Multiparametric MRI Characterization and Prediction in Autism Spectrum Disorder Using Graph Theory and Machine Learning

This study employed graph theory and machine learning analysis of multiparametric MRI data to improve characterization and prediction in autism spectrum disorders (ASD). Data from 127 children with ASD (13.5±6.0 years) and 153 age- and gender-matched typically developing children (14.5±5.7 years) were selected from the multi-center Functional Connectome Project. Regional gray matter volume and cortical thickness increased, whereas white matter volume decreased in ASD compared to controls. Small-world network analysis of quantitative MRI data demonstrated decreased global efficiency based on gray matter cortical thickness but not with functional connectivity MRI (fcMRI) or volumetry. An integrative model of 22 quantitative imaging features was used for classification and prediction of phenotypic features that included the autism diagnostic observation schedule, the revised autism diagnostic interview, and intelligence quotient scores. Among the 22 imaging features, four (caudate volume, caudate-cortical functional connectivity and inferior frontal gyrus functional connectivity) were found to be highly informative, markedly improving classification and prediction accuracy when compared with the single imaging features. This approach could potentially serve as a biomarker in prognosis, diagnosis, and monitoring disease progression.


Introduction
Autism spectrum disorders (ASD) are a group of polygenetic developmental brain disorders with behavioral and cognitive impairment [1]. Affected individuals exhibit stereotypical repetitive movements, restricted interests, lack of impulse control, speech deficits, impaired intelligence and social skills compared to typically developing (TD) children [2]. The underlying neurological changes and their association with the clinical manifestations remain an active area of research.
Imaging studies have been instrumental in mapping aberrant connections in the brains of ASD children. Several studies revealed both structural and functional connectivity deficits in ASD [3,4]. Structural connectivity derived from diffusion tensor imaging in ASD children demonstrate increased diffusivity and/or reduced fractional anisotropy in the long occipitofrontal fasciculus and inter-hemispheric corpus callosal (e.g., minor and major forceps) commissure [5], asymmetric and under-connected arcuate fasciculus language pathways [6,7], as well as reduced cerebellarcortical interconnectivity [8]. Functional connectivity MRI (fcMRI) shows abnormal dis-inhibition of some subcortical circuits [9], over-or under-connectivity in the superior temporal gyrus and amygdala [10]. The caudate nucleus, which plays an important role in behavior impulsivity control, novelty seeking trait, procedural skill learning, and memory function [11], has been reported to increase in volume and its functional connectivity to the cortices is enhanced in autistic adolescents and young adults [12,13]. These abnormal caudate volume and caudate-cortical connectivity have been associated with repetitive autistic behaviors [12,13].
A key clinical manifestation of ASD is impaired learning and social interactions [14]. Mirror mechanisms in frontoparietal and sensorimotor networks are involved in the imitation of others' actions in normal subjects [15], and have been suggested to be dysfunctional in children with ASD [16,17]. In addition, neural networks underlying reflective mentalization [18] as well as emotional and interoceptive awareness [19] may be impaired in ASD. The default mode network (DMN) that consists of the medial frontal, posterior cingulate gyri and the temporo-parietal connection (which is involved in self awareness, social integration, learning and memory functions [20] and is usually deactivated under cognitive-demanded task conditions) has been found to be deficient in ASD children as well [21]. Furthermore such DMN dysfunction has been associated with decreased volumes of the structures involved [21].
The inferior frontal gyrus (IFG), which is involved in high-level memory, language production and comprehension, and learning interactions [22][23][24], has been reported to be abnormal in ASD children. Within the IFG, the pars opercularis plays a role in social interactions including imitation control [25], while the pars triangularis is associated with language comprehension [26]. Taskrelated fMRI results have demonstrated IFG abnormalities in ASD patients, including impaired social function and affective emotion [27,28]. FcMRI shows decreased functional connectivity in IFG inhibitory circuits, consistent with disruption of mirror neurons and their projections involved in social communication and language development [29,30].
Given the large amount of anatomical and functional connectivity imaging data, a unified model integrating multiple imaging measures may be helpful to better characterize ASD and predict the phenotypic outcome [31]. Small-world network analysis based on graph theory offers some advantages in analyzing complex and multidimensional data by providing global and local inter-regional modulation information of structural and functional brain networks [32]. A potential challenge is the possibility of retrieval redundancy (''curse of dimensionality''). Principal component analysis is a feature selection method that has been widely used to reduce dimensionality by identifying essential components in the data structure, while retaining most of the data variation (i.e., information) [33]. Maximal relevance and minimal redundancy (mRMR) [34] is another feature selection algorithm to reduce dimensionality which uses filters based on mutual information and correlation to account for maximal dependency and minimal redundancy.
The goals of this study were: i) to evaluate multi-parametric functional and structural MRI of the brain in ASD versus TD children using small-world network analysis based on graph theory to derive local and global efficiency, ii) to use machine-learning algorithms to evaluate the ability of these multiparametric MRI matrices to classify ASD versus TD groups, and iii) to employ machine-learning algorithms of these multiparametric MRI matrices to predict ASD clinical phenotypic outcomes, such as the revised autism diagnostic interview (ADI-R), autism diagnostic observation schedule (ADOS), and intelligence quotient (IQ) scores reflecting different aspects of social and learning abilities of subjects [35].

