as
was done for regional time courses. Then, for each individual, a matrix of 9,730 FCs
between 140 ROIs was calculated by exhaustively evaluating pair-wise temporal
Pearson correlations of blood oxygenation level dependent signals time courses
while discarding ﬂagged frames, if any, in the previous procedure (scrubbing). We
note that unﬁltered motion-related regressors, such as six head motion parametersin the present case, could reintroduce high-frequency ﬂuctuations into the timecourse data61. The scrubbing procedure was employed to remove any frames
exhibiting abrupt head motions that could be the source of high-frequency
ﬂuctuation in the ﬁltered time course64. In addition, we conﬁrmed that there wasno statistically signiﬁcant difference in any of the motion parameters between the
ASD and TD populations (Supplementary Table 6). Thus, the chance that theclassiﬁcation was inﬂuenced by head motion remained minimal.
Selecting FCs as the ASD classiﬁer. Two major challenges exist in constructing aclassiﬁer for ASD. The ﬁrst challenge is the problem of over-ﬁtting, because of thesmall sample size. As previously mentioned, the dimension of the input to theclassiﬁer is M ¼ 9,730. However, the amount of data is only N ¼ 181. Because N ismuch smaller than the dimension of data M, the parameters of the classiﬁer can beeasily over-ﬁtted to the training data. Because of this over-ﬁtting, the constructedclassiﬁer will likely exhibit extremely poor performance with newly sampled test
data, which are not used in training the classiﬁer. Therefore, we need to properly
introduce regularization to identify and utilize only essential FCs to ensure good
generalization of the classiﬁer. Here we adopted a cascade of the L1-regularization
method, a well-known approach for managing the problem of small sample size,
and a sparse estimation method with automatic relevance determination65,66,
as detailed below and in the next two sections.
The second major challenge is related to NVs and is due to the fact that an ASD
classiﬁer is clinically useful and scientiﬁcally trustworthy only if it maintains good
performance for MRI data scanned at imaging sites different from the sites where
the training data were collected. This is the so-called generalization capability
across imaging sites. However, in clinical applications, it has often been observedthat a classiﬁer trained using data acquired from a particular site cannot be
generalized to the data scanned at other sites7,8,26. We overcame the second

