Autism spectrum disorder (ASD) is a serious lifelong condition characterized by repetitive, restricted behavior as well as deficits in communication and reciprocal social interactions (American Psychiatric Association, 2013). The traditional procedure for diagnosing ASD is largely based on narrative interactions between individuals and clinical professionals (Yahata et al., 2016). Such methods, lacking biological evidence, not only are prone to generate a high variance during the diagnosis (Mandell et al., 2007) but also require a long period to detect abnormalities (Nylander et al., 2013). As a complement to the current behavior-based diagnoses, functional magnetic resonance imaging (fMRI) has been widely applied to explore the functional characteristics or properties of a brain. It is able to assist neuroscientists to get valuable insights into different neurological disorders (Martin et al., 2016). A human brain can be understood as a complex system with various regions performing different functions. Although, some structural regions may not be connected locally, they are integrated globally to process different types of information. fMRI measuring the changes of blood oxygen level-dependent (BOLD) signal in a non-invasive way has been applied to reveal regional associations or brain networks. In 1995, Biswal et al. (1995) discovered that various brain regions still actively interact with each other while a subject was at rest (not in any cognitive task). Since then, resting-state fMRI (rs-fMRI) has become an important tool for investigating brain networks of different brain disorders such as Alzheimer's disease (Chase, 2014), schizophrenia (Lynall et al., 2010), and ASD (Monk et al., 2009) and has generated many invaluable insights into neural substrates that underlie brain disorders.

Previous ASD studies based on rs-fMRI images have examined anatomical and functional abnormalities associated with ASD from cohorts at different age levels, e.g., for the adolescence cohort (10–19 years approximately; Assaf et al., 2010; Keown et al., 2013; Starck et al., 2013; Bos et al., 2014; Chen S. et al., 2015; Doyle-Thomas et al., 2015; Iidaka, 2015; Jann et al., 2015), for the adult cohort (≥20 years) (Cherkassky et al., 2006; Monk et al., 2009; Tyszka et al., 2013; Itahashi et al., 2014, 2015; Chen C. P. et al., 2015; Jung et al., 2015), and for the cohort covered all age levels (Alaerts et al., 2015; Cerliani et al., 2015). The results helped clarify the relevant neurological foundations of ASD in different age levels. Extant literature suggests that the basic organization of functional networks is similar across all age levels. However, the levels of connectivity and modulation appear altered in ASD. The results suggested that both hypo- and hyper-connectivity occurred in ASD relative to typical developed (TD) controls. By studying an adult cohort, Monk et al. (2009) found that poorer social functioning in the ASD group was correlated with hypo-connectivity between the posterior cingulate cortex and the superior frontal gyrus, and more severe restricted and repetitive behaviors in ASD were correlated with stronger connectivity between the posterior cingulate cortex and right parahippocampal gyrus. These findings indicated that ASD adults showed altered intrinsic connectivity within the default network, and connectivity between these structures is associated with specific ASD symptoms. Assaf et al. (2010) discovered that compared to adolescent controls, adolescent ASD patients showed decreased functional connectivities (FCs) between the precuneus and medial prefrontal cortex/anterior cingulate cortex, DMN core areas, and other default mode sub-network areas. The magnitude of FCs in these regions inversely correlated with the severity of patients' social and communication deficits. Keown et al. (2013) found that local FCs were atypically increased in adolescents with ASD in temporal-occipital regions bilaterally by applying rs-fMRI and a graph model. Hyper-connectivity in the posterior brain regions was found to be associated with higher ASD symptom severity. Supekar et al. (2013) claimed that hyper-connectivity of short range connections in ASD was observed at the whole-brain and subsystems levels. It demonstrated that at earlier ages, the brains of children with ASD are largely functionally hyper-connected in ways that contribute to social dysfunction. Above finding are spread in different brain networks including cingulo-opercular (CO), default-mode (DM), cerebellum (CB), and frontal-parietal (FP).

The above findings indicated that aberrant ASD-associated FCs were widely distributed throughout the entire brain, as opposed to showing a restricted pattern within only a few specific brain regions. Thus, in this research, we developed the machine learning model to explore ASD-related FCs from the whole-brain FC pattern (FCP) which is a set of FCs including each FC between every pair of pre-defined brain regions. The method was tested on the dataset from an adolescent cohort.