Participants and phenotypic information and MRI Imaging
Data was obtained from the multi-center Functional Connectome Project, which released MRI data of over 500 ASD patients (http://fcon_1000.projects.nitrc.org/indi/abide/). We downloaded the Autism Brain Imaging Data Exchange database from the COINS website (http://coins.mrn.org/) that hosted copies of data samples. In accordance with HIPAA guidelines and 1000 Functional Connectomes Project/INDI protocols, all datasets were de-identified. Consistent with the policies of the 1000 Functional Connectomes Project, data usage was approved for research purposes.
127 children with ASD (mean age: 13.566.0 years, 24.1% of female), 153 age-and gender-matched control TD children (mean age: 14.565.7 years, 24.8% of female) from the NYU/Yale/ Stanford centers were selected for analyses based on age ranges. The full IQ scores were slightly lower in the ASD (104.3618.9) compared to the TD group (111.7614.4), with P = 0.001. Imaging data consisted of high spatial resolution 3D T1-based MPRAGE sequence (image size = 16062566256, resolution = 16161 mm 3 ) and resting-state (RS)-fMRI obtained using a gradient echo EPI sequence (TR = 2000 msec, resolution = 36364 mm 3 , 180 volumes) with 33 slices covering the whole cerebrum.
The corresponding clinical data from five categories were also obtained, consisting of the ADOS scores, the ADI-R, and IQ tests (full scale and sub-functionality), social responsiveness scale (SRS) and Vinland adaptive behavior scale (VABS) with five domains. Detailed information regarding the phenotypic data was outlined in previously published articles [10,14]. Briefly, the ADI-R is composed of 93 items focusing on the triadic functional domains, and administered via interview with categorical results provided. The full IQ tests evaluated both verbal IQ (VIQ) and performance IQ (PIQ). The ADOS is a semi-structured assessment of social affection and communication behaviors, using four modules to account for individual expressive language level and chronological age. The SRS rating scale measures the social ability of ASD children (including total and subdomains of cognition, communication, awareness and motivation). The VABS instrument consists of social and personal skills for everyday living, including subdomains such as interpersonal empathy and socialization.

