Identification of infants at high‐risk for autism spectrum disorder using multiparameter multiscale white matter connectivity networks

Abstract

Autism spectrum disorder (ASD) is a wide range of disabilities that cause life‐long cognitive impairment and social, communication, and behavioral challenges. Early diagnosis and medical intervention are important for improving the life quality of autistic patients. However, in the current practice, diagnosis often has to be delayed until the behavioral symptoms become evident during childhood. In this study, we demonstrate the feasibility of using machine learning techniques for identifying high‐risk ASD infants at as early as six months after birth. This is based on the observation that ASD‐induced abnormalities in white matter (WM) tracts and whole‐brain connectivity have already started to appear within 24 months after birth. In particular, we propose a novel multikernel support vector machine classification framework by using the connectivity features gathered from WM connectivity networks, which are generated via multiscale regions of interest (ROIs) and multiple diffusion statistics such as fractional anisotropy, mean diffusivity, and average fiber length. Our proposed framework achieves an accuracy of 76% and an area of 0.80 under the receiver operating characteristic curve (AUC), in comparison to the accuracy of 70% and the AUC of 70% provided by the best single‐parameter single‐scale network. The improvement in accuracy is mainly due to the complementary information provided by multiparameter multiscale networks. In addition, our framework also provides the potential imaging connectomic markers and an objective means for early ASD diagnosis. Hum Brain Mapp 36:4880–4896, 2015. © 2015 Wiley Periodicals, Inc.

INTRODUCTION

Autism spectrum disorder (ASD) is a group of developmental disabilities that can cause difficulties in cognitive wellness, social communication, and social interaction. About 1 percent of world population is affected by ASD. It is usually first diagnosed in childhood. In the US, 1 out of 68 children has ASD. Prevalence of ASD in children in the US has increased by 120% since 2000. Now ASD becomes one of the fastest‐growing developmental disabilities, which results in approximately annual $250 billion healthcare expenses in the US [Centers for Disease Control and Prevention, 2014].

Although symptom severity differs among individuals, the common characteristics of ASD include: (1) repetitive body movements or behaviors, (2) difficulty in using or understanding language, and (3) trouble in making friends and interacting with people [Gillberg, 1993; Wing, 1997]. Unfortunately, there is no single medical test that can accurately diagnose ASD. The diagnosis is mostly confirmed by the specially trained physicians based on an individual's abnormal behaviors compared with other children of the same age [Lord and Jones, 2012]. In most cases, ASD is a life‐long disorder. Early diagnosis and treatment are therefore tremendously important for improving the life quality of patients and their families, as well as for reducing the financial burden borne by the society. Although evidence suggests that a number of risk behavioral markers can be observed at as early as 12 months after birth [Landa et al., 2007; Ozonoff et al., 2010; Zwaigenbaum et al., 2005], little is known prior to this, especially in the first 6 months of life.

ASD has long been thought of as a disorder with disrupted brain connectivity patterns [Shi et al., 2013], first disclosed by functional magnetic resonance imaging (fMRI) [Belmonte et al., 2004; Di Martino et al., 2011]. In the last decades, diffusion‐weighted MRI (DWI) [Basser et al., 1994] has emerged as a powerful noninvasive neuroimaging technique for providing biologically and clinically relevant information on white matter (WM) integrity and connectivity that is not available from other imaging modalities. It has been increasingly used to study connectivity of WM pathways in a variety of psychiatric or neurological disorders such as Alzheimer's disease [Jin et al., 2015], bipolar disorder [Torgerson et al., 2013], schizophrenia [Lee et al., 2013], traumatic brain injury [Dennis et al., 2015a, 2015c], or even genetics [Jin et al., 2012, 2013, 2014]. For ASD, various studies have shown widespread abnormalities in many WM tracts [Alexander et al., 2007; Barnea‐Goraly et al., 2010; Cheon et al., 2011]. Specifically, Wolf et al. [2012] suggested that the aberrant development of WM tracts was ahead of the manifestation of ASD symptoms in the first year of life. For example, the failure of flexibly orienting gaze and visual attention to the most salient or biologically relevant information in the environment implied abnormal functional specialization of posterior cortical circuits in 7‐month‐old ASD infants [Elison et al., 2013].

The term connectome, that is, a comprehensive map of neural connections in the brain, was first introduced in 2005 [Hagmann, 2005; Sporns et al., 2005]. DWI can be used to map structural connectome of the human brain and has been used to study normal subjects [Klein et al., 2007; Tomassini et al., 2007], neurological diseases such as Alzheimer's disease [Daianu et al., 2013, 2015; Li et al., 2013; Zhu et al., 2013, 2014], and neuropsychiatric diseases such as schizophrenia [Shi et al., 2012a; van den Heuvel et al., 2010]. Using the DWI data of ASD infants acquired at the 24th month, Lewis et al. [2014] reported both local and global network deficits in the regions of temporal, parietal, occipital, as well as frontal lobes. Those results are in line with the findings in a number of studies involving infants and older children affected by ASD [Courchesne et al., 2005; Elsabbagh et al., 2013]. Since abnormalities are spread over different brain regions, a network‐based approach for early identification of ASD infants seems reasonable.

Machine learning and pattern recognition technologies have been widely used to aid the diagnosis of neurodisorders, such as Alzheimer's disease [Davatzikos et al., 2008; Guo et al., 2014; Zhang et al., 2011; Zhu et al., 2014], schizophrenia [Ardekani et al., 2011; Calhoun et al., 2008], and Parkinson's disease [Haller et al., 2012; Pan et al., 2012]. In particular, different imaging modalities have been used for ASD diagnosis, including anatomical MRI [Wee et al., 2014], resting‐state fMRI [Price et al., 2014], electroencephalogram and magnetoencephalography [Duffy and Als, 2012; Tsiaras et al., 2011], and DWI [Ingalhalikar et al., 2012]. However, the subjects involved in these studies were at least 2 years old with a typical age range of 7–10 years, during which ASD has progressed considerably. It is desirable to identify infants with ASD at a much earlier stage, preferably even before the first trace of symptomatic behaviors. However, identifying ASD infants is challenging and not well studied, because of the difficulty in infant image acquisition and the lack of obvious symptoms at this stage.