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challenge by using a wide variety of training data sets obtained at the three imaging
sites, and by the unique combination of two sophisticated machine-learningalgorithms: L1-SCCA and SLR. Through additional analyses, we conﬁrmed that
MRI data scanned from at least three sites, and obtained under a variety of imaging
conditions, are necessary to train a classiﬁer that generalizes across multiple sites(see Supplementary Table 4 for the results obtained when data from only one or
two sites were used). Furthermore, to extract FCs essential for ASD classiﬁcationand to reduce undesirable effects due to different scanning conditions anddemographic distributions at different sites, that is, irrelevant NVs, we adopted theL1-regularized sparse canonical correlation analysis (L1-SCCA)37 (see also
Supplementary Note 6).
Altogether, the procedure for selecting relevant FCs, training a predictive modeland assessing its generalization ability was carried out as a sequential process of9  9 nested feature-selection and leave-one-out cross-validation (see also theschematic diagram in Supplementary Fig. 2). In each leave-one-out (LOO)
cross-validation (CV) fold, all-but-one subjects were used to train a SLR38 classiﬁer,
while the remaining subject was used for evaluation. SLR has the ability to train alogistic regression model, while objectively pruning FCs that are not useful for the
purpose of classifying ASD. Before training SLR, it is necessary to reduce the input
dimension to some extent and simultaneously remove the effects of NVs that may
cause catastrophic over-ﬁtting. Therefore, prior to LOOCV, nested FS was
performed using L1-SCCA. L1-SCCA identiﬁes the latent relationships between FCs
and various attributes of each individual, including the diagnostic label, available
demographic information and imaging conditions (see details in the next section).
By selecting FCs that have a connection with a canonical variable related only
to the ‘Diagnosis’ label and not to NVs, we aimed to reduce the interferential
effects of NVs.
The feature (FCs) selection procedure was similar to 9  9 nested crossvalidation, with the difference being that the test set was never used for validation
or feature (FCs) selection (Supplementary Fig. 2). In this way, L1-SCCA was trainedon different subsamples of the data set, to increase the stability of the selectedfeatures. The ‘test set’ of the outer loop FS process was kept as a testing pool for
LOOCV, whereas the nine folds of the inner loop FS were used to select features.
Consequently, the LOOCV folds that belonged to the same testing pool of the outer
loop FS shared the same reduced features. In the inner loop FS, the L1-SCCA
hyperparameters l1 and l2 were varied independently between 0.1 and 0.9 (l1rl2)
with a step of 0.1. For each instance of L1-SCCA, we found the canonical variables
connected only with the label ‘Diagnosis’ and kept the features associated withthose canonical variables. On average, the number of l combinations that compliedwith this constraint was 17.6±5.0% of the total 45 possible combinations. The
features selected at each inner fold and l combination were combined by the union
operation, to include features that are important for any possible subsample (innernine folds) of the training data set. This procedure leads to the selection of
4,529±161 FCs (mean and s.d. across outer folds). Once the inner loop FS was
executed, one sample was taken from the testing pool of the outer loop FS, andused as the test set of the LOOCV. The remaining samples were used to train SLR
on the FCs retained during the inner loop FS. The advantage of this nested FS
procedure was that it used most of the data to train the models (LOOCV),
while performing time-efﬁcient FS (9  9 nested FS). The FS procedure based on
L1-SCCA is time consuming, and doing it for each fold of the LOOCV is notcomputationally feasible. Instead, we kept one of the nine outer folds as a ‘testing
pool’ for the LOOCV and ran L1-SCCA on the remaining eight folds. This meansthat we could reuse the selected features for all the samples in the ‘testing pool’,
during the LOOCV. That is, by performing ninefold nested FS we kept the test setof the LOOCV separate from the data set used to select features. We could
efﬁciently (from a computational time perspective) avoid information leakage andover-optimistic results20. It should be noted that, to split the data into nine folds,
we used a stratiﬁed approach, so as to keep an equal amount of (diagnosis, genderand site) combinations per fold.
One of the advantages of the proposed algorithm is that it does not relyon parameter tuning. Indeed, the L1-SCCA procedure is inspired by the‘stability-selection67’ approach, where subsampling is combined with selection
algorithms. Speciﬁcally, it was designed in such a way that the amount ofregularization is not chosen explicitly based on the L1-penalty tuning, but rather on
concatenation of the features selected by different L1-penalties and subsamples.
In the original ‘stability-selection’ paradigm, features are selected based on thefrequency of selection across subsampling repetitions, which typically requires
threshold tuning by additional cross-validation. In this study, the union of the FCs
selected by L1-SCCA on different subsamples aims to avoid the tweaking of such
additional parameters. Moreover, SLR relies on automatic relevance determination,a Bayesian procedure that does not require parameter tuning.
To classify the independent cohort data sets (for example, the US ABIDE dataset), we trained the ﬁnal SLR classiﬁer based on the union of the features selected
throughout the 9  9 nested FS, using all the Japanese subjects as the training set.
L1-regularized sparse canonical correlation analysis. In general, by employing
canonical correlation analysis (CCA)68, we can identify latent relationship between
paired observations. Speciﬁcally, CCA can derive projection vectors so that thepaired projected variables (called canonical variables) have maximum correlation.
Suppose thatof the paired variables x1 2 Rp1 and x2 2 Rp2 .
 we have N observations
T
Let X1 ¼ x11 ; x21 ; . . . ; xN1
denote the N  p1 matrix comprising the ﬁrst set of10Tvariables, and let X2 ¼ x12 ; x22 ; . . . ; xN2 denote the N  p2 matrix comprising thesecond set of variables. As we explained in the previous section, we use sparse CCA
with L1-norm regularization, L1-SCCA37. We assume that the columns listing X1
and X2 of the training set have been centred to have zero mean and scaled to haveunit variance. For one canonical variable, L1-SCCA can then be formulated as
max v T1 XT1 X2 v2 subject to kv1 k21  l1 ; kv2 k21  l2 ; kv 1 k22  1; kv2 k22  1;v1 ;v2

