1. Introduction

Autism spectrum disorder (ASD) is a common and well-known neurodevelopmental multi-factorial brain disorder. Recent tests ^[1] estimate that at least 1% of children are affected by ASD. Autistic people may experience serious difficulties with cognitive development, communication, and motor functions. ASD is usually diagnosed by behavioral tests ^[2]. The accuracy of these tests is influenced by the examiners’ experience, access to side information, and the test’s periodicity. Recently, some researchers have focused on developing an automatic diagnostic techniques based on artificial intelligence that is free from human errors and dependence on side information.

Recent advancements in magnetic resonance imaging (MRI) provide an opportunity for researchers to design automatic diagnostic tools for ASD. ASD diagnosis based on MRI is non-invasive, free from human error, and can be processed at any time suitable for doctors and patients. Data extracted from the MRI of ASD patients can be analyzed to highlight brain regions with higher significance for ASD. Precise analysis of such brain regions may lead to better understanding of the nature of ASD and support ASD research.

ASD has been tested by using functional MRI (fMRI) and structural MRI (sMRI). Functional MRI is a set of time-series brain scans that can highlight time-dependent neurological abnormalities. fMRI is usually used when researchers study brain responses to different inputs such as sounds, visual information, or both. sMRI is a set of brain scans with fixed time. The spatial resolution of sMRI is much higher than that of fMRI and may give more relevant data for accurate analysis.

Researchers generally rely on sMRI when searching for neurological abnormalities caused by ASD. Such abnormalities are microscopic and usually very hard to define by visual or statistical analysis. Hence, a more efficient method for searching for neurological abnormalities connected to ASD in sMRI is needed.

The Autism Brain Imaging Data Exchange (ABIDE) database ^[3] is widely used for ASD research. The ABIDE database unifies structural and fMRI and other important data collected from many institutions worldwide. In this paper, we propose an efficient diagnostic tool for accurate classification of ASD patients versus healthy controls. A set of 1054 ASD patients and healthy controls from the ABIDE database was used for the experiments. For the proposed ASD diagnostic tool, a set of voxels extracted from the whole brain of each subject was processed by voxel-based morphometry (VBM) ^[4], and a reduced set of relevant features was extracted. Extensive experiments with the extracted VBM features indicated that the VBM feature set is still redundant, and further reduction is possible.

A tailored binary coded genetic algorithm (tBCGA) is proposed to search for an optimal subset of features, which can significantly improve the efficiency of the proposed ASD diagnosis tool. The selected optimal set of VBM features was used to build an extreme learning machine (ELM) classifier. Experiments with the proposed ASD diagnostic tool based on the tBCGA show promising results.

2. Related Work

Researchers have studied sMRI and reported about abnormalities in the gray matter of many brain regions, such as the temporal sulcus ^[5], orbito-frontal cortex ^[6], fusiform gyrus ^[7], middle frontal gyrus ^[8], and the inferior parietal lobule ^[9]. Deep brain analysis is extremely difficult because often, children’s brains are still developing, and brain segmentation may not be always possible. To resolve a problem, researchers may analyze the whole brain scan ^[10,11]. A whole brain analysis involves large amount of information. Hence, a new method for efficiently analyzing data extracted from the whole brain is needed.

A whole brain analysis of using MRI starts with extracting data from volumes of gray or white matter in different physical locations of the brain called voxels. The number of voxels extracted from the whole brain can be huge (~100k) ^[10,11]. The number of relevant voxels for ASD can be significantly decreased by special methods like VBM or region-of-interest (ROI) methods. VBM ^[4] can automatically separate statistically important voxels for the classification of ASD versus healthy controls. In this paper, the VBM reduced the number of extracted voxels from ~40,000 to ~1000, which makes analysis faster and simpler.

It has been reported that ASD affects the brain regions of males and females differently ^[10]. According to recent data, people diagnosed with ASD are roughly 90% male and 10% female. Nowadays, it is common for researchers to do a separate analysis for males and females, which significantly increases the accuracy of ASD analysis.

Automatic ASD diagnostic tools based on various machine learning techniques and features extracted from MRI are presented in the literature ^{[13-15, 18,19]}. Vigneshwaran et al. ^[13] proposed an efficient meta-cognitive radial based function method to build a classifier for ASD diagnosis. Their used a reduced set of samples from ABIDE and VBM features. Authors reported 78% overall testing accuracy. A reduced set of samples from the ABIDE database was processed separately for a male and a female, and higher classification accuracy was achieved ^[14,15]. The widely used support vector machine and separate male/female databases were used to build an ASD classifier ^[14,15]. A deep learning model was used to build an efficient ASD classifier based on samples from the ABIDE database ^[18]. The authors reported an overall accuracy of around 79%. Other authors utilized fMRI and time series data to build an automatic ASD with 80% accuracy ^[19].