In this study, we propose a novel multichannel machine learning based classification framework to identify infants at high‐risk for ASD when they are as young as 6 months old. Infants with autistic siblings are considered as high‐risk. High‐risk infants were reported up to 20 times higher probability to develop ASD than low‐risk infants [Constantino et al., 2010; Lauritsen et al., 2005; Ritvo et al., 1989; Spencer et al., 2011] since they presumably carry some of the genes associated with ASD [Abrahams and Geschwind, 2008; Bailey et al., 1995]. Investigating them could help understand the mechanism of the ASD and prevent or mitigate the full onset of ASD through effective treatment if necessary. The major contribution of this work is as follows: First, we develop a new brain parcellation strategy to partition a publicly available atlas “infant AAL” (Automatic Anatomical Labeling) [Shi et al., 2011] into anatomical meaningful regions of interest (ROIs) of various sizes; Second, unlike Ingalhalikar et al. [2012], we propose to use the features from multiscale whole‐brain WM connectivity networks, instead of the conventional region‐based features, to identify high‐risk ASD infants; Finally, we use an effective two‐stage feature selection scheme and a multikernel support vector machine (SVM) classifier that can incorporate the complementary information from multiple sources to improve the classification accuracy.

METHODS

Overview

This study involved infants who were at genetic risk for ASD (since their older siblings have ASD). For comparison, age‐matched low‐risk ASD infants (no first‐degree relatives with ASD) were also included in this study. The study is aimed to distinguish high‐risk from low‐risk 6‐month‐old infants. Since WM abnormalities seem to be one of the first signs that appears in ASD infants, we employ features derived from the whole‐brain connectivity networks that are constructed from pairwise connections between ROIs. More specifically, we start with a publicly available infant AAL atlas and parcellate its 90 cerebral ROIs into 203 and 403 sub‐ROIs with our proposed parcellation algorithm, respectively. By using these ROIs, the connectivity networks of each subject are constructed using whole‐brain tractography. Specifically, the WM networks of three different scales are constructed based on the average values of the DWI‐derived parameters such as fractional anisotropy (FA), mean diffusivity (MD), and fiber length, all computed over the WM tracts connecting a pair of ROIs. Those values are considered features. Due to the large number of ROIs, the number of features is also large. For example, for the connectivity network at the 403‐ROI scale, the maximum number of the possible features can be 81,003. Hence, a feature selection step, combining t‐test and the Least Absolute Shrinkage and Selection Operator (LASSO) logistic regression [Tibshirani, 1996], is necessary to remove irrelevant or redundant features. Finally, the selected relevant features are fed into a multikernel SVM classifier for classification. The diagram of the complete workflow for our proposed method is shown in Figure 1.

Figure 1.

The proposed classification framework based on multiparameter multiscale WM connectivity networks. [Color figure can be viewed in the online issue, which is available at http://wileyonlinelibrary.com.]

Subjects and Image Acquisition

The participants in this study were chosen from the Lab Study 19 of National Database for Autism Research (NDAR), an on‐going quadro‐site study of brain and behavioral development in infants funded by the National Institute of Health (NIH). The study sites included Children's Hospital of Philadelphia, University of North Carolina at Chapel Hill (UNC‐CH), University of Washington, and Washington University in St. Louis. The infants of interest were considered carrying high familial risk for ASD if at least one of their older siblings had ASD. The neuroimaging data were first collected at the 6‐month visit stage. Parents or legal guardians signed on the informed consent forms. In the meantime, the infants were considered to have low familial risk if they had no first‐degree relatives with ASD. They were also enrolled for comparison. All the subjects were screened to exclude other medical conditions that could affect the study. Institutional review boards at all sites approved the study. 40 high‐risk infants (29 males and 11 females) and 40 low‐risk infants (27 males and 13 females) were used in this study.

All the MRI images were scanned using a 3T Siemens Tim Trio scanner at each site. The scans were acquired during the natural sleeping of infants. Three types of MRI images were acquired: (a) T1‐weighted (T1w) images with a 3D MPRAGE sequence (voxel dimensions: 1.0 × 1.0 × 1.0 mm³; image dimensions: 160 × 224 × 256, TE = 3.16 ms, TR = 2400 ms); (b) T2‐weighted (T2w) images with a 3D FSE sequence (voxel dimensions: 1.0 × 1.0 × 1.0 mm³; image dimensions: 160 × 256 × 256, TE = 499 ms, TR = 3200 ms); (c) Diffusion‐weighted images with 3D EPI sequence (voxel dimensions: 2.0 × 2.0 × 2.0 mm³; image dimensions: 96 × 96 × 75, TE = 102 ms, TR = 12,800 ms). The diffusion‐weighted images consisted of one b ₀ volume with no diffusion sensitization, and 25 volumes with a dynamic range of diffusion gradient b from 0 to 1000 s/mm².

Image Preprocessing

T1w and T2w images were first skull‐stripped using an open source Skull Stripping Toolkit [Shi et al., 2012b]. DWI images were skull‐stripped using Brain Extraction Tool (BET) from FSL (http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/) [Smith, 2002]. The skull‐stripped T1w and T2w images then underwent field bias correction using nonuniform intensity normalization (N3) algorithm [Sled et al., 1998]. The DWI images were corrected for eddy‐current induced distortion using FSL. The diffusion gradient tables were adjusted accordingly. FA and MD images were then extracted from the DWI data after diffusion tensor fitting.

Multiscale ROI Parcellation

The AAL atlas [Tzourio‐Mazoyer et al., 2002] is a widely used high‐resolution T1w brain parcellation based on a single adult subject, where the main sulci were used as landmarks to parcellate the entire brain into 90 ROIs (cerebellum excluded) based on anatomical definitions. However, directly applying adult atlas into infant brains may compromise its performance due to their large anatomical variations. Instead, we used a publicly available 1‐year‐old infant brain atlas [Shi et al., 2011], which adapted the original AAL atlas to infant space and has been proven effective in infant normalization and parcellation tasks. To promote the characterization of brain connectivity at different scales, we propose a novel strategy to further parcellate the infant AAL atlas into smaller sub‐ROIs.

Similar to [Hagmann et al., 2008], we created normalized sub‐ROIs by controlling them to have a similar size. Given a user‐specified size $a$, we first initialized a group of sub‐ROIs by dividing the entire volume of the infant AAL template into cubes of size $a^3$. Then, for each sub‐ROI, its center was calculated by taking the mean coordinates of all the voxels involved. If the resulting sub‐ROI was too small, for example, if it was near the boundary of the original ROI and had less than 30% of the standard size, we would attach it to a neighboring bigger divided region located in the same ROI whose center was the closest. The new center of the combined region was accordingly recalculated. After doing this for each of the 90 original ROIs, we had a series of center points inside each original ROI. Finally, we performed Voronoi partition [Aurenhammer, 1991], that is, for each original ROI, we assigned each voxel inside it a sub‐ROI index based on its shortest distance to one of those sub‐ROI centers. The steps described above are summarized in Algorithm 1. In our case, 203 and 403 ROIs were obtained when the target ROI size was chosen at around 20 and 16 mm, respectively. Figure 2 provides the 3D views of the ROIs in three different scales.

Figure 2.