Machine learning algorithms have been successfully employed in the automated classification of altered FC patterns related to ASD based on rs-fMRI images (Uddin et al., 2013). For example, Yahata et al. (2016) developed a classifier achieves high accuracy (85%) for a Japanese discovery cohort and demonstrates a remarkable degree of generalization (75% accuracy) for two independent validation cohorts in the USA and Japan. Models developed by Deshpande et al. (2013) and Nielsen et al. (2013) achieved 95.9 and 60% accuracy on a self-collected dataset and the autism brain imaging data exchange I (ABIDE I) dataset, respectively.

As an important machine learning tool, deep learning has been widely applied in various research areas (Krizhevsky et al., 2012; Graves et al., 2013). Stacking several auto-encoders (AEs) or restricted Boltzmann machine (RBMs) is a common way of building a DNN. The DNN architecture is able to improve the feature learning capacity by exploring latent or hidden low-dimensional representations which are inherent in high-dimensional raw data. With such representations, the classification model performance can be enhanced effectively. The DNN is widely used in neuroimaging studies (Brosch et al., 2013; Suk et al., 2014; Kim et al., 2016). Hjelm et al. (2014) demonstrated that the DNN constructed by stacking RBMs extracted better spatial and temporal information from fMRI data compared with ICA and PCA algorithms. Suk et al. (2015) stacked several AEs to build the DNN which was applied in a task of discriminating AD patients from mild cognitive impairment patients, and obtained the accuracy of 83.7% on the ADNI dataset. Plis et al. (2013) conducted a validation study on structural and functional neuroimaging data to show that a stacked RBMs can learn physiologically important representations and detect latent relations in neuroimaging data. Although, the DNN obtained many competitive results, its feature learning capacity is still able to be improved. Recently, researchers have tried using multiple AEs to learn better representations of the data. Zhu et al. (2014) developed a DNN-based framework to learn multi-channel deep feature representations for the face recognition task. In their design, multiple deep learning networks are applied to extract representations of different parts of the face, e.g., eyes, nose and mouth, and the combined representations used to train a classification model. Similar studies can be found in literature (Hong et al., 2015; Zhao et al., 2015). Inspired by ideas in above papers, a novel feature selection method based on multiple SAEs was proposed. Different from above studies, we constructed one SAE with high feature learning capacity by selecting features from multiple trained SAEs instead of just stacking multiple SAEs together to form several DNNs.

In this study, a DNN-based classification model has been developed for distinguishing ASD patients from TD controls based on the whole-brain FCP of each subject. The DNN model consists of the stacked SAEs for data dimension reduction, and a softmax regression (SR) on the top of the stacked SAEs for the classification. Moreover, a novel feature selection method based on multiple trained sparse auto-encoders (SAEs) has been developed. It can initialize weights between the first hidden layer and the input layer (the first feature layer) of the DNN by selecting a set of dissimilar features with high discriminative power from multiple trained SAEs. In this study, the first objective is to enhance the performance of the DNN for classifying ASD patients and TD controls by applying a novel feature selection method. The DNN-FS (3/150 hidden layers/nodes) obtained the best classification accuracy of 86.36%. Most importantly, it outperformed the DNN-woFS for each comparison scenario. The most significant improvement, of 9.09%, occurred when the architecture had three hidden layers with 150 nodes each. Meanwhile, by comparing the average discriminating power of the same layer in both DNN-FS and DNN-woFS, we found that the discriminating ability of any layer in DNN-FS is higher than the discriminating ability of the corresponding layer in DNN-woFS. In addition, using two other feature selection methods—a two-sample t-test and an elastic net—results showed that the proposed method (86.82%) outperformed both the other methods (two-sample t-test: 70.67%, elastic net: 79.54%). The second objective is to identify abnormal FCs related to ASD. To achieve the goal, a DNN-based biomarker identification method was developed to locate 32 FCs associated with ASD. Generally, the findings supported the points of view in literature that (1) both hyper- and hypo-connectivity exist in certain brain networks (e.g., DM) of the ASD patients; (2) abnormal between-network connectivity exists in ASD patients. More explanation is given in the Discussion section. For readers' convenience, the abbreviations of terminologies used in the following sections are listed in Table 1.