Image Processing and Data Analysis
Preprocessing: Standard preprocessing for RS-fMRI data analysis was performed using both FMRIB Software Library (FSL) and Analysis of Functional NeuroImages (AFNI) software packages with adapted scripts (http://www.nitrc.org/projects/fcon_1000). The steps included standard realignment, spatial Gaussian smoothing with full width at half maximum (FWHM) of 6 mm, band pass temporal filtering of 0.005-0.1 Hz, co-registration with the MPRAGE images, removal of nuisance signals (motion parameters, the global signal, and signals derived from cerebrospinal fluid and white matter), and non-linear transformation to Montreal Neurological Institute (MNI) standard space. For instance, in order to control for motion artifacts, regression and residual analyses of six motion parameters including three angular rotations (roll, pitch, and yaw in units of degrees) and three directional displacements (x,y,z in units of mm) were implemented in the preprocessing step.

Volumetry analysis
Anatomical data were processed to derive the total supratentorial volume, regional subcortical volumes (45 regions), white matter (WM) volumes (70 regions), and cortical gray matter (GM) volumes (148 regions) using Freesurfer software (version 5.1.0) [36]. Regional volume comparisons were implemented after supratentorial volume normalization. The cortical thickness of 148 cortical regions was measured automatically based on minimal communication distance between the gray and white matter ribbon of the projected cortical surface [37]. Thickness measured with Freesurfer has been shown to be especially useful in characterizing the cortical folding and cytoarchitecture shaping in different age ranges [38].

fcMRI analysis
The seed-based fcMRI was derived with seeds in the bilateral pars triangularis and opercularis regions of the IFG, the caudate, and the DMN core seed in the MNI 2 mm template space. These seed regions or networks were selected based on previously reported abnormalities in ASD [12,13,27,28]. The total number of voxels (N) and average correlational z-value (Z) were computed from the functional connectivity map of each seed using a threshold of cluster corrected P,0.05. The statistical multiplecomparison correction was done based on Gaussian random field (GRF) theory and implemented with the FSL easythresh command using empirical minimum Z.2.3 threshold with cluster significance of P,0.05. In addition, to examine the functional interhemispheric coordination, voxel-mirrored homotopic correlations (VMHC) were derived. The global VMHC voxel number (minimum Z.2.3; cluster significance P,0.05, corrected) and average Z-value were then quantified [39].

fALFF analysis
Fractional amplitude of low frequency fluctuation (fALFF) of the fcMRI data at 0.01-0.08 Hz, which reflects spontaneous neuronal or functional activity, was analyzed with adapted scripts in FSL and AFNI [39].
Graph theory via small-world network analysis Inter-regional correlations of individual fMRI time courses of 112 bilateral cortical and subcortical ROIs based on functional parcellation in FSL template space [40] were derived. Graph theory-based small-world network analysis for absolute and relative, local and global efficiency quantification at different connectivity sparsity levels, was then performed for each subject Table 1. Significant regional volume differences (P,0.01) comparing children with autism spectrum disorder (ASD) to agematched typically developing (TD) children after supratentorial volume normalization. Note-Data (V1, V2) are mean brain volumes after normalization to the supratentorial volume with a scale factor of 1000, no unit. **Calculated with two-sample t test to obtain original p-value (shown with P,0.01) between two groups, and with Bonferroni multiple region correction (x8 factor given 4 brain lobes in two hemispheres). *Indicates a significant difference with corrected P,0.05 after Bonferroni adjustment. D1 Indicates percentage change between volume of ASD children (V2) and volume of TD children (V1), calculated as D1 = (V2-V1)/V1*100%. doi:10.1371/journal.pone.0090405.t001 [32]. Group differences of mean local and global efficiency parameters derived from in-house software were compared with a 2-sample t-test. The inter-regional correlations of group-wise cortical thickness based on 148 bilateral cortical regions and volumetry measured with Freesurfer (148 cortical regions, as well as 115 subcortical and white matter regions) were also derived, and small world network analysis based on structural measures (including relative and absolute local as well as global efficiency parameters) was then performed and compared between the two groups.