The 3D views of ROIs of three different scales ‐ 90 ROIs, 203 ROIs, and 403 ROIs, respectively (from left to right). [Color figure can be viewed in the online issue, which is available at http://wileyonlinelibrary.com.]

Algorithm 1 Multiscale ROI Parcellation.

Set cube size a and load the original infant AAL ROIs.
Divide the entire volume (including the background) evenly into cubes of size a3.
for ROI i = 1:90 //compute the center of each new sub‐ROI
 if any interior volume is at least 0.3*a3, e.g., Vcube > 0.3*a3, calculate the center of the cube.
 else Find a neighboring cube whose center is the closest to its center and combine the two regions.
  Recompute the new center of the combined region.
 end if
end for
for ROI 
$i$ = 1:90 //assign new sub‐ROIs
 Perform Voronoi partition based on the new centers inside each ROI 
$i$.
end for

Multiscale Connectivity Networks

Features derived from structural connectivity networks provide rich information for identifying ASD subjects due to its comprehensive characterization of connections between brain regions. Furthermore, a multiscale set of connectivity networks may provide a range of complementary coarse‐to‐fine information for the multilevel analysis of brain connections. A connectivity network can be described mathematically as a graph consisting of (1) a collection of nodes, representing the ROIs and (2) a set of edges between nodes, describing the connections between ROI pairs.

To transfer the ROIs to the DWI space of each subject for construction of the connectivity networks, we performed the following steps. First, the infant AAL template was nonlinearly registered to the T1w image of the subject. Then, to further align the infant AAL template to the space of the DWI data, the T1w image was linearly aligned to the T2w image and the T2w image was nonlinearly registered (considering EPI distortion) to the MD image, since a T2w image had the similar contrast as an MD image. Here, we used the T1w and T2w images as the intermediate targets to transfer the AAL ROIs to the DWI space of the subject smoothly. It actually achieved the better accuracy than directly registering the T1w AAL template to the FA image of the subject, since both inter‐modality and inter‐subject made the latter process much more difficult. The deformation fields estimated in these series of registration were concatenated and then used to warp the atlas ROIs to the individual DWI space. All the registration steps were performed using ANTs [Avants et al., 2008].

Whole‐brain tractography was performed using an image resolution enhanced deterministic streamline tractography with peaks detected from the WM orientation distribution functions [Yap and Shen, 2012]. This tractography algorithm allowed for a closer investigation of fiber structures and more accurate assessment of brain connectivity [Yap et al., 2014]. Seed points were chosen as voxels with FA > 0.3. To eliminate excess false positives, the maximum turning angle was set to 45°, and tracking was stopped when FA < 0.15. The final tractography of all subjects was checked manually to ensure the anatomical correctness.

Two ROIs were considered anatomically connected if there were common fibers traversing them. Three different metrics, that is, FA, MD, and fiber length, were used to indicate the connection strength. For each pair of ROIs, connection strengths were computed based on the values of these metrics spatially averaged over the fibers connecting these ROIs. To exclude noisy connections, any node pairs that had <4 average fiber connections across the entire population of subjects were considered unconnected [Zalesky et al., 2011]. By using ROIs of three different scales, we constructed three sets of multiscale connectivity networks (nine in total) for each subject. Figure 3 shows the FA connectivity networks of three different scales for a pair of low‐risk and high‐risk ASD subjects from our dataset. We notice that when the scale becomes finer, the connections between the coarse ROIs in Figure 3a,d are spread into more detailed connections between the embedded sub‐ROIs in Figure 3b,c,e,f. Notice that the multiscale networks of a low‐risk subject (Figure 3a–c) contain stronger connections (i.e., more and thicker edges) than those of a high‐risk subject (Figure 3d–f).

Figure 3.

The 3D views of connectivity networks of three different scales, thresholded by mean FA = 0.4 (considered as strong connection), from a randomly selected pair of low‐risk and high‐risk ASD subjects. At each scale, each sphere represents the center of an ROI and its size indicates the normalized volume of the ROI. The colors of the sub‐ROIs in (b–c) and (e–f) correspond to those of the original ROIs in (a) and (d), respectively. The thickness of edges represents the mean value of FA averaged over the fibers connecting two respective ROIs. [Color figure can be viewed in the online issue, which is available at http://wileyonlinelibrary.com.]

Feature Selection

We considered each element of a connectivity network as a feature. Since the connectivity network was symmetric, we only took the elements from its lower triangular part (since the diagonal values were always set zero). There are several reasons why feature selection is necessary: First, the number of features increases with the square of the number of ROIs, from thousands in a 90‐ROI network to tens of thousands in a 403‐ROI network, and many of these features may be irrelevant to the classification task. Second, feature selection is needed in order to improve generalization performance. Finally, reducing the number of features will reduce the computation time significantly. Here, we first normalized the features by their z‐scores, and then performed a two‐stage feature selection procedure to select the optimal subset of features that would both improve the accuracy and ease the computation burden.

Specifically, we first performed a t‐test and then followed by the LASSO logistic regression [Tibshirani, 1996]. A t‐test was conducted between the high‐risk and the low‐risk groups for each feature. Only the features whose P‐values were below an empirical threshold were selected for LASSO logistic regression. Here, the t‐tests acted as a feature ranking technique to select an initial set of most relevant features based on their individual discriminative powers [Fan et al., 2007], which also greatly eased the computation cost for the following steps. By considering the correlation among features, the LASSO logistic regression model further optimized the selection. The LASSO logistic regression is a commonly used feature selection algorithm that can select a parsimonious set of features from a large collection of possible candidates to improve the classification accuracy. It only keeps the most discriminative features while discarding the redundant ones. Mathematically, the LASSO logistic regression model can be described as follows:

$\mathrm{L}\mathrm{e}\mathrm{t} \mathit{X}=\left[\begin{array}{c}{\mathit{x}}_1^T\\ ⋮\\ {\mathit{x}}_M^T\end{array}\right]\in {\mathbb{R}}^{M\times N}$, $\mathit{A}=\left[\begin{array}{c}{a}_1\\ ⋮\\ a_N\end{array}\right]\in {\mathbb{R}}^{N\times 1}$, and $\mathit{Y}=\left[\begin{array}{c}{y}_1\\ ⋮\\ y_M\end{array}\right]\in {\mathbb{R}}^{M\times 1}$. Here ${\mathit{x}}_i\in {\mathbb{R}}^{N\times 1}$ is the feature vector of the $i$‐th subject. $a_i$ is the feature regression coefficient for the $i$‐th feature. $y_i$ is the label for the $i$‐th subject (i.e., +1 for high‐risk and −1 for low‐risk). $M$ is the total number of subjects and $N$ is the total number of features. The LASSO logistic regression aims to solve $\mathit{A}$ by minimizing the following cost function:

$${\mathrm{m}\mathrm{i}\mathrm{n}}_{\mathit{A}}{\sum }_{i=1}^M{w}_i\log \left(1+\exp \left(-y_i\left({\mathbf{A}}^T{\mathit{x}}_i+c\right)\right)\right)+\lambda {||\mathit{A}||}_1+\frac{\rho }{2}{‖\mathit{A}‖}_2^2$$ (1)

$$\mathrm{s}.\mathrm{t}. {\sum }_{i=1}^M{w}_i=1 \mathrm{a}\mathrm{n}\mathrm{d} w_i=w_j if y_i=y_j$$

where $w_i$ is the weight for the $i$‐th subject, ${‖\mathit{A}‖}_1={\sum }_{i=1}^N\left|a_i\right|$ is the ${\mathcal{\ell }}_1$ norm of $\mathit{A}$, and ${‖\mathit{A}‖}_2^2={\sum }_{i=1}^N{a}_i^2$ is the squared ${\mathcal{\ell }}_2$ norm. Here, $\lambda$ is the $L_1$ norm regularization parameter that controls the model sparsity. The larger the value of $\lambda$, the sparser the model. Meanwhile, $\rho$ is the regularization parameter for the squared ${\mathcal{\ell }}_2$ norm that helps to achieve numerical stability and increase predictive performance. We performed the LASSO logistic regression on each individual network separately and retain features with nonzero coefficients in $\mathit{X}$.

Multikernel Classification

Kernel methods such as SVM have been proven to be efficient for classification problems [Scholkopf and Smola, 2001]. It has been demonstrated that multikernel SVM is able to utilize the complementary information from multiple representations for achieving higher accuracy than single‐kernel SVM [Liu et al., 2014; Liu et al., 2015; Wee et al., 2014; Zhang et al., 2011; Zhu et al., 2015a, 2015b]. Here, we used it to incorporate the selected features from all nine networks for classification.

A multikernel SVM classification framework is described as below. Let $\left\{\left({\mathit{x}}_i^j, y_i\right), i=1,\dots ,M, j=1,\dots ,K\right\}$ be the set of training data, where ${\mathit{x}}_i^j\in {\mathbb{R}}^{n_j\times 1}$ represents the feature vector of the $i$‐th subject for network $j$ and $y_i\in$ 1 (high‐risk) or −1 (low‐risk) is the label. $M$ is the number of training subjects, and $K$ is the number of networks (i.e., $K=9$ in our study). The primal formulation of multikernel SVM is given as:

$${\text{min}}_{{\mathit{P}}_j,b,{\xi }_i}\frac{1}{2}\sum _{j=1}^K{\beta }_j{‖{\mathit{P}}_j‖}^2+C\sum _{i=1}^M{\xi }_i$$ (2)

$$\mathrm{s}.\mathrm{t}.\hspace{0.17em}{y}_i(\sum _{j=1}^K{\beta }_j({\mathit{P}}_j^T{\mathit{\varphi }}_j\left({\mathit{x}}_i^j\right)+b))\ge 1-{\xi }_i$$

$$\mathrm{a}\mathrm{n}\mathrm{d} {\xi }_i>0, \sum _{j=1}^K{\beta }_j=1, {\beta }_j>0$$

where ${\beta }_j$, ${\mathit{P}}_{j,}$ and ${\mathit{\varphi }}_j$ denote the weight, the normal vector of the classification hyperplane, and the kernel‐induced mapping function for the $j$‐th network, respectively. $b$ denotes the bias term, ${\xi }_i$ denotes the slack variable (for misclassification), and $C$ is a parameter that controls the degree of misclassification. Given a test feature vector $=\left\{{\mathit{x}}^j, j=1,\dots ,K\right\}$, the predicted label $\widehat{y}$ is

$$\widehat{y}=\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\left({\sum }_{j=1}^K{\beta }_j\left({\mathit{P}}_j^T{\mathit{\varphi }}_j\left({\mathit{x}}^j\right)+b\right)\right)$$ (3)

Here, we applied an open‐source software package SimpleMKL [Rakotomamonjy et al., 2008] that can decide the weights simultaneously during the optimization of the cost function.

Implementation and Evaluation

The classification performance was evaluated on a nested 5‐fold cross validation. The 80 subjects were randomly divided into 5 folds. Each fold was comprised of 8 high‐risk infants and 8 low‐risk infants, respectively. Each fold was alternatively used as a testing fold, and the rest of the four folds were used as the training set.

For each network, during each of the five training sessions, a t‐test was to select the features whose p‐values < 0.001. Those features were fed into the LASSO logistic regression. In machine learning, feature ranking and selection can use a performance evaluation metric computed directly from the data and not based on the direct feedback from the classifier [Guyon et al., 2006]. In other words, we used the predicted results directly from the logistic regression to make feature selection without the classifier involved. The 64 subjects in the training set were divided into 5 folds again and an inner loop of 5‐fold cross validation was performed. The binarized results of the regression (the result = 1 if positive and −1 otherwise) were compared to the ground truth. The set of parameters $\lambda$ and $\rho$ in Eq. (1) with the best average accuracy over the inner 5‐fold cross validation were used to select the features for the corresponding testing fold.

The selected features were then fed into the SimpleMKL package with the Gaussian radial basic function (RBF) as the kernel. Note that another inner 5‐fold cross validation was performed on the training set to find the optimal parameter $C$ in Eq. (2) and the test fold was classified with that determined $C$.

The statistics we used to evaluate our classification algorithm performance are accuracy (ACC), sensitivity (SEN), specificity (SPE), positive predictive value (PPV), negative predictive value (NPV), and the area under the receiver operating characteristic curve (AUC). Letting TP, TN, FP, and FN denote, respectively, true positive, true negative, false positive, and false negative, the ACC, SEN, SPE, PPV, and NPV are defined as

$$\mathrm{A}\mathrm{C}\mathrm{C}=\frac{\mathrm{T}\mathrm{P}+\mathrm{T}\mathrm{N}}{\mathrm{T}\mathrm{P}+\mathrm{T}\mathrm{N}+\mathrm{F}\mathrm{P}+\mathrm{F}\mathrm{N}}$$

$$\mathrm{S}\mathrm{E}\mathrm{N}=\frac{\mathrm{T}\mathrm{P}}{\mathrm{T}\mathrm{P}+\mathrm{F}\mathrm{N}}$$

$$\mathrm{S}\mathrm{P}\mathrm{E}=\frac{\mathrm{T}\mathrm{N}}{\mathrm{T}\mathrm{N}+\mathrm{F}\mathrm{P}}$$

$$\mathrm{P}\mathrm{P}\mathrm{V}=\frac{\mathrm{T}\mathrm{P}}{\mathrm{T}\mathrm{P}+\mathrm{F}\mathrm{P}}$$

$$\mathrm{N}\mathrm{P}\mathrm{V}=\frac{\mathrm{T}\mathrm{N}}{\mathrm{T}\mathrm{N}+\mathrm{F}\mathrm{N}}$$

To avoid the biased result due to the fold selection, the entire process was repeated 10 times, each with different partitions of subjects. The average statistics of the 10 repetitions were finally reported.