3. ABIDE Database

The ABIDE ^[3] collected sMRI and fMRI scans from 508 ASD patients and 546 healthy controls totaling 154 females and 900 males. All available samples were divided into 6 groups: ``all females'' (59 ASD and 95 healthy controls), ``adolescent females under age 18'' (44 ASD and 72 healthy controls), ``adult females age 18 or over'' (15 ASD and 23 healthy controls), ``all males'' (449 ASD and 451 healthy controls), ``adolescent males under age 18'' (308 ASD and 292 healthy controls), and ``adult males age 18 or over'' (141 ASD and 159 healthy controls). All available MRIs from the 1054 subjects in the ABIDE database were processed by VBM to extract 989 features.

Voxel Based Morphometry

VBM ^[4] is an automatic tool for the analysis of MRI scans in neurological research. VBM was used to identify statistically important differences in between the white or gray matter of ASD patients and healthy controls. VBM has three major steps: segmentation, smoothing, and statistical analysis. Segmentation in VBM detects tissue, processes classification, corrects bias, and segments images. In the smoothing step, segmented images are processed by a 10-mm full-width half-maximum isotopic Gaussian filter. Finally, voxels with the maximum differences in between ASD patients and healthy controls are identified. A set of 989 features extracted by VBM from the 508 ASD patients and 546 healthy controls was used for further analysis.

4. The Proposed Automatic Autism Diagnostic Tool

The proposed ASD diagnostic tool contains 3 major steps: the VBM, tBCGA, and automatic autism diagnostic tool (see Fig. 1). In the first step, all available ABIDE samples are processed by VBM, and a set of 989 VBM features for each sample is extracted. In the second step, the tBCGA selects an optimum subset of significant VBM features for ASD. In the third step, the optimum VBM features selected by the tBCGA are used to train an ELM model for ASD-patient and healthy-person classification.

Fig. 1. Framework of the proposed automatic autism diagnostic tool.

4.1 Tailored Binary Coded Genetic Algorithm

The presented tBCGA is a modification of a famous genetic algorithm specifically designed for efficient search of the optimum subset of VBM features in the proposed automatic autism diagnostic tool. The genetic algorithm is widely used for solving extremely complex optimization problems in industrial and scientific applications. In general, the genetic algorithm is a heuristic optimization tool that utilizes powerful gene adaptation mechanisms from nature. In the first and most challenging step, the optimization problem is translated into a set of meaningful chromosomes. This combination of chromosomes forms a solution of the genetic algorithm. Each solution may or may not describe the given optimization problem’s characteristics well. Each solution is numerically evaluated by using a fitness function. It iteratively updates chromosomes, forms solutions, and calculates fitness. In this way, it may find a solution with high fitness, which can be a pseudo-optimum solution for the examined optimization problem.

The performance can be affected by many factors. The examined problem must be converted into a set of the chromosomes correctly. Incorrect transformation may cause significant performance loss. A basic and systematic way of updating chromosomes given by genetic algorithm operators must be carefully chosen based on the characteristics of the problem, and the parameters must be properly adjusted. Incorrect choice of operators leads to poor convergence of the optimization process.

In the proposed tBCGA, each solution is a vector of 989 binary coefficients, where each coefficient defines the status of a corresponding VBM feature. A binary coefficient of 1 implies that the corresponding VBM feature is selected, and a binary coefficient of 0 implies that the corresponding feature is skipped. Thus, the proposed solution forms a set of features for further analysis.

Fig. 2. Framework of the proposed Tbcga.

The framework of the proposed tBCGA is presented in Fig. 2. It starts from creating an initial population of 100 binary vectors $\mathrm{F}^{0}$, which are generated randomly by placing 50-200 binary 1 values in random locations. Each binary vector $\mathrm{F}_{\mathrm{i}}^{0}$ forms a set of VBM features, which is used to train an ELM classifier. Each binary vector $\mathrm{F}_{\mathrm{i}}^{0}$ is evaluated by fitness value $\mathrm{f}_{\mathrm{i}}^{0}$, which is the overall training accuracy of the ELM classifier. Finally, the union of 100 binary vectors $\mathrm{F}_{\mathrm{i}}^{0}$ and corresponding fitness values $\mathrm{f}_{\mathrm{i}}^{0}$ forms the initial population $(\mathrm{F}_{\mathrm{i}}^{0};\mathrm{f}_{\mathrm{i}}^{0}),\,\,i=1,\ldots ,100$. The proposed method iteratively updates populations until a termination criteria is triggered. Each iteration (see Fig. 2) consists of 3 main operations:

· Selection

· Statistical selective crossover and mutation

· Fitness

The proposed tBCGA settings are a population size n of 100, crossover/mutation rate of 0.8, and a termination criterion that stops the process if there is no fitness improvement for the last 10 populations. After extensive experiments, we found that it stops in around 50 populations. The final ASD diagnostic tool was created from the generated ELM classifier with the best fitness value (or overall training accuracy).