Integration model for two-group classification
To reduce possible classifier overfitting and improve generalization, feature selection was performed in two steps. First, principal component analysis was used to decompose the covariance matrix of the imaging features using the singular value decomposition program in Matlab (release 2010b; MathWorks, Natick, Mass) [33] after variance normalization. Then the number of sorted components based on singular values that contained 99% or 95% of the information from the covariance matrix of all features was determined. Finally, an advanced feature selection algorithm, based on mutual-information and integration of both mRMR criteria [34], was used to select imaging features based on the number of features (components) determined via principal component analysis.
A total of 22 quantitative local and global imaging features were generated from the structural and functional datasets based on preliminary data showing statistical differences between the two groups. These features include: i) volumes of 9 local subcortical regions (the bilateral caudate, thalami, pallidum, hippocampi and cerebellum), ii) 8 features from the fcMRI voxel number N and average Z values seeding from the bilateral caudate, bilateral IFG pars opercularis and triangularis, and DMN core seeds respectively, iii) 3 fALFF values (averaged values from the bilateral caudate, IFG pars opercularis, and IFG pars triangularis), and iv) global VMHC voxel number (corrected P,0.05) and average Z value (subtotal of 2 features).
To differentiate the two groups based on the selected imaging features, a total of 67 available classifiers, including support vector machine (SVM), Bayes network (BayesNet), radial basis function (RBF), and sequential minimal optimization (SMO) algorithms, were tested with batch-mode scripts developed in WEKA software (http://www.cs.waikato.ac.nz/ml/weka, version 3.6.7).
To evaluate each classifier, a cross validation method with different folds (numbering from 2 to 10) or percentage splits (from 10% to 90%) was applied to the training data set as well as to the whole dataset in WEKA software. After the dataset was randomly reordered and splitted into n folds of equal size, one fold was used for testing and the other n-1 folds were used for training the classifier for each iteration. The performances of these classifiers Table 2. Cortical thickness increment (in a degree of 2.5-5%) comparing autism spectrum disorder (ASD) children to age-matched typically developing (TD) children (P,0.01). Note-Data (C1, C2) are mean cortical thickness in mm. **Calculated with two-sample t test to obtain original p-value (shown with P,0.01) between two groups, and with Bonferroni multiple region correction (x8 factor given 4 brain lobes in two hemispheres). *Indicates a significant difference with corrected P,0.05 after Bonferroni adjustment. were further assessed in WEKA by using margin curves and threshold curves to show the cumulative probability of difference between true and false positives as a function of population size.

Correlational analysis between imaging and phenotypic data
Quantitative analysis of single imaging features of regional volume, N and Z from fcMRI, as well as the combined selected imaging features were correlated with the clinical data (i.e., ADOS, ADI-R, SRS, VABS, and IQ tests including both full and sub-domain scores). Bonferroni adjustment was implemented by multiplying the original p-values with both the number of category tests (x5 in this study) and the number of sub-domain tests (e.g., x10 for ADOS, x3 for IQ, x5 for ADI-R, x7 for SRS and x15 for VABS) of each category.

Integration model of imaging data for phenotypic prediction
To improve previous phenotypic correlation with multiparametric imaging data, regression analysis in WEKA (i.e., prediction of clinical data from imaging metrics) between the imaging features and clinical data was implemented. A total of 23 available advanced regression models were evaluated. These regressors were divided into seven families: Kstar, linear and non-linear ZeroR rule-based regressors, decision stump trees, and Gaussian process classifiers for full data sets. For example, Kstar was taken as an instance or memory based classifier using entropy and similarity functions with the advantage of updating models based on relevance to the previously established database [41].