RESULTS

Multiscale Connectivity Networks

To evaluate the benefits of using multiscale connectivity networks on the ASD classification, we compared its performance with single‐scale networks. Figures 4, 5, 6 compare the classification performance of the single‐scale networks with that of the multiscale networks (using all three scales) for FA (Multi‐FA), MD (Multi‐MD), and fiber length (Multilength). Note that the results of the single‐scale network were obtained by applying the single RBF kernel SVM on the selected features, while the results of the multiscale networks were obtained using multikernel SVM. The error bars denote the standard deviations obtained from 10 repetitions. Not surprisingly, the multiscale networks outperformed any single‐scale network for each imaging parameter. In particular, the accuracies of Multi‐FA, Multi‐MD, and Multilength were 73.1, 73.1, and 73.6%, respectively. They achieved relative gains of 5.4, 4.5, and 4.6%, respectively, compared to the best single‐scale networks (the 403‐ROI networks). The AUCs were 0.789, 0.784, and 0.786 for Multi‐FA, Multi‐MD, and Multilength, respectively. They had the most significant improvement among all the statistics, by relative gains of 14, 12, and 12% against the best single networks (the 403‐ROI networks) for FA, MD, and fiber length, respectively. We also noticed that the standard deviations of all statistics were smaller in the multiscale networks, especially for AUC, suggesting a more stable performance. To test whether the improvement was statistically significant, we also conducted pair‐wise t‐tests between the accuracy results of both the single‐scale and the multiscale networks over the 50‐fold tests in our experiment, with the results shown in Table 1. The fact that all p‐values < 0.05 implied that the improvements using the multiscale network approach were indeed statistically significant.

Figure 4.

The mean statistics of the 6‐month‐old infant ASD classification (high‐risk vs. low‐risk) with the 90‐ROI (blue), 203‐ROI (cyan), 403‐ROI (green) network, respectively, and the integration (yellow) of all the three networks using mean FA. The error bars stand for the standard deviations of the measures after 10 repetitions. The multiscale networks outperform any single‐scale network in all statistics. [Color figure can be viewed in the online issue, which is available at http://wileyonlinelibrary.com.]

Figure 5.

The mean statistics of the 6‐month‐old infant ASD classification (high‐risk vs. low‐risk) with the 90‐ROI (blue), 203‐ROI (cyan), 403‐ROI (green) network, respectively, and the integration (orange) of all the three networks using mean MD. The error bars stand for the standard deviations of the measures after 10 repetitions. The multiscale networks outperform any single‐scale network in all statistics. [Color figure can be viewed in the online issue, which is available at http://wileyonlinelibrary.com.]

Figure 6.

The mean statistics of the 6‐month‐old infant ASD classification (high‐risk vs. low‐risk) with the 90‐ROI (blue), 203‐ROI (cyan), 403‐ROI (green) network, respectively, and the integration (dark red) of all the three networks using mean fiber length. The error bars stand for the standard deviations of the measures after 10 repetitions. The multiscale networks outperform any single‐scale network in all statistics. [Color figure can be viewed in the online issue, which is available at http://wileyonlinelibrary.com.]

Table 1.

The p‐values of the t‐tests on the mean accuracies with the single‐scale networks versus the multiscale networks using FA, MD, and fiber length

Method	403 ROIs	203 ROIs	90 ROIs
Multi‐FA	0.016	<0.001	<0.001
Multi‐MD	0.003	0.002	0.019
Multilength	0.040	<0.001	0.005

The t‐tests were the pair‐wise t‐tests on the classification results from the total 50 testing folds, that is, over 10 iterations of 5‐fold cross validation.

Multiparameter Multiscale Connectivity Networks

In this section, we demonstrate that our proposed method using all the 9 networks (multiscale networks with FA, MD, and fiber length) achieved the best result for our classification task. Figure 7 shows the comparison of the classification performance of the multiparameter multiscale network framework (Multi‐Multi) and the results of single‐parameter multiscale networks (i.e., Multi‐FA in Figure 4, Multi‐MD in Figure 5, and Multilength in Figure 6). The accuracy of Multi‐Multi (75.6%) had an improvement of 2.5, 2.5, and 2% against that of Multi‐FA, Multi‐MD, and Multilength, respectively. Other statistical measures, sensitivity (72%), specificity (79.3%), PPV (78.7%), NPV (75.5%), and AUC (80.3%), were also the best. We further conducted pair‐wise t‐tests on the accuracy results of Multi‐Multi against Multi‐FA, Multi‐MD, and Multilength over the 50 testing folds conducted in our classification protocol. The results are shown in Table 2. The fact that all the p‐values < 0.05 further indicated the statistically significant improvements using the proposed multiparameter multiscale network framework. The processing time of the classification (5‐fold cross validations with 10 iterations) with our proposed method was 7 min in the Matlab environment on an iMac equipped with a 3.4 GHz Intel Core i7 CPU and 16 GB RAM. The same task with a single‐scale network took 2 min. The computing time was tripled, but we think that it was still manageable and worthy spending, considering the much improved performance by our method.

Figure 7.

The mean statistics of the 6‐month‐old infant ASD classification (high‐risk vs. low‐risk) with the single‐parameter multiscale network framework using FA (yellow), MD (orange), and fiber length (dark red), vs. our method with multiparameter multiscale networks (red). The error bars stand for the standard deviations of the measures after 10 repetitions. It can be seen that our multiparameter multiscale networks outperform each of the single‐parameter networks in all statistics. [Color figure can be viewed in the online issue, which is available at http://wileyonlinelibrary.com.]

Table 2.

The p‐values of the t‐tests on the mean accuracies between the multiparameter multiscale networks (multi‐multi) and the single‐parameter multiscale networks (multi‐FA, multi‐MD, and multilength)

Method	Multi‐FA	Multi‐MD	Multilength
Multi‐multi	0.004	0.012	0.006

The t‐tests were the pair‐wise t‐tests on the classification results from the total 50 testing folds, that is, over 10 iterations of 5‐fold cross validation.

Feature Selection

To evaluate the effect of feature selection on the final classification results, we further conducted the classifications with and without feature selection. Table 3 proves that the feature selection greatly improved the performance of classification. With feature selection, the accuracy was improved by 16% (i.e., a relative 27% increase), the AUC by 21% (i.e., a relative 33% increase), and the sensitivity by 26% (i.e., a relative 57% increase). The standard deviations of all the measures were also smaller, which indicated a more stable performance in each fold with feature selection.