In the present study, a DNN model with a novel feature selection method was developed for classifying ASD patients and TD controls based on the whole-brain FCPs. The first contribution of this work is the proposed feature selection method based on multiple trained SAEs to improve the quality of low-dimension representations learned from stacked SAEs. The proposed method (DNN-FS) was able to select diverse features with high discriminating power from a large feature pool consisting of all features from multiple trained SAEs, and these selected features, in turn, led to better classification of ASD patients and TD controls compared to the performance of DNN-woFS, and models with other feature selection methods (two sample t-test and elastic net). To test the efficacy of the method, both DNN-FS and DNN-woFS systems were trained and evaluated by the five-fold nested CV scheme under different comparison scenarios. Both models had the same architecture (the same number of hidden layers/nodes) in each scenario, and different scenarios used different architectures. The DNN-FS (3/150 hidden layers/nodes) obtained the best classification accuracy of 86.36%. Most importantly, the DNN-FS outperformed the DNN-woFS for each comparison scenario. The most significant improvement, of 9.09%, occurred when the architecture contained three hidden layers with 150 nodes each. Among many ASD diagnosis models, Deshpande et al. (2013) developed a recursive cluster elimination based support vector machine classifier using effective connectivity weights, behavior assessment scores, FC, and fractional anisotropy obtained from DTI data. The model achieved a maximum classification accuracy of 95.9%. Unlike the work presented here, they combined analysis of multiple types of data. The feature selection part of the model was thus able to extract and integrate discriminating features from heterogeneous data, which potentially enhanced classification accuracy. In addition, the number of ROIs (18) defined in their model was small, which kept their input data dimension a reasonable size compared to the sample size (30 adolescents and young adults), and inhibited overfitting. However, this method still needs to be validated on a larger dataset. Nielsen et al. (2013) developed a classification model to perform ASD classification, but only achieved up to 60% accuracy. They collected data from multiple sites of ABIDE I, and different sites had different imaging protocols and quality control protocols. Training the model with a large dataset was the most likely reason for obtaining the low accuracy. In addition, the lower heterogeneity of the large dataset might be another reason for the low accuracy. Compared to the dataset (964) they used, the present study used a smaller dataset from one site of ABIDE I, so the data quality is expected to be higher. To avoid overfitting of the DNN model, a nested cross validation evaluation scheme was applied. The effectiveness of the proposed feature selection method was also compared with others feature selection methods: two sample t-test and elastic net. Results showed that the classification model trained by representations from the stacked SAEs outperformed the models trained by features from other two methods. A comparison of the average Fisher's score of features in each layer in the DNN-FS and DNN-woFS also showed that discriminative power increased layer-wise in both DNN-FS and DNN-woFS, with higher layers providing more discrimination.

The second contribution of this work is a DNN-based biomarker identification method to locate 32 FCs associated with ASD, and exploration of the biological implications of the findings. Among these 32 FC elements, 13 were within pre-defined brain networks including CO, DM, CB and FP, and 19 were between-network FCs. 13 FCs were statistically significant (p < 0.05) between ASD and TD groups. Five significant FCs (1, 17, 23, 30, and 32 in Table 6) were associated with the insula. The previous study showed that this area was involved in interoceptive, affective, and empathic processes. Network analysis indicated that it was uniquely positioned as a hub mediating interactions between large-scale networks involved in externally- and internally-oriented cognitive processing, and it was a consistent locus of hypo- and hyper- activity in autism (Uddin and Menon, 2009). Menon and Uddin (2010) have hypothesized that impaired hub function of the anterior insula would reduce the ability of people with ASD to flexibly move from the executive control networks to the default mode. In the findings, one FC (1 in Table 6) was within-network (CO), and four FCs were between-network (one CO and CB, two DM and CO, one CO and CP). The results indicated that both hyper- and hypo-connectivities associated with the insula were existed within certain network or between networks, which can back up the point view in literature. Four significant FCs (4, 11, 15, and 31 in Table 6) were detected associated with the cingulate cortex. The right posterior cingulum were strongly correlated with the superior parietal gyrus, and were weakly correlated with the superior frontal gyrus in the ASD group. The left anterior cingulum was weakly correlated with the right pars triangularis, and the left middle cingulum was strongly correlated with the left pars orbitalis in the ASD group. The connections of the cingulate cortex to other brain structures are extensive, and thus the functions of the region are varied and complex. It makes important contributions to emotion, and various types of cognition such as the decision-making and the management of social behavior (Ikuta et al., 2014). The findings can help people to explore the neurological basis associated with abnormal symptoms in emotion and cognition. Meanwhile, another four ASD-related significant FCs were identified: LITG was strongly connected to LSPL (7 in Table 6), RSFG was weakly connected with RITG (14 in Table 6), LPT was strongly connected RP (19 in Table 6), and LCCB was strongly connected to LSPL (21 in Table 6). Brain areas associated with these FCs are involved in different brain functions such as spatial orientation (LSPL), visual shape processing (LITG&RITG), self-awareness (RSFG), and motor skills (LPT; Frackowiak, 2004; Lee et al., 2007). The dysfunctionality of certain brain areas might lead to such abnormal FCs in autistic children. However, the mechanism is unclear, and needed to be explored in the future. Other than above findings, 19 FCs which were not statistical significant were detected by the method too. They are not, respectively, discriminating may be because the sample size was not large enough to build the significant statistical power for each of them. However, they should be important in the classification task because all FCs made contribution during the learning process, and the model performance is supposed to be decreased if any of them is missing.