Volumetry analysis
Volume and cortical thickness differences between the ASD and TD groups are shown in Figure 1 and Table 1. A key finding is that the ASD group demonstrated significantly larger GM volume (with exception of the right medial orbital olfactory region) but less WM volume compared to the TD group. Consistent with GM volumetric findings, the ASD group also showed significantly increased cortical thickness ( Table 2).  . A: Small-world network analysis based on fMRI data showed similar efficiency (including both local and global) between children with ASD and TD controls. Small-worldness analysis based on regional volume (red and blue colors) showed no significant differences of total efficiency (B) and global efficiency (C) between children with ASD and controls neither. However, small-worldness analysis based on structural cortical thickness measure showed reduced total efficiency (B), specifically decreased global efficiency (i.e. shortest path length) (C) in ASD group (magenta color) compared to TD group (cyan color). Error bar denotes standard deviation at each sparsity level after scaling to a random network with the same number of degree. doi:10.1371/journal.pone.0090405.g003 fcMRI analysis With seeding in the caudate, the ASD children demonstrated reduced functional connectivity in the cingulum and middle temporal cortex compared to TD children, but increased connectivity in several regions including the inferior and dorsolateral frontal areas (Figure 2A). With seeding in the IFG pars triangularis, the ASD group showed reduced fcMRI of visual and temporal regions, but increased in the medial temporal areas ( Figure 2B). With seeding from the IFG pars opercularis, the ASD group predominantly exhibited reduced functional connectivity with the superior frontal regions (corrected P,0.05; Figure 2C).

Graph theory via small-world network analysis
Small-worldness analysis showed no statistically significant difference in the mean total (local and global) efficiency between ASD and TD children based on fcMRI ( Figure 3A) and volumetric data ( Figure 3B,C). However, there was reduced total efficiency in ASD children ( Figure 3B) based on cortical thickness, especially in global efficiency, as indicated by increased shortest path lengths ( Figure 3C).

Classification of ASD and TD groups
Co-variance matrix of the 22 imaging features ( Figure 4A) showed correlated intra-module volumetry of 9 subcortical regions, as well as a strong association between the average Zvalue and the voxel number of fcMRI, both regionally and globally. However, the inter-module correlation was not significant (r,0.3), suggesting volumetry and fcMRI provided complementary information. Singular value decomposition of the co-variance matrix ( Figure 4B) found that 4 primary components accounted for .95% data variation, and 6 primary components accounted for .99% data variation. The four primary features were the right caudate volume, fcMRI Z values seeded from the bilateral caudate, IFG pars opercularis, and IFG pars triangularis; the additional two features were the mean Z score maps of the DMN and VMHC ( Figure 4C).
For the 6 imaging features selected by the mRMR algorithm, the random tree classifier had the highest classification accuracy (100%) for correctly identifying ASD patients with the full dataset, and 70% accuracy for differentiating ASD patients from TD children using 80% percentage split cross validation. Based on the 4 imaging features, the random tree classifier also had the highest accuracy (98%) for the full dataset for two-group classification, with 68% accuracy for 10-fold cross validation. The performance of the 6-feature classifier was slightly better than that of the 4-  feature classifier, with faster convergence and higher margins (i.e. better accuracy) maintained ( Figure 5). Table 3 summarizes the correlation analysis of the quantitative imaging features with phenotypic scores in ASD children, with both uncorrected and multiple-comparison corrected p-values. Significant correlations were found: i) between the number of connections N based on fcMRI from the caudate and the full scale IQ in ASD children (r = 20.47, P = 0.034), ii) between caudate fcMRI N and ADOS scales (r#20.43, P,0.005), iii) between caudate fcMRI N and VABS social skill scores (r = 0.35, P,0.001), iv) between caudate fcMRI N and VABS interpersonal skills (r = 2 0.3, P,0.001), v) between the caudate connectivity strength, Z score and the full scale IQ (r = 20.47, P = 0.034), vi) between caudate fcMRI Z and VABS scores (P,0.001), vii) between the connections (both N and Z) from the two IFG seeds and ADOS tests (r#20.46, P#0.04), and viii) between the functional connections from the two IFG seeds and VABS scores (P,0.001).