Table 3.

Comparison of the classification performance with and without feature selection

Mean (standard deviation)	No feature selection	Feature selection
ACC	0.591 (0.036)	0.756 (0.020)
SEN	0.460 (0.064)	0.720 (0.028)
SPE	0.723 (0.065)	0.793 (0.033)
PPV	0.656 (0.076)	0.787 (0.036)
NPV	0.577 (0.057)	0.755 (0.028)
AUC	0.591 (0.036)	0.803 (0.016)

We also investigated how different regression models could affect the classification results. Table 4 compares the performance of logistic regression with the commonly used linear regression. Logistic LASSO regression yielded better classification with accuracy, sensitivity, and specificity gains of 4.5, 4, and 5%, respectively.

Table 4.

Comparison of the classification performance between linear and logistic regression

Mean (standard deviation)	Linear regression	Logistic regression
ACC	0.711 (0.027)	0.756 (0.020)
SEN	0.680 (0.045)	0.720 (0.028)
SPE	0.743 (0.033)	0.793 (0.033)
PPV	0.734 (0.038)	0.787 (0.036)
NPV	0.715 (0.033)	0.755 (0.028)
AUC	0.783 (0.026)	0.803 (0.016)

Choice of Classifier

We chose the RBF kernel for SVM since it usually performs better than a linear kernel. Table 5 compares the performance between these two kernels with our dataset. Better performance was seen in all the measures when the RBF kernel was used. In particular, the accuracy with RBF kernel was 0.76, while the accuracy with linear kernel was only 0.70. The relative improvement was 8%. Specificity and PPV had the most relative increase, that is, by 14 and 11%, respectively.

Table 5.

Comparison of the classification performance between linear and RBF kernels

Mean (standard deviation)	Linear	RBF
ACC	0.703 (0.032)	0.756 (0.020)
SEN	0.708 (0.051)	0.720 (0.028)
SPE	0.698 (0.045)	0.793 (0.033)
PPV	0.709 (0.029)	0.787 (0.036)
NPV	0.723 (0.051)	0.755 (0.028)
AUC	0.781 (0.031)	0.803 (0.016)

Table 6 compares the performance of the single kernel and the multikernel SVM. The single kernel SVM classification was implemented by concatenating all the features from the nine networks into a long feature vector and feeding it into the RBF‐kernel SVM classifier. Again, all statistics were improved by using a multikernel SVM (SimpleMKL in our case). The accuracy jumped from 0.72 to 0.76, a relative 6% increment. The increments of AUC, specificity, and PPV were among the largest, which were 12, 11, and 10%, respectively.

Table 6.

Comparison of the classification performance between the single kernel SVM and the multikernel SVM

Mean (standard deviation)	Single kernel SVM	Multikernel SVM
ACC	0.715 (0.019)	0.756 (0.020)
SEN	0.715 (0.038)	0.720 (0.028)
SPE	0.715 (0.021)	0.793 (0.033)
PPV	0.715 (0.020)	0.787 (0.036)
NPV	0.736 (0.031)	0.755 (0.028)
AUC	0.715 (0.019)	0.803 (0.016)

Multiparameter Multiscale vs. Multiparameter Selected‐Scale

For each parameter (FA, MD, and length), we also picked the network with the best performance (highest accuracy) in multiscale networks. The 403‐ROI networks performed the best for each parameter. We combined these three 403‐ROI networks to form the new multiparameter networks. They were fed into the same multikernel SVM classifier and the performance was compared with our proposed algorithm. The results are shown in Table 7. Our proposed method achieved a better accuracy by almost 4%.

Table 7.

Comparison of the classification performance between the multiparameter selected‐scale networks (i.e., the three best single networks using FA, MD, and length) and our proposed multiparameter multiscale networks

Mean (standard deviation)	Multiparameter selected‐scale	Multiparameter multiscale
ACC	0.719 (0.033)	0.756 (0.020)
SEN	0.700 (0.048)	0.720 (0.028)
SPE	0.740 (0.066)	0.793 (0.033)
PPV	0.745 (0.041)	0.787 (0.036)
NPV	0.722 (0.030)	0.755 (0.028)
AUC	0.792 (0.027)	0.803 (0.016)

Number of Networks

We have shown that using multiscale networks constructed from different scales of the infant AAL ROI improved the accuracy of classification. The 403‐ROI networks were better networks than both the 203‐ROI networks and the original 90‐ROI networks, in terms of classification performance. Here, we further partitioned the infant AAL atlas into 604 ROIs in the same way as described in the “multiscale ROI Parcellation” section to examine whether adding the networks constructed from those ROIs would further improve the classification result. Table 8 shows the classification results using the single‐parameter (FA, MD, and length) networks constructed from these 604 ROIs. Despite the finer ROIs, the performance actually deteriorated. For instance, the accuracies of the 604‐ROI networks were 67.6, 65.6, and 66.4%, for FA, MD, and length, respectively, while those of the 403‐ROI networks were 69.3, 70.0, and 70.3%, respectively. We further integrated the three 604‐ROI networks into our multiparameter multiscale network framework. With a total of 12 networks, the mean accuracy went down from 75.6 to 70%.

Table 8.

Classification performance of the 604‐ROI network for each parameter (FA, MD, and length)

Mean (standard deviation)	604 ROIs ‐ FA	604 ROIs ‐ MD	604 ROIs ‐ Length
ACC	0.676 (0.039)	0.656 (0.030)	0.664 (0.038)
SEN	0.638 (0.041)	0.610 (0.070)	0.655 (0.048)
SPE	0.715 (0.064)	0.703 (0.076)	0.673 (0.077)
PPV	0.704 (0.063)	0.684 (0.055)	0.680 (0.052)
NPV	0.676 (0.036)	0.656 (0.036)	0.676 (0.040)
AUC	0.676 (0.039)	0.656 (0.030)	0.664 (0.038)

Choice of Parameters

Fiber count is another popular measure in WM connectivity analysis [Jahanshad et al., 2011; Zhan et al., 2013a,b,c]. We also investigated how good fiber count acted as a feature in our infant ASD classification. The fiber count connectivity network refers to the matrix consisting of the relative fiber count connecting pairwise ROIs (normalized by the total number of fibers in the whole‐brain tractography). We performed classification with the 90‐ROI, 203‐ROI, and 403‐ROI fiber count networks, respectively. The results are shown in Table 9. The mean accuracies from those fiber count networks were much lower than those built on other parameters we used in the proposed algorithm (FA, MD, and length). Therefore, we did not include fiber count in our classification model.

Table 9.