ð1Þ

where hyperparameters l1 and l2 indicate the sparseness of the projection vectors
v1 and v2, respectively. Since the maximum number of canonical variables is
q ¼ min(p1, p2), the projection matrices are deﬁned as V1 2 Rp1 q and V2 2 Rp2 q ,where each column contains the projection vector that is associated with acanonical variable.
To identify the latent relationships between demographic information and FC,
we constructed two data matrices. A row of the ﬁrst data matrix X1 lists theproperties and attributes of a subject, including the diagnosis (ASD or TD), site
information indicating where the brain activities of the subject were scanned,
age, sex, imaging conditions (open or closed eyes) and status of medication(antipsychotics, antidepressant and anxiolytics, separately) (see Supplementary
Fig. 7). More speciﬁcally, the number of columns of the demographic information
data matrix X1 is 10, that is, p1 ¼ 10. The ﬁrst column contains either 1 ( ¼ ASD) or
0 ( ¼ TD). The next three columns contain either [1 0 0] ( ¼ site A), [0 1 0] ( ¼ site B)or [0 0 1] ( ¼ site C). The ﬁfth column contains age value, the sixth column
contains either 1 ( ¼ male) or 0 ( ¼ female), the seventh column contains either 1( ¼ eye open) or 0 ( ¼ eye closed) and the last three columns contain status of thethree medications, where each column contains either 1 ( ¼ with medication) or 0
( ¼ without medication). The second data matrix X2 pools a row-vector form of theoff-diagonal lower triangular portion of a correlation matrix that represents the FC
of a subject. L1-SCCA was applied to the pair of matrices X1 and X2, from which
the sparse projection matrices V1 and V2 were derived. In this study, we deﬁned theconstraint that at least one canonical variable should be associated only with thediagnostic label, and we called it diagnostic canonical constraint. In addition, wecall canonical variables that are associated only with the diagnostic label as
diagnostic canonical variables. This was achieved by looking at the columns of V1
that had a non-zero element only in the ﬁrst row (that corresponds to thediagnostic label). Subsequently, only the columns of V2 corresponding to thediagnostic canonical variables were used to form the vector vD
2 , by computing thesum of the absolute value across columns (that is, union of features across‘diagnostic canonical variables’). Moreover, we obtained the union of features(that is, v 2D; union ) across repetitions of the inner loop FS and across hl1 ; l2 i
meeting diagnostic canonical constraint, by computing the sum of all the v D2
union
derived in the process. Then, we used vD;
to identify the indices of the2connectivity vector relevant to the diagnosis label. We projected the original
union
connectivity vector into a subspace deﬁned by the nonzero elements of vD;.
2
Here we deﬁned a variable ik to denote the index number of the k-th nonzero
unionelement of vD;, where 1rkrm and m denotes the number of nonzero
2elements. We then considered the projection matrix E ¼ ½ei1 ; ei2 ; . . . ; eim T to thesubspace, where eik 2 Rp2 is the standard basis vector containing ‘1’ in the ik-th
element and ‘0’ in the other elements. Finally, we derived the vector in the subspacezARm by projecting the original connectivity vector x2 as
z ¼ Ex2 :ð2Þ
By choosing the FCs that corresponded to the canonical variables that areconnected only with the diagnostic label, we could select essential FCs forclassiﬁcation. Simultaneously, undesirable effects caused by demographic andimaging differences at different imaging sites, that is NVs, were reduced throughL1-SCCA, as explained in Supplementary Notes 6,4 and Supplementary Fig. 8.
This procedure makes the MRI data from the three imaging sites useful inconstructing a robust classiﬁer that generalizes across ‘foreign’, that is, USA,imaging sites.
Prediction of the diagnostic label. To predict the diagnostic label from theextracted feature input z of equation (2) (identiﬁed FCs), we employed logistic
regression as the classiﬁer. In logistic regression, a logistic function is used to deﬁne
the probability of a participant belonging to the ASD class asPðy ¼ 1 j ^z; wÞ ¼

1;
1 þ expð  wT ^zÞð3Þ

where y represents the diagnosis class label, that is, y ¼ 1 indicates ASD and y ¼ 0
T
indicates the TD class, respectively. ^z ¼ ½zT ; 1 2 Rm þ 1 is a feature vector with anaugmented input, where the feature vector z is extracted from the connectivity
matrix of one participant’s resting-state MRI sample (for more detail about data
standardization, see Supplementary Note 7). Using the augmented input ‘1’ is astandard approach to introduce constant (bias) input for the classiﬁer. wARm þ 1 is
the weight vector of the logistic function. To further decrease the dimension of thefeature vector, which was already reduced by L1-SCCA according to equation (2),
we used an SLR method, as described in the next paragraph. SLR automaticallyselects the features related to the ASD label as input for the logistic function. In
SLR, the probability distribution of the parameter vector is estimated using thehierarchical Bayesian estimation approach, in which the prior distribution of eachelement of the parameter vector is represented as a Gaussian distribution. Because