Integration model for prediction
As for prediction, multiple combined imaging features in each domain showed improved correlations with clinical data compared to single imaging features for ASD children. For instance, fcMRI seeding from the pars opercularis of IFG showed a correlation coefficient of 20.64 between ADOS score and single imaging features ( Figure 6 A1-A5). The correlation coefficient was significantly improved with four selected imaging features to predict clinical phenotypic data. The fitted score using the Kstar classifier showed tight coupling (linear slope = 1, r = 0.95, P, 0.0001) to the original ADOS module score, with only a few outliers ( Figure 6B). Similarly, among all regressors, Kstar also showed the best predictive power for highly correlating with other phenotypic data including full IQ test (r = 0.94, P,0.0001) and ADI-R total score (r = 0.97, P,0.0001) when using the four as well as six essential imaging features.

Discussion
We applied advanced automatic classification and machine learning algorithms to multiparametric functional connectivity and structural data (i.e., volumetry and cortical thickness) to improve characterization and prediction in autism spectrum disorders. The major findings of this study were: 1) small-world network analysis based on volumetry and fcMRI did not find differences between ASD and TD children, while small-world network analysis based on cortical thickness revealed reduced total and global efficiency in ASD, and 2) through advanced machine learning algorithms, four essential imaging features (caudate volume, caudate-cortical fcMRI and IFG pars opercularis as well as triangularis fcMRI) were able to accurately differentiate the two groups and were highly predictive of phenotypic features (e.g. IQ, ADOS and ADI scores) in ASD.

Brain volume and thickness differences
Our findings of GM volume and cortical thickness increases and WM volume decreases in ASD compared to TD group are in general agreement with prior studies [42][43][44]. The increased cortical thickness in multiple regions throughout the cerebrum, together with decreased WM volumes in frontal and temporal regions, may represent a reduction in long-distance pathways with accompanying local GM volume increments. These changes could lead to a reduction in global efficiency, consistent with EEG/MEG results [45,46] supporting the hypothesis of unbalanced networks in autism [47].

Functional connectivity differences
Changes in caudate volume, caudate-cortical fcMRI, and IFG fcMRI were found to be highly predictive based on advanced machine learning algorithms. Most of the published literature on classification in autism is based on single imaging measures (such as volume, connectivity, or perfusion) [48][49][50]. Our integrated multiparametric model demonstrates markedly improved accuracy (i.e., sensitivity and specificity) for classification and prediction.
Consistent with task-based fMRI results [29,30], we found altered IFG functional connectivity, suggesting deficits in the mirror mechanism in autistic children. Disrupted DMN fcMRI and altered interhemispheric functional connectivity are in agreement with previously reported studies in ASD [51,52]. In addition, we found that caudate-cortical connectivity differed between ASD and TD children, and this metric correlated with full-scale IQ scores. A recent study reported aberrant functional connectivity from the caudate seed involving early developing brain areas and implicated developmental derangement of related functional brain circuits in ASD begin at a young age (from 7-14 years old) [14].
Small-world network analysis of fcMRI could not distinguish between ASD and TD groups, suggesting there might be functional compensatory mechanism in autism, including increased regional functional connectivity and reduced global, longdistance connectivity in ASD. These plasticity changes have been reported in other functional and structural connectome studies. For example, a recent fcMRI study found that there are changes in local efficiency in the posterior cingulum associated with autistic trait accompanied with changes in local tissue integrity in ASD as measured by diffusion tensor imaging [53]. The notion of rerouting of brain structural connectivity has also been reported in less severely cognitively impaired (IQ.70) ASD patients [54]. In particular, they found that these patients utilized more visuospatial processing networks as opposed to linguistically mediated pathways.

