Autism Classification and Identification of Significant Brain Lobe Using Cepstral Coefficients

Autism, a neurodevelopmental disorder, profoundly influences cognitive processing and impedes communication and social interaction. The distinct behavioral traits associated with this condition, such as social isolation, significantly impact the affected individual's quality of life. The neurological underpinnings of Autism Spectrum Disorder (ASD) were postulated through clinical case studies conducted by pioneering medical professionals Hans Asperger and Leo Kanner [1, 2]. ASD arises from a complex interplay of genetic and environmental factors. Genetic risk factors, including chromosomal abnormalities and gene deficiencies, affect an estimated 10% to 20% of individuals with ASD. The recurrence rate of ASD in siblings is estimated at 5% to 8%, indicating a higher susceptibility within ASD households [3].

Accurate prevalence estimates of ASD are indispensable for shaping public policy, raising awareness, and guiding research [3]. In the United States, the Centers for Disease Control and Prevention (CDC) established the Autism and Developmental Disabilities Monitoring (ADDM) Network to track the prevalence of ASD. This national surveillance program collects data on ASD in children, utilizing health and education records to monitor the incidence and characteristics of the disorder [4]. Similarly, in Canada, the National Autism Spectrum Disorder Surveillance System monitors children aged 5 to 17 across several provinces and territories [5].

Conventional ASD diagnoses predominantly rely on subjective caregiver questioning. Advances in brain imaging, particularly through structural Magnetic Resonance Imaging (MRI), have unveiled atypical brain structures in individuals with ASD. Functional MRI studies also highlight unusual brain activity during social cognition tasks. However, the high cost of MRI and its unsuitability for newborns have steered researchers towards Electroencephalogram (EEG) as a cost-effective and portable alternative [6]. Despite containing crucial information about brain function, EEG signals have lacked a standardized approach for analysis. Previous studies have employed anomaly detection methods such as Isolation Forest, Angle-based Outlier Detector, and Minimum Covariance Determinant models to analyze EEG patterns in autistic children [7]. The coherence between EEG channels has assessed using the NeuCube architecture [8]. The analysis focused on the strength of self-similarity in the signals, utilizing Hurst exponents derived from Detrended Fluctuation Analysis (DFA) outputs [9].

Within the area of EEG classification, techniques have automated to improve accuracy [10]. These techniques involve extract features from the time, frequency, and time-frequency domains. In this current research, the focus is on extracting cepstral domain features. In 1937, Mel was proposed as a pitch unit, and in 1963, the cepstrum was introduce by BP Bogert, MJ Healy, and JW Tukey for analyzing periodic structures in frequency spectra. Cepstral analysis, coupled with a frequency scale developed by Davis and Mermelstein in the 1980s, emerged as a potent tool for speech signal processing and natural language recognition [11]. Mel Frequency Cepstral Coefficients (MFCC), which extracts features from signals in the frequency domain, help reduce dimensionality and aid in anomaly detection in brain activity [12, 13]. MFCC offers benefits such as noise resistance and pattern identification in the frequency domain [14], and it has been successful in speech recognition and natural language processing [15-17].

Linear Frequency Cepstral Coefficients (LFCC) retains lower and higher frequency characteristics, rendering it more effective than MFCC in specific applications [18]. In this research, LFCC is utilizing to characterize the spectral envelope of EEG to improve classification between ASD and TD individuals [19]. Parameters such as Cepstral Energy and Signal energy, along with their derivatives, are incorporated to enhance the accuracy [20].

The classification of EEG signals in this research involves four classifiers: K-Nearest Neighbors (KNN), Decision Tree, Multi-Layer Perceptron (MLP), and Support Vector Machine (SVM), along with ensemble methods like Bagging and Random Forest. These techniques aim to distinguish ASD and TD children using EEG signals, demonstrating promising results.

The significant contributions of this work are as follows:

1. The proposed study aims to develop two distinct linear scale filter banks. One filter bank designed and employed to capture all frequency bands present in EEG, while the other specifically designed and used for extracting the alpha and beta frequency bands.
2. An analysis is conducted separately on all frequency bands and alpha and beta frequency bands in EEG to identify the brain region that exhibits the highest level of discrimination between individuals with ASD and those with TD.

The article has organized as follow: Section 2 provides a comprehensive review of previous experiments that utilized EEG data for the ASD and TD classification. The methodology has briefly outlined, and the model presented in Section 3. Section 4 extensively details the EEG signal classification results, which are then compared to existing machine learning models and discussed. Finally, Section 5 concludes the paper.