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NATURE COMMUNICATIONS | DOI: 10.1038/ncomms11254

of the automatic relevance determination property of the hierarchical Bayesianestimation method, some of the Gaussian distributions become sharply peaked atzero so that the irrelevant features are not used in the classiﬁcation.
Linear regression to the clinical indices. Using the identiﬁed 16 FCs in theclassiﬁer, we predicted the four domain scores of the two standard diagnostic
instruments measured: the ADOS47 and the ADI-R48 (see also Supplementary
Table 3). Speciﬁcally, in each domain of an instrument, the score of each individual
was predicted by calculating the linear weighted sum of his/her 16 correlation
coefﬁcients that corresponded to the 16 FCs in the classiﬁer. The set of weights forthis summation was determined through LOOCV, in which the domain scores ofall-but-one participants were linearly regressed using the respective 16 correlation
coefﬁcients as explanatory variables. Because previous studies indicated age- andsex-related differences in cognition across the lifespan of adult ASDs69,70,
behavioural measures such as ADOS and ADI-R can be assumed to exhibit
dependence on these factors. We therefore incorporated age and sex into theregression model as additional explanatory variables. The LOOCV was necessary to
avoid any information leakage from the individual to be predicted. The agreement
between the measured and predicted domain scores was evaluated by the Pearson
correlation coefﬁcient and the statistical signiﬁcance was tested against the null
hypothesis that there is no relationship between measured and predicted scores.
For the domain score with a signiﬁcance correlation, the reliability of the prediction
was further tested by a bootstrapping analysis (10,000 repetitions) where thealternative prediction was performed using 16 randomly selected FCs from thepool of 9,688 ( ¼ 9,730  42) FCs, which were not selected by SLR in the LOOCV
procedure for the ASD/TD classiﬁcation (Supplementary Note 1). At each
permutation, a new regression model was computed for each of the eight domainscores and the correlation between the predicted and measured domain score wascalculated. The highest of the eight correlations (corresponding to the eight
domains) was then selected and pooled over the permutations. The reliability of theprediction using the original 16 FCs was evaluated by integrating the normalized
cumulative distribution of the pooled correlation coefﬁcients derived through thisbootstrapping procedure.
Code availability. The classiﬁcation code and the correlation matrix data used in
the present study are available at a secure server of ATR Brain Information
Communication Research Laboratory. Please contact the server administrator(asd-classiﬁer@atr.jp) for access.