Machine learning and prediction
Changes in caudate volume, caudate-cortical fcMRI, and IFG fcMRI were found to be highly predictive based on advanced machine learning algorithms. Most of the published literature on Figure 6. Kstar, an instance (similarity) based classifier for regression analysis had the greatest prediction power for ADOS module score for ASD children among all the regressors combining 4 selected imaging features. A1-A4: standardized histogram distribution showing x-axis as the z-scores of each feature and y-axis being the frequency. A1-right caudate volume, A2-average Z of caudate fcMRI, A3-average Z of IFG opercularis fcMRI, A4-average Z of IFG triangularis fcMRI. A5: phenotypic ADOS module score histogram distribution with x-axis as the original score and y-axis being the frequency. B: The correlation coefficient between integrated imaging features and ADOS module score improved largely from 20.64 based on single best imaging feature to 0.95 combining 4 imaging features. The fitted score using Kstar classifier with 4 selected imaging features showed a tight coupling (linear slope = 1; r = 0.95, P,0.0001) with the original ADOS module score with only a few outliers. doi:10.1371/journal.pone.0090405.g006 classification in autism has been based on single imaging measures (such as volume, connectivity, or perfusion) [48][49][50]. Our integrated multiparametric model demonstrates markedly improved accuracy (close to 100% sensitivity and specificity) for classification of ASD from TD groups.
The PCA and mRMR selected key features (i.e. right caudate volume, the average fcMRI Z values seeded from bilateral caudate, bilateral IFG opercularis and triangularis parts, the DMN average Z, and the VMHC average Z) are consistent with previous studies that found changes associated with ASD in each of the six imaging features. Our results based on machine learning algorithms also suggest that caudate volume and connectivity imaging features are important components in the composite score for ASD diagnosis.
Cross-validation minimizes classification error estimation bias and is thus primarily used for small sample datasets. As expected, the classification accuracy dropped from ,100% for the full dataset to ,70% with 10-fold or percentage-split cross-validation. The decreased accuracy in the cross-validation evaluation also reflected the heterogeneity of our data sample and a potential over-fitting problem. Nevertheless, the remarkable improvement in outcome prediction from multiple combined imaging features compared to any single imaging features (r$0.94, P,0.0001) in all three phenotypic domains supports the notion that these key imaging features are reflective of the behavioral deficits in autism.

Limitations and future works
Although we used substantially large numbers of classifiers and reported the optimal one, our results were limited by the selection criteria. Incorporating other factors such as different feature and subset selection criteria besides PCA and mRMR may improve the classifier performance in the future. The current quantitative fcMRI features include local and network-based features. Further expanding the fcMRI feature space, such as using whole-brain ROI-based fcMRI and fALFF of with dual regression template model [39], may reduce ROI-selection bias. Application of recently developed deep learning algorithms [55] to prevent feature overfitting problems could provide more comprehensive results. In order to minimize motion-related errors in RS-fMRI data, further investigation of motion parameters, such as frame displacement with dynamic temporal screening criteria, could be implemented in the future [56].
The regional parcellation with Freesurfer used in our study has been shown to be a robust method. However, the results of direct volumetry and cortical thickness could be affected by the normalization errors of projecting individual brains to a template brain, given the younger age range of our subjects compared to the averaged template. Implementing spatial normalization using agespecific templates in Freesurfer is likely important. An additional limitation is that the clinical phenotypic scales were obtained in the first years of life of participants, and not necessarily the period during which they underwent MRI scanning. This may potentially increase the possibility of mismatch between symptoms and brain features.

Conclusion
This study applied advanced automatic classification and machine learning algorithms to multiparametric structural and functional connectivity data to improve characterization and prediction in autism spectrum disorders. A major finding of this study is that the small-world network analysis based on volumetry and fcMRI did not find differences between ASD and TD children, while the small-world network analysis analysis based on cortical thickness revealed reduced total and global efficiency in ASD. Moreover, we also found caudate volume, caudate-cortical fcMRI and IFG pars opercularis as well as triangularis fcMRI to be highly predictive of phenotypic features in ASD. Graph theory and machine learning analysis of multiparametric MRI may prove useful in identifying using imaging biomarkers for disease prognosis and monitoring disease progression in ASD.