Classification performance of the normalized fiber count networks in three different scales

Mean (standard deviation)	403 ROIs	203 ROIs	90 ROIs
ACC	0.586 (0.027)	0.531 (0.046)	0.586 (0.055)
SEN	0.583 (0.065)	0.560 (0.062)	0.628 (0.103)
SPE	0.590 (0.068)	0.503 (0.081)	0.545 (0.078)
PPV	0.595 (0.046)	0.536 (0.056)	0.588 (0.055)
NPV	0.603 (0.028)	0.538 (0.048)	0.627 (0.081)
AUC	0.586 (0.030)	0.531 (0.046)	0.586 (0.055)

Most Discriminative Connections

We summed the counts of each connection selected by our proposed method for each network scale (90, 203, and 403 ROIs) over the 50 folds. The counts for FA, MD, and fiber length were combined at each level. We ranked the connections by the counts of selection. For the purpose of visualization, Figure 8a–c illustrates the top 20 most discriminative representations of connectogram, a circular representation tool called Circos (http://www.cpan.org/ports) [Krzywinski et al., 2009], for the 90‐ROI, 203‐ROI, and 403‐ROI networks, respectively. Note that for the 90‐ROI networks, the connections between the original ROIs were reported. While, in the 203‐ROI and 403‐ROI networks, the connections in the original 90 ROIs that contained those selected connections between sub‐ROIs were reported for comparison. The connections in the same hemisphere were represented in red while inter‐hemisphere in black. Thickness of each line reflected its selection frequency, that is, the thicker the line, the higher the frequency. A total of 65% connections (13 pairs) overlapped between the 90‐ROI scale and the 203‐ROI scale, 20% (4 pairs) between the 90‐ROI scale and the 403‐ROI scale, and 15% (3 pairs) between the 203‐ROI scale and the 403‐ROI scale. 10% connections (2 pairs) appeared in all the three scales. They were the connections between the left middle occipital gyrus and the left middle orbitofrontal cortex, as well as between the right superior temporal gyrus and the right middle occipital gyrus. The ROIs used in Figure 8 are listed in Table 10.

Figure 8.

Connectogram of the top 20 discriminative connections selected by our framework in the (a) 90‐ROI, (b) 203‐ROI, and (c) 403‐ROI networks, respectively. The intrahemisphere and interhemisphere connections are shown in red and black colors, respectively. For the abbreviations of the ROIs, please refer to Table 10. [Color figure can be viewed in the online issue, which is available at http://wileyonlinelibrary.com.]

Table 10.

The ROIs used in Figure 8

Index (odd ‐> left, even ‐> right)	Region	Abbreviation
		Left	Right
1, 2	Precentral gyrus	PreCG.L	PreCG.R
3, 4	Superior frontal gyrus (dorsal)	SFGdor.L	SFGdor.R
5, 6	Orbitofrontal cortex (superior)	ORBsupb.L	ORBsupb.R
7, 8	Middle frontal gyrus	MFG.L	MFG.R
9, 10	Orbitofrontal cortex (middle)	ORBmid.L	ORBmid.R
11, 12	Inferior frontal gyrus (opercular)	IFGoperc.L	IFGoperc.R
13, 14	Inferior frontal gyrus (triangular)	IFGtriang.L	IFGtriang.R
15, 16	Orbitofrontal cortex (inferior)	ORBinf.L	ORBinf.R
17, 18	Rolandic operculum	ROL.L	ROL.R
19, 20	Supplementary motor area	SMA.L	SMA.R
21, 22	Olfactory	OLF.L	OLF.R
23, 24	Superior frontal gyrus (media)	SFGmed.L	SFGmed.R
25, 26	Orbitofrontal cortex (medial)	ORBmed.L	ORBmed.R
27, 28	Rectus gyrus	REC.L	REC.R
29, 30	Insula	INS.L	INS.R
31, 32	Anterior cingulate gyrus	ACG.L	ACG.R
33, 34	Middle cingulate gyrus	MCG.L	MCG.R
35, 36	Posterior cingulate gyrus	PCG.L	PCG.R
37, 38	Hippocampus	HIP.L	HIP.R
39, 40	ParaHippocampal gyrus	PHG.L	PHG.R
41, 42	Amygdala	AMYG.L	AMYG.R
43, 44	Calcarine	CAL.L	CAL.R
45, 46	Cuneus	CUN.L	CUN.R
47, 48	Lingual gyrus	LING.L	LING.R
49, 50	Superior occipital gyrus	SOG.L	SOG.R
51, 52	Middle occipital gyrus	MOG.L	MOG.R
53, 54	Inferior occipital gyrus	IOG.L	IOG.R
55, 56	Fusiform gyrus	FFG.L	FFG.R
57,58	Postcentral gyrus	PoCG.L	PoCG.R
59, 60	Superior parietal gyrus	SPG.L	SPG.R
61, 62	Inferior parietal lobule	IPL.L	IPL.R
63, 64	Supramarginal gyrus	SMG.L	SMG.R
65, 66	Angular gyrus	ANG.L	ANG.R
67, 68	Precuneus	PCUN.L	PCUN.R
69, 70	Paracentral lobule	PCL.L	PCL.R
71, 72	Caudate	CAU.L	CAU.R
73, 74	Putamen	PUT.L	PUT.R
75, 76	Pallidum	PAL.L	PAL.R
77, 78	Thalamus	THA.L	THA.R
79, 80	Heshl gyrus	HES.L	HES.R
81, 82	Superior temporal gyrus	STG.L	STG.R
83, 84	Temporal pole (superior)	TPOsup.L	TPOsup.R
85, 86	Middle temporal gyrus	MTG.L	MTG.R
87, 88	Temporal pole (middle)	TPOmid.L	TPOmid.R
89, 90	Inferior temporal	ITG.L	ITG.R

DISCUSSION

The population size of our study (40 high‐risk vs. 40 low‐risk) has been commonly seen in previous classification studies. For example, for schizophrenia classification, Ardekani et al. [2011] used 50 healthy controls and 50 patients, and Calhoun et al. [2008] used 26 healthy controls, 21 schizophrenia patients, and 14 bipolar patients. For ASD, Bosl et al. [2011] used 33 normal controls and 46 ASD patients, and Ingalhalikar et al. [2012] used 30 normal controls and 45 ASD patients.

The way to divide sub‐ROIs is a critical step for building the multiscale connectivity networks. If we use a fixed number to divide every ROI, the sub‐ROIs generated from the smaller ROIs may be too little to have any fibers traversing them, thus resulting in the heavy weights on the connections between the sub‐ROIs generated from those larger ROIs. However, those larger regions may not be discriminative in classification. It is more reasonable to have each sub‐ROI be as the equal size as possible so that it can be weighted fairly in a connectivity network. The 203 and 403 sub‐ROIs were the results of an approximately size of 20 and 16 mm for each sub‐ROI, respectively. They were anatomically meaningful considering that the structure of the original AAL ROIs was retained. For example, the superior temporal gyrus was a single ROI in the original AAL atlas while we subdivided it into multiple sub‐ROIs with similar sizes. In this way, we retained the anatomical information of each sub‐ROI.