In the future, we are going to extend the current research in two aspects. First of all, the proposed method will be tested on datasets from cohorts in different age groups. Age is an important factor in the ASD diagnosis. ASD biomarkers may be altered due to the age difference. It is especially meaningful to make a convincing prediction before children develop ASD symptoms at their early age. Hazlett et al. (2017) demonstrated that they can make reasonably accurate forecast about which of these high-risk infants will later develop ASD themselves by examining the growth rate of brain volume of infants between 6 and 24 months based on anatomical brain images. The finding motivates us to evaluate the proposed method on a dataset from early-age children. NDAR (Hall et al., 2012) is an NIH-funded research data repository that aims to accelerate progress in ASD research, and it contains neuroimaging datasets from cohorts in different age groups. We plan to validate the generalization of the method on multiple NDAR datasets from infants, adolescents, and adults. We are optimistic about the model classification performance. No matter what the age group the dataset belongs to, the strength difference of certain FCs should exist between ASD patients and the age-matched TD controls. The DNN-FS can not only capture the discriminating FCs but also can learn high-quality discriminating features from the whole-brain FCP to enhance the classification accuracy of the SR model. However, the identified ASD-related FCs may be altered in different age groups. So it is necessary to work with neuroscientists closely to explore the neurological basis of identified FCs in each age groups.

Second of all, more systematic methods will be developed to decide the size of the feature pool for the proposed feature selection method, and to determine how the size affects the final performance. In addition, we will continue to explore the way of deciding the architecture (No. of layers/No. of nodes per layer) of the DNN-FS. It was found that the performance of the DNN-FS did not increase by adding more hidden layer nodes when the number of hidden layers was fixed. The most plausible explanation is that additional hidden layer nodes may learn many redundant features, which decreases the feature learning capacity of the stacked SAEs and further reduces classification accuracy. It was also found that the performance of the DNN-FS cannot be increased simply by adding more hidden layers when the number of hidden layer nodes is fixed. The most reasonable explanation is that the gradients vanish quickly in lower layers when the DNN has a very deep architecture, and even the pre-training step is not able to help much. Both these issues will be studied further as part of future research to obtain optimal DNN-FSs for classifying ASD patients and TD controls.

The Autism data used in this research was acquired through the public ABIDE I database through a data use agreement. The Autism database has de-identified all the patient health information (PHI) associated with the data. The original study to collect patients data was approved by IRB at University of Michigan. The potential risks of this project are limited to the unauthorized usage of the Autism data. To mitigate the potential risk, we will take the utmost care to ensure that there is no abuse of protected information.

XG, LL, and AM conceived the project idea. XG implemented the method and performed the experiments. LL supervised the project. AM supervised the development of the feature selection method. KD and CE provided the detailed analysis of brain FCs discovered by the method. HL provided critical suggestions for the experiments design.