References
1. American Psychiatric Association. Diagnostic and Statistical Manual of Mental
Disorders 5th edn (American Psychiatric Association, 2013).
2. Frith, C. D. & Frith, U. Cognitive psychology—interacting minds—a biologicalbasis. Science 286, 1692–1695 (1999).
3. Mandell, D. S., Ittenbach, R. F., Levy, S. E. & Pinto-Martin, J. A. Disparities indiagnoses received prior to a diagnosis of autism spectrum disorder. J. Autism
Dev. Disord. 37, 1795–1802 (2007).
4. Nylander, L., Holmqvist, M., Gustafson, L. & Gillberg, C. Attention-deﬁcit/
hyperactivity disorder (ADHD) and autism spectrum disorder (ASD) in adultpsychiatry. A 20-year register study. Nord. J. Psychiatry 67, 344–350 (2013).
5. Kapur, S., Phillips, A. G. & Insel, T. R. Why has it taken so long for biologicalpsychiatry to develop clinical tests and what to do about it? Mol. Psychiatry 17,
1174–1179 (2012).
6. Castellanos, F. X., Di Martino, A., Craddock, R. C., Mehta, A. D. & Milham, M.
P. Clinical applications of the functional connectome. NeuroImage 80, 527–540(2013).
7. Ecker, C. et al. Describing the brain in autism in ﬁve dimensions--magnetic
resonance imaging-assisted diagnosis of autism spectrum disorder using a
multiparameter classiﬁcation approach. J. Neurosci. 30, 10612–10623 (2010).
8. Ecker, C. et al. Investigating the predictive value of whole-brain structural MR
scans in autism: a pattern classiﬁcation approach. NeuroImage 49, 44–56(2010).
9. Uddin, L. Q. et al. Multivariate searchlight classiﬁcation of structuralmagnetic
resonance imaging in children andadolescents with autism. Biol. Psychiatry 70,
833–841 (2011).
10. Anderson, J. S. et al. Functional connectivity magnetic resonance imaging
classiﬁcation of autism. Brain 134, 3742–3754 (2011).
11. Ingalhalikar, M., Parker, D., Bloy, L., Roberts, T. P. L. & Verma, R. Diffusion
based abnormality markers of pathology: toward learned diagnostic predictionof ASD. NeuroImage 57, 918–927 (2011).
12. Wang, H., Chen, C. & Fushing, H. Extracting multiscale pattern information offMRI based functional brain connectivity with application on classiﬁcation ofautism spectrum disorders. PLoS ONE 7, e45502 (2012).
13. Deshpande, G., Libero, L. E., Sreenivasan, K. R., Deshpande, H. D. &Kana, R. K. Identiﬁcation of neural connectivity signatures of autism using
machine learning. Front. Hum. Neurosci. 7, 670 (2013).
14. Dosenbach, N. U. F. et al. Prediction of individual brain maturity using fMRI.
Science 329, 1358–1361 (2010).