The original 90‐ROI infant AAL cortical parcellation might not be the most suitable for identifying differences between high‐risk and low‐risk ASD infants. Smaller networks (with larger ROIs) might be more beneficial for group studies since more stable features within groups can be extracted, while larger networks (with smaller ROIs) provide more detailed connectivity information at the individual level and more precise distinction can be captured [Cammoun et al., 2012]. The right scale depends on the studies [Fornito et al., 2010; Zalesky et al., 2010]. In this study, we further divide the original ROIs into smaller ROIs to form atlases of three different scales, that is, 90 ROIs, 203 ROIs, and 403 ROIs. The 403‐ROI networks give the highest classification accuracy for all three measures (FA, MD, and length) (see Figures 4, 5, 6). The multiscale networks improve the classification accuracy for each metric (FA, MD, and length) by 5.4, 4.5, and 4.6%, compared with the best single networks, respectively. The AUCs are improved by 13.8, 12, and 11.7%, respectively (see Figures 4, 5, 6). Integrating multiscale networks further improves classification performance. We note that, however, adding the 604‐ROI networks does not further improve the classification accuracy (see the “Number of Atlases” section).

Wee et al. [2011] demonstrated that utilizing networks constructed from multiple DWI‐derived parameters enhances classification performance. In this work, we confirm this and show that, using the multiparameter networks based on FA, MD, and length, we can improve the accuracy by 2.5, 2.5, and 2% compared with any single parameter network (see Figure 7).

The top 20 most discriminative connections (see Figure 8) from the networks of three different scales overlap, that is, the top selected connections in the original 90‐ROI network contain many selected sub‐ROI connections in the 203‐ROI and the 403‐ROI networks. The relevant regions include (1) multiple cortical regions, such as the orbital part of the left frontal lobe, the bilateral temporal lobes, the bilateral occipital lobes, the bilateral calcarine fissures, the bilateral lingual gyri, the right cuneus, the right insula and (2) several subcortical regions, such as the left globus pallidum, the left putamen, and the bilateral parahippocampal gyri. Those findings are consistent with the regions identified in a number of ASD infant or child studies. The temporal lobes, the occipital lobes, the calcarine fissures, the lingual gyri, and the cuneus are involved in processing auditory and visual stimuli, language and nonlinguistic social stimuli. Abnormalities exist in all these regions in ASD patients [Johnson et al., 2005; Redcay, 2008; Schultz et al., 2000; Wetherby et al., 2004]. The frontal cortical connectivity abnormalities were also well documented in ASD [Just et al., 2012]. Among the subcortical regions, insula is positioned as a hub to mediate external and internal cognitive processes. Its dysfunction plays an important role in ASD [Uddin and Menon, 2009]. The basal ganglia region that contains globus pallidum and putamen also shows shape deformation in ASD patients [Qiu et al., 2010]. Attenuated neural activities in parahippocampal regions may explain some aspects of ASD [Sumiyoshi et al., 2011].

It is also interesting to notice the asymmetry between the left hemisphere and the right hemisphere in the three connectograms in Figure 8. The majority of the top 20 discriminative connections lie in the left hemisphere in all three‐scale networks. This is consistent to the left‐hemisphere hypothesis for ASD [Chandana et al., 2005; Chugani et al., 1997]. The hypothesis can explain many of the symptoms of ASD, most notably the language deficits, as language is a left‐brain skill. On the other hand, while more connections in the right hemisphere become discriminative in the 403‐ROI networks with additional interhemisphere connections. This demonstrates that subtler changes in the connectome can be detected with smaller ROIs.

Our framework uses features extracted from multiple networks constructed from multiscale ROIs. The number of features increases to tens of thousands when more ROIs are used. Our feature selection step removes irrelevant features and eventually retains only hundreds of features. Moreover, the classification accuracy is improved 16%, that is, from 60 to 76%, demonstrating the effectiveness of our feature selection strategy. The $t$‐test acts as an effective feature ranking method that is preferable in high dimensional problems because of its computational scalability. Feature subset selection methods such as LASSO select a subset of features that may have better discriminative power jointly. The latter methods usually have better classification performance, but its high computational cost limits their applications to those problems. In our case, approximately a quarter of a million of features were retrieved from the nine networks. Simply applying the subset feature selection may not be realistic. It is possible that the $t$‐test may miss some of the features that were irrelevant individually yet relevant when considered jointly. However, the $t$‐test filtered much more irrelevant features and reduced the computational cost for the LASSO logistic regression. It has been proved to be an effective feature selection step in other studies [Fan et al., 2007; Wee et al., 2014]. The fact that the logistic regression performs better than the linear regression (76 vs. 71%) implies that the relationship between the features and the labels may not be linear. This observation is also consistent with the observation that the SVM with RBF kernel performs better than the SVM with linear kernel (76 vs. 70%).

The fiber count is a common measure used in the connectivity analysis. However, the mean values of FA, MD, and fiber length take the whole tract path between two ROIs into account. Adding or missing a few more fibers will probably not change their overall characteristics as much as that of fiber count. Therefore, they provide more reliable connectivity features than fiber count, and it has been demonstrated by our experiment results (i.e., the mean ACC of FA at the 90‐ROI scale was 0.675 vs. that of fiber count at 0.586).

Many factors, such as field strength [Dennis et al., 2013; Zhan et al., 2013a], scanners [Zhan et al., 2014a], feature space [Zhan et al., 2014b], and imaging acquisition parameters [Zhan et al., 2012, 2013b], affect the construction of connectivity network. The choice of diffusion models (e.g., tensor, multitensor, and spherical deconvolution), tracking parameters, seed locations, maximum turning angle, and stopping criteria will also introduce variability in network construction and classification results [Dennis et al., 2015b; Zhan et al., 2013c, 2015]. Tractography is even more challenging given that the image quality at the 6‐month‐old is generally insufficient, both in terms of contrast and resolution. In the future, more efforts need to be dedicated to refining these tractography and imaging parameters.

CONCLUSION

We propose a classification framework that uses the complementary information from multiparameter multiscale structural networks for identification of 6‐month‐old infants who are at high‐risk for ASD. The experiment results confirm the effectiveness of the proposed framework. The discriminative connections identified in our study may serve as potential imaging connectomic biomarkers for ASD diagnosis or prediction. Our method can also be generalized for detecting other WM related diseases.