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These videos received recommendations from an occupational therapist affiliated with Sri Ramachandra Medical College Research Institute (SRMC-RI). EEG signal acquisition involved the placement of Ag/AgCl electrodes on the scalp using conductive gel and tapes to improve conduction. The acquisition process followed the 10-20 International Standard, encompassing EEG signals recorded from 19 channels and two earlobes at a sampling rate of 500 Hz. Electrodes were positioned over specific cortical lobes, including the frontal (Fp1, Fp2, F3, F7, F4, F8, and Fz), temporal (T3, T5, T4, and T6), occipital (O1 and O2), parietal (P3, P4, and Pz), and central (C3, C4, and Cz) areas. Subsequently, the recorded EEG signals underwent analysis using Nihon Kohden Neurofax MEB9000 version 05-81 and software tools to apply filtering and remove artifacts. The electrode polarization was overcome by using Ag/AgCl electrodes, and powerline interference, eye movement, muscle artifacts, electrode drift, cardiac activity, and environmental noise were removed. The electroencephalogram was recorded with a sensitivity of 7 μV, with low-pass and high-pass filters applied at a cut-off frequency range of 0 to 70 Hz. The stimuli presented to the children included a video, each with duration of 60 seconds. Each participant received instructions to view five videos. The concentration level of the children with ASD during the stimuli could not be observed visually, making EEG signal acquisition necessary for better insights. The diagram is presented in Figure 1. Depicts the block diagram of the proposed system.

3.2 Feature extraction

In this section, the extraction of absolute features, delta features, and delta-delta features is described in detail.

3.2.1 Absolute features

Absolute features are defined as quantitative characteristics or measures that are directly computed from the EEG data without undergoing any additional transformation. In this work, absolute features encompass features such as LFCC, cepstral energy, and signal energy, which are extracted from the EEG data.

A. Linear Frequency Cepstral Coefficients

In essence, LFCCs are representing the spectral envelope of a signal using a set of coefficients. Due to its non-linear frequency scale, de-correlated makeup, and noise resistance, this representation is frequently utilized in signal processing [31]. Signals behave as quasi-stationary in short periods; hence a small window size should be employed while analysing LFCC features frame by frame. The inverse Fourier transform is not used as the final transform in the LFCC; instead, the Discrete Cosine Transform (DCT) is used [32]. Since the resulting coefficients are real-valued, the DCT offers an advantage over the Fourier transform in terms of ease of processing and storage. The coefficients of LFCCs are the first few DCT coefficients that describe the coarse spectral structure. The average power of the spectrum is represented by the first DCT coefficient. The broad form of the spectrum is roughly represented by the second coefficient, which is connected to the spectral centroid.

A matrix of feature vectors taken from each frame is the result of employing LFCC. In this output matrix, the columns correspond to the associated feature vector coefficients, and the rows to the corresponding frame numbers. LFCC systems in this work use only seven cepstral coefficients. Finally, the categorization method uses cepstral coefficients.

LFCC extraction from EEG using following steps:

Step 1: Framing and Windowing

The EEG signal is divided into short frames in the time domain and is quickly analyzed because it is difficult to evaluate a signal at once. The signal is split into frames that contain almost stationary signal blocks before the windowing operation is applied. Results can be improved by processing data with hamming before applying FFT.

$w(n)=0.54-0.46 \cos (2 \pi n N) \quad 0 \leq n \leq N-1$                 (1)

N is the length of the window, w(n) is the window value.

Step 2: Fast Fourier Transform

To examine the various frequencies of a signal, an FFT transforms a time-domain representation of the signal into a frequency-domain representation. If a clear signal in the time domain contains cross talk, noise, or jitter, the frequency domain is excellent at revealing it. Windowing can be used to reduce the spectral leakage that results from discontinuities in the initial, non-integer number of periods of a signal. The digitizer acquires each finite sequence, and windowing decreases the amplitude of the discontinuities at the boundaries.

$X(k)=\frac{1}{N} \sum_{n=0}^{N-1} x(n) \cdot w(n) e^{-j \frac{2 \pi k n}{N}} \mathrm{n}=0,1,2, \ldots, \mathrm{N}$                   (2)

x(n) is the windowed signal and N is the size of the domain.