15. Tomasi, D. & Volkow, N. D. Gender differences in brain functional
connectivity density. Hum. Brain Mapp. 33, 849–860 (2011).
16. Klaassens, B. L. et al. Single-dose serotonergic stimulation shows widespread
effects on functional brain connectivity. NeuroImage 122, 440–450 (2015).
17. Friedman, L., Glover, G. H. & The FBIRN Consortium. Reducing interscannervariability of activation in a multicenter fMRI study: controlling for signal-toﬂuctuation-noise-ratio (SFNR) differences. NeuroImage 33, 471–481 (2006).
18. Thulborn, K. R., Chang, S. Y., Shen, G. X. & Voyvodic, J. T. High-resolution
echo-planar fMRI of human visual cortex at 3.0 tesla. NMR Biomed. 10,
183–190 (1997).
19. Van Dijk, K. R. A. et al. Intrinsic functional connectivity as a tool for humanconnectomics: theory, properties, and optimization. J. Neurophysiol. 103,
297–321 (2010).
20. Whelan, R. & Garavan, H. When optimism hurts: inﬂated predictions in
psychiatric neuroimaging. Biol. Psychiatry 75, 746–748 (2014).
21. Whelan, R. et al. Neuropsychosocial proﬁles of current and future adolescentalcohol misusers. Nature 512, 185–189 (2015).
22. Chen, H. et al. Multivariate classiﬁcation of autism spectrum disorder using
frequency-speciﬁc resting-state functional connectivity—a multi-center study.
Prog. Neuropsychopharmacol. Biol. Psychiatry 64, 1–9 (2016).
23. Iidaka, T. Resting state functional magnetic resonance imaging and neuralnetwork classiﬁed autism and control. Cortex 63, 55–67 (2015).
24. Nielsen, J. A. et al. Multisite functional connectivity MRI classiﬁcation ofautism: ABIDE results. Front. Hum. Neurosci. 7, 599 (2013).
25. Plitt, M., Barnes, K. A. & Martin, A. Functional connectivity classiﬁcation ofautism identiﬁes highly predictive brain features but falls short of biomarker
standards. Neuroimage Clin. 7, 359–366 (2015).
26. Yoshihara, Y. et al. in The 17th Annual Meeting of the Organization on Human
Brain Mapping (Quebec City, Canada, 26–30 June, 2011).
27. Deen, B. & Pelphrey, K. Perspective: brain scans need a rethink. Nature 491,
S20 (2012).
28. Walsh, P., Elsabbagh, M., Bolton, P. & Singh, I. In search of biomarkers for
autism: scientiﬁc, social and ethical challenges. Nat. Rev. Neurosci. 12, 603–612(2011).
29. Kelly, C., Biswal, B. B., Craddock, R. C., Castellanos, F. X. & Milham, M. P.
Characterizing variation in the functional connectome: promise and pitfalls.
Trends Cogn. Sci. 16, 181–188 (2012).
30. Cross-Disorder Group of the Psychiatric Genomics Consortium. Identiﬁcationof risk loci with shared effects on ﬁve major psychiatric disorders:a genome-wide analysis. Lancet 381, 1371–1379 (2013).
31. Geschwind, D. H. & Flint, J. Genetics and genomics of psychiatric disease.
Science 349, 1489–1494 (2015).
32. King, B. H. & Lord, C. Is schizophrenia on the autism spectrum? Brain Res.
1380, 34–41 (2011).
33. Pinkham, A. E., Hopﬁnger, J. B., Pelphrey, K. A., Piven, J. & Penn, D. L. Neuralbases for impaired social cognition in schizophrenia and autism spectrum
disorders. Schizophr. Res. 99, 164–175 (2008).
34. Adam, D. Mental health: on the spectrum. Nature 496, 416–418 (2013).
35. Goodkind, M. et al. Identiﬁcation of a common neurobiological substrate formental illness. JAMA Psychiatry 72, 305–311 (2015).
36. Perrot, M., Rivière, D. & Mangin, J. F. Cortical sulci recognition and spatial
normalization. Med. Image Anal. 15, 529–550 (2011).
37. Witten, D. M., Tibshirani, R. & Hastie, T. A penalized matrix decomposition,with applications to sparse principal components and canonical correlation
analysis. Biostatistics 10, 515–534 (2009).
38. Yamashita, O., Sato, M.-A., Yoshioka, T., Tong, F. & Kamitani, Y. Sparse
estimation automatically selects voxels relevant for the decoding of fMRI
activity patterns. NeuroImage 42, 1414–1429 (2008).
39. Noirhomme, Q. et al. Biased binomial assessment of cross-validated estimationof classiﬁcation accuracies illustrated in diagnosis predictions. Neuroimage Clin.
4, 687–694 (2014).
40. Di Martino, A. et al. The autism brain imaging data exchange: towards alarge-scale evaluation of the intrinsic brain architecture in autism. Mol.
Psychiatry 19, 659–667 (2014).
41. Hahamy, A., Behrmann, M. & Malach, R. The idiosyncratic brain: distortion of
spontaneous connectivity patterns in autism spectrum disorder. Nat. Neurosci.
18, 302–309 (2015).
42. Tu, P.-C., Hsieh, J.-C., Li, C.-T., Bai, Y.-M. & Su, T.-P. Cortico-striatal
disconnection within the cingulo-opercular network in schizophrenia revealed
by intrinsic functional connectivity analysis: a resting fMRI study. NeuroImage59, 238–247 (2012).
43. Just, M. A., Keller, T. A., Malave, V. L., Kana, R. K. & Varma, S. Autism
as a neural systems disorder: a theory of frontal-posterior underconnectivity.
Neurosci. Biobehav. Rev. 36, 1292–1313 (2012).
44. Hughes, J. R. Autism: The ﬁrst ﬁrm ﬁnding ¼ underconnectivity? Epilepsy
Behav. 11, 20–24 (2007).
45. Welchew, D. E. et al. Functional disconnectivity of the medial temporal lobe inAsperger’s syndrome. Biol. Psychiatry 57, 991–998 (2005).

NATURE COMMUNICATIONS | 7:11254 | DOI: 10.1038/ncomms11254 | www.nature.com/naturecommunications