Selection

In the genetic algorithm framework, the selection procedure determines the chance for each solution from population n-1 to contribute to the next population n. The selection procedure computes the probabilities for each solution in the population based on corresponding fitness values such that solutions with a lower fitness value have lower probability to be selected, and vice versa. Solutions with a low fitness value have a small but non-zero chance to contribute to the next generation, whereas solutions with high fitness have a significant chance to contribute to the next generation. The selection procedure is one of the basic evolutionary processes in nature, where individuals with better survival skills have a higher chance to reproduce.

The geometric ranking method ^[18] was used as a selection procedure in this paper. The geometric ranking method sorts solutions in descending order based on fitness values and computes selection probability as follows:

(1)

$ \mathrm{P}_{\mathrm{j}}=\mathrm{q}'\left(1-\mathrm{q}\right)^{{\mathrm{r}_{\mathrm{j}}}-1} $

where

$ \mathrm{q}'=\frac{\mathrm{q}}{1-\left(1-\mathrm{q}\right)^{\mathrm{n}}} $

$\mathrm{q}'$ is a normalization factor, $\mathrm{r}_{\mathrm{j}}$ is the rank of the j-th solution in the sorted set, n is the population size, and q is $10^{-3}$.

Proposed statistical selective crossover and mutation

Crossover and mutation play a vital role in the genetic algorithm. Crossover is a basic gene exchange procedure in nature that increases the diversity of individuals. Crossover randomly mixes genes of two individuals to produce a child. If this gene mixture produces individuals that have higher chances to survive and reproduce, then it can increase the average resistance against harsh environments found in nature.

The genetic algorithm’s crossover process mimics that of nature. A crossover picks genes from two parents (or two solutions from the population) and creates one child solution, which may have better characteristics. The design of crossover must maximize the ability of gene exchange to achieve higher fitness. Each new solution generated by crossover should maximize the effect of positive characteristics and neglect negative characteristics of parents, to increase fitness value. The design of crossover defines the efficiency. In this paper, a statistical selective crossover (see Fig. 3) was designed specifically for the proposed tBCGA.

Fig. 3. Proposed statistical selective crossover.

The proposed statistical selective crossover uses two solutions selected by the selection procedure and uses binary vectors, $F_{1}$ and $\mathrm{F}_{2}$, to build a new binary vector $F_{\mathrm{new}}$. The statistical selective crossover is designed to balance the number of binary 1 values, which are the selected VBM features for further analysis, between populations. In the first step, the statistical selective crossover defines all coefficients as 1 in $F_{1}$ and$F_{2}$. In Fig. 3, $~ I_{1}$ = (1,2,4,5,7,8,11) and $I_{2}$ = (2,4,5,6,9,10). In the second step, all positions of 1 are unified together as $I=~ I_{1}\cup I_{2}$= (1,2,2,4,4,5,5,6,7,8,9,10,11). In the third step, a random binary vector $R=\left(0,1,0,1,1,0,1,0,1,1,0,0,1\right)$ is generated, with size equal to the length of the unified set$I$. A subset of I is created by selecting only indices with a corresponding binary 1 in R, explicitly $I_{new}^{*}$ = (2,4,4,6,7,8,11) in the example above. A new set $I_{\mathrm{new}}$ = (2,4,6,7,8,11) is created by removing duplicates from $I_{new}^{*}$. A new binary vector $F_{\mathrm{new}}$ is created by placing binary 1 into the positions listed in $I_{\mathrm{new}}$.

Mutation is another basic gene alteration procedure in nature and is as important as crossover. Mutation randomly modifies genes, which may lead to positive or negative change in characteristics. A significant portion of mutations causes minimal positive or negative change. With small probability, mutations may cause a massive and deadly change in the genome. In the opposite scenario, mutations may significantly improve the genome, giving individuals new characteristics, which could not be produced via crossover. Crossover only mixes genes available in past populations, so it is limited in how it can modify current characteristics and cannot create completely novel genes not present in older populations. The proposed mutation operator creates a new binary vector F, where 50-200 coefficients of 1 are randomly allocated. A set of n binary vectors F generated by mutation is the initial population (see Fig. 2).