11

ARTICLE

NATURE COMMUNICATIONS | DOI: 10.1038/ncomms11254

46. Courchesne, E. & Pierce, K. Why the frontal cortex in autism might be talking
only to itself: local over-connectivity but long-distance disconnection. Curr.
Opin. Neurobiol. 15, 225–230 (2005).
47. Lord, C. et al. The autism diagnostic observation schedule-generic: a standard
measure of social and communication deﬁcits associated with the spectrum ofautism. J. Autism Dev. Disord. 30, 205–223 (2000).
48. Lord, C., Rutter, M. & Le Couteur, A. Autism Diagnostic Interview-Revised: arevised version of a diagnostic interview for caregivers of individuals withpossible pervasive developmental disorders. J. Autism Dev. Disord. 24, 659–685(1994).
49. Uddin, L. Q. et al. Salience network-based classiﬁcation and prediction ofsymptom severity in children with autism. JAMA Psychiatry 70, 869–879 (2013).
50. Zou, H. & Hastie, T. Regularization and Variable Selection via the Elastic Net.
J. R. Stat. Soc. Ser. B Stat. Methodol. 67, 301–320 (2005).
51. ATR Brain Information Communication Research Laboratory Group. DecNef
Project. Available at http://www.cns.atr.jp/decnefpro/ (2016).
52. Shibata, K., Watanabe, T., Sasaki, Y. & Kawato, M. Perceptual learning inceptedby decoded fMRI neurofeedback without stimulus presentation. Science 334,
1413–1415 (2011).
53. Megumi, F., Yamashita, A., Kawato, M. & Imamizu, H. Functional MRI
neurofeedback training on connectivity between two regions induces
long-lasting changes in intrinsic functional network. Front. Hum. Neurosci. 9,160 (2015).
54. Hashimoto, R. in The 36th Meeting of Japan Neuroscience Society (Kyoto, Japan,
20–23 June 2013).
55. Kawato, M. in The 11th World Congress of Biological Psychiatry (Kyoto, Japan,
23–27 June 2013).
56. American Psychiatric Association. Diagnostic and Statistical Manual of Mental
Disorders. 4th edn, Text Revision (DSM-IV-TR) (American Psychiatric
Association, 2000).
57. Otsubo, T. et al. Reliability and validity of Japanese version of themini-international neuropsychiatric interview. Psychiatry Clin. Neurosci. 59,
517–526 (2005).
58. Matsuoka, K., Uno, M., Kasai, K., Koyama, K. & Kim, Y. Estimation of
premorbid IQ in individuals with Alzheimer’s disease using Japaneseideographic script (Kanji) compound words: Japanese version of National
Adult Reading Test. Psychiatry Clin. Neurosci. 60, 332–339 (2006).
59. Oldﬁeld, R. C. The assessment and analysis of handedness: the Edinburgh
inventory. Neuropsychologia 9, 97–113 (1971).
60. Wakabayashi, A., Baron-Cohen, S., Wheelwright, S. & Tojo, Y. The
autism-spectrum quotient (AQ) in Japan: a cross-cultural comparison.
J. Autism Dev. Disord. 36, 263–270 (2006).
61. Satterthwaite, T. D. et al. An improved framework for confound regression andﬁltering for control of motion artifact in the preprocessing of resting-statefunctional connectivity data. NeuroImage 64, 240–256 (2013).
62. Power, J. D., Barnes, K. A., Snyder, A. Z., Schlaggar, B. L. & Petersen, S. E.
Spurious but systematic correlations in functional connectivity MRI networks
arise from subject motion. NeuroImage 59, 2142–2154 (2012).
63. Tzourio-Mazoyer, N. et al. Automated anatomical labeling of activations
in SPM using a macroscopic anatomical parcellation of the MNI MRI
single-subject brain. NeuroImage 15, 273–289 (2002).
64. Griffanti, L. et al. ICA-based artefact removal and accelerated fMRI acquisition
for improved resting state network imaging. NeuroImage 95, 232–247 (2014).
65. Mackay, D. J. C. Probable networks and plausible predictions—a review ofpractical Bayesian methods for supervised neural networks. Network Comp.
Neural Syst. 6, 479–505 (1995).
66. Neal, R. M. Bayesian Learning for Neural Networks 118 (Springer Science &Business Media, 1996).
67. Meinshausen, N. & Bühlmann, P. Stability selection. J. R. Stat. Soc. Ser. B Stat.
Methodol. 72, 417–473 (2010).
68. Hotelling, H. Relations between two sets of variates. Biometrika 28, 321 (1936).
69. Lever, A. G. & Geurts, H. M. Age-related differences in cognition across the adult
lifespan in autism spectrum disorder. Autism Res. doi: 10.1002/aur.1545 (2015).
70. Lehnhardt, F.-G. et al. Sex-related cognitive proﬁle in autism spectrum
disorders diagnosed late in life: implications for the female autistic phenotype.
J. Autism Dev. Disord. 46, 139–154 (2015).

12

Acknowledgements
This research was conducted under the ‘Development of BMI Technologies for ClinicalApplication’ of the Strategic Research Program for Brain Sciences supported by Japan
Agency for Medical Research and Development (AMED). This research was also partially
supported by the grants ‘Development of Biomarker Candidates for Social Behavior’and ‘Integrated Research on Neuropsychiatric Disorders’ of the Strategic Research
Program for Brain Sciences and Grant-in-Aid for Scientiﬁc Research on Innovative Areas(Comprehensive Brain Science Network) by the Ministry of Education, Culture, Sports,
Science and Technology (MEXT) of Japan, Japan Society for the Promotion of
Science (JSPS) KAKENHI (25461752 to N.Y.), Grant-in-Aid for JSPS Fellows (to K.S.)
and NIH Research Project Grant Program (R01EY015980 to T.W. and R01MH091801 toY.S.). We thank Masa-aki Sato, Okito Yamashita, Yu Takagi, Masahiro Yamashita
and Ayumu Yamashita for their insightful comments on an early draft. We also thank
Saori C. Tanaka, Naho Ichikawa and Yujiro Yoshihara for their technical assistance inthis study.

Author contributions
N.Y., R.H., K.S., Y.S., T.W. and M.K. conceived and designed the study. N.Y., R.H., Y.K.,
H.K., M.K., T.Y., F.M., H.I., K.K., N.K., H.T. and Y.O. recruited participants of the study
and collected their clinical and imaging data, and Y.K., H.K., M.Ku., T.Y., K.K., H.T.,
Y.O. and N.K. were in charge of the clinical assessments. N.Y., J.M., R.H., G.L. and K.S.
carried out the analysis of the data. N.Y., J.M., R.H., G.L., K.S., J.N., Y.S., T.W. and M.K.
wrote the manuscript.

Additional information
Supplementary Information accompanies this paper at http://www.nature.com/
naturecommunications
Competing ﬁnancial interests: M.K., J.M., N.Y., R.H., F.M., K.S., H.I., T.W., Y.S., N.K.
and K.K are inventors of a patent owned by Advanced Telecommunications Research(ATR) Institute International related to the present work [PCT/JP2014/061543(WO2014178322)]. J.M., M.K., N.Y., R.H., K.S., T.W., Y.S., N.K. and K.K. are inventors
of a patent owned by ATR Institute International related to the present work
[PCT/JP2014/061544 (WO2014178323)]. G.L., J.M., M.K. and N.Y. are inventors of apatent application submitted by ATR Institute International related to the present work
[JP2015-228970]. H.K. received honoraria for lectures related to the Japanese version of
ADI-R from Kanekoshobo. M.Ku. was previously involved in the publication of theJapanese version of ADOS and ADI-R. M.Ku. also received honoraria for lectures related
to the Japanese version of ADI-R and ADOS from Kanekoshobo. H.I. received honoraria
for lectures by Shimadzu Co. and Nippon Boehringer Ingelheim Co., Ltd. H.T. received
research grants from Takeda. H.T. has received honoraria for lectures by Otsuka, Meiji
Seika, MSD, Dainippon-Sumitomo and GlaxoSmithKline. For the past three years, Y.O.
declare the following potential conﬂicts of interest, although they are all unrelated to thecurrent study. Y.O. has received honoraria for lectures by Otsuka, Dainippon Sumitomo,
Astellas, Pﬁzer, Eli Lilly, Janssen, Meiji Seika Pharma, Mochida, Yoshitomi Yakuhin,
Eizai and GlaxoSmithKline. For the past three years, K.K. declare the following potential
conﬂicts of interest, although they are all unrelated to the current study. K.K. received
research grants from Astellas, GlaxoSmithKline, Dainippon-Sumitomo, Eisai, MSD andYoshitomi. K.K. has received honoraria for lectures by Daiichi-Sankyo, Otsuka, Meiji
Seika, MSD, Astellas, Yoshitomi, Novartis, Eli Lilly, Dainippon-Sumitomo, Janssen,
GlaxoSmithKline and Pﬁzer.
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How to cite this article: Yahata, N. et al. A small number of abnormal brain
connections predicts adult autism spectrum disorder. Nat. Commun. 7:11254
doi: 10.1038/ncomms11254 (2016).
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