4.2 Fitness

In the proposed tBCGA, the fitness step generates a new solution and computes its fitness. In the first step, the fitness procedure uses a statistical selective crossover twice and generates two new binary vectors $\mathrm{F}_{\mathrm{new}}^{1}$ and $\mathrm{F}_{\mathrm{new}}^{2}$. In the second step, feature set #1 and set #2 are created from autism VBM features by using binary vectors $\mathrm{F}_{\mathrm{new}}^{1}$ and $\mathrm{F}_{\mathrm{new}}^{2}$, as displayed in Fig. 4. Feature set #1 and set #2 are used to build two ELM classifiers. A binary vector $\mathrm{F}_{new}$ ($\mathrm{F}_{\mathrm{new}}^{1}$ or $\mathrm{F}_{\mathrm{new}}^{2}$) that creates an ELM classifier with higher training accuracy (or fitness value f) is added to the new population. The detailed framework of the fitness procedure is presented in Fig. 4.

Fig. 4. Fitness calculation.

5. Performance Evaluation

The ASD data have been intensively tested according to the recent recommendations from the scientific community. All available ASD patients were divided into a few groups: adults, children, males, and females. In was proven that segmentation of children’s developing brains is not always the same as adults, and direct comparison in not possible. To avoid this problem, researchers divide experiments into adolescent ASD patients and adult ASD patients. According to recent reports, ASD also affects male and female brains differently. Thus, experiments for males and females must be separate.

The experiments with ASD involve 6 possible combinations of ASD groups of males, females, adolescents under age 18, and adults over 18. The groups for experiments are presented below:

Group 1) All females. 154 patients: 59 ASD and 95 healthy controls.

Group 2) Adolescent females (age < 18). 116 patients: 44 ASD and 72 healthy controls.

Group 3) Adult females (age ${\geq}$ 18). 38 patients: 15 ASD and 23 healthy controls.

Group 4) All males. 900 patients: 449 ASD and 451 healthy controls.

Group 5) Adolescent males (age < 18). 600 patients: 308 ASD and 292 healthy controls.

Group 6) Adult males (age ${\geq}$ 18). 300 patients: 141 ASD and 159 healthy controls.

Experiment results are presented in Table 1. The proposed automatic autism diagnosis tool based on tBCGA has been used to train the best classifier using the data available for each group. For fair comparison with previous research, we chose a method presented by Vigneshwaran et al. ^[15] that used exactly the same group of ASD patients and VBM features. The tool proposed here outperforms the previous method in all 6 scenarios. In groups 1-6, the proposed method improves upon the previous method by 1%, 1%, 1%, 3%, 3%, and 1.6%, respectively, in terms of overall testing accuracy.

Vigneshwaran et al. ^[15] did experiments with female data differently. To boost classification accuracy, the VBM method was modified, and a set of voxels for group 1 (all females) was reduced to 66 features only from the original total of 989 features, group 2 was reduced to 104 features, and group 3 was reduced to 43 features. In comparison, the tBCGA proposed here needs a large set of features for further reduction.

If the initial set of features is already reduced, the efficiency of tBCGA is limited. Thus, for groups 1, 2, and 3, a full set of 989 VBM features was used. The proposed method reduced the feature space from 989 to 68, 88, and 39 features for groups 1, 2, and 3, respectively, and achieved better overall testing accuracy compared to the other method ^[15]. Similar feature space reduction was done for groups 4-6, and the reduced sets of 64, 132, and 177 VBM features were selected by tBCGA.

Comparison with other methods

The ABIDE database has been used to develop various automatic ASD diagnostic tools by using different machine learning techniques. A meta-cognitive radial based function classifier was used for classifying ASD and healthy controls ^[13]. The classification problem was simplified by reducing the set of samples from the ABIDE database. Significant improvement was achieved after separating male and female patients into two groups ^[14]. Extracted VBM features were used to build a support vector machine classifier. In papers which used a reduced set of samples for training and testing a direct comparison is not possible ^[13-15].

In the method presented by Epalle ^[18], samples were not divided into 6 groups, so a direct comparison is not possible. The tBCGA method proposed in this paper has an overall testing accuracy of 78.1% for the combined set of all examined samples.

6. Conclusion

In this paper, we proposed an automatic autism diagnostic tool based on tBCGA for efficient classification of ASD patients and healthy controls. The proposed tBCGA searches for an optimal subset of VBM features extracted from the ABIDE database within 6 examined scenarios. A statistical selective crossover was introduced, which was used in the tBCGA to increase the efficiency of the optimization process. A reduced set of VBM features selected by tBCGA was used to train an ELM with high classification accuracy. In the near future, the proposed approach can also be applied for other neurodevelopmental disorders.