Step 3: Design an Optimized Linear Scale Filter Bank for EEG Signal

The initial filter bank will commence at position one, attain its peak at position two, and subsequently recede to zero at position three. The succeeding filter bank will start at position two, achieve its maximum at position three, reduce to zero at position four, and so on. The subsequent Eq. (3) outlines the procedure for determining these values:

$H_i(k)=\left\{\begin{array}{cc}0 & k<f_{b_i-1} \\ \frac{\left(k-f_{b_i-1}\right)}{\left(f_{b_i}-f_{b_i-1}\right)} & f_{b_i-1} \leq k \leq f_{b_i} \\ \frac{\left(f_{b_i+1}-k\right)}{f_{b_i+1}-f_{b_i}} & f_{b_i} \leq k \leq f_{b_i+1} \\ 0 & k>f_{b_i-1}\end{array}\right.$                       (3)

where, the index i represents the filter number, with $f_{b_i}$ indicating the filter boundaries, which are expressed as positions determined by the sampling frequency used. Similarly, the index k pertains to the coefficients of the N-point FFT. Figure 2 depicts the linear filter bank with different frequencies.

Step 4: Log

The log energy of each filter of the linear filter bank is computed using Eq. (4)

$x_i=\ln \left(\sum_{i=0}^{N-1}|X(k)|^2 H_i(k)\right) \quad 0 \leq i \leq M$                     (4)

$H_i(k)$ is the transfer function of $i^{th}$ filter.

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Figure 2. Illustrate the Linear-filter bank (a) Filter bank consists of 70 filters for frequency range of 0-70 Hz (b) Filter bank consists of 22 filters for frequency range of 8 to 30Hz

Step 5: Discrete Cosine Transform

For the given frame analysis, the Cepstral representation of the EEG spectrum provides a comprehensive depiction of the signal's local spectral characteristics. Using the DCT, transform the linear spectrum coefficients (and consequently their logarithm) to a domain that resembles time, known as the quefrency domain. These features are referred to as the linear scale cepstral coefficients.

$X_k=\sum_{n=0}^{N-1} x_i \cos \left[\frac{\pi}{N}\left(n+\frac{1}{2}\right) k\right]$                      (5)

B. Cepstral energy

The cepstral energy is computed by the sum of squares of the cepstral coefficients. The following equation is used to calculate the cepstral energy:

$E_C=\sum_{k=0}^{N-1}|C(k)|^2$                     (6)

This type of energy is frequently employed in speech recognition systems because it offers a smoother, more reliable estimate of the energy that takes advantage of the cepstral representation of the signal [33].

C. Signal energy

The input EEG signal energy is computed by the sum of squares of the input signal [34]. The following equation is used to calculate the Signal energy:

$E=\sum_{n=0}^{N-1}|X(n)|^2$                       (7)

3.2.2 Deltas and delta-deltas features

Delta features are calculated by taking the first-order difference of consecutive absolute features. They provide information about the rate of change or slope of the absolute features over time and can be useful in capturing trends or dynamics in the data.

Delta-delta features are obtained by taking the first-order difference of consecutive delta features. These features provide information about the acceleration or change in the rate of change of the absolute features and can help capture higher-order changes or patterns in the data. Both Features are utilized to analyze the temporal dynamics of a frame [35]. The following equation is used to calculate the delta coefficients:

$d_t=\frac{\sum_{n=1}^N n\left(c_{t+n}-c_{t-n}\right)}{2 \sum_{n=1}^N n^2}$                      (8)

where, $d_t$ is a delta coefficient, derived from frame t and calculated using static coefficients $c_{t+n}$ to $c_{t-n}$. The usual value of N is 2. The same formula is used to produce Delta-Delta (Acceleration) coefficients, however this time; deltas are used instead of static coefficients [36].

Since LFCCs frequently only include data from a single window, these cepstral coefficients are regarded as static characteristics. Calculating cepstral energy, signal energy, and first and second derivatives also referred to as delta and delta-delta derivative coefficients will provide insight into the temporal dynamics of cepstral coefficients [37]. The feature vector used in this research work has a length of 27, and it contains nine absolute features, including seven Linear Frequency Cepstral Coefficients, one cepstral energy, and one signal energy. To account for those absolute properties, nine deltas are introduced. There are added nine delta-deltas. End up with 27 features (27 features/frame ×120 frame/channel × 19 channels) for each audio-video stimuli of each ASD and TD child. Figure 3. depicts the total number of EEG features extracted.

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Figure 3. Illustrates the feature extraction (a) The total number of features extracted from all channels; (b) The number of features extracted from each frame

3.3 Classifiers

The methodology consisted of two phases. In the first stage, the classification utilized the training data to build a model by establishing the correlation between the extracted features and their associated labels. Subsequently, in the second phase, the trained classification model was evaluated using new, untrained features, and the labels of the new features set were compared with the real labels to determine the accuracy of the classification algorithm. This work employed various machine learning algorithms, including KNN, MLP, SVM, Decision Tree, and ensemble classifiers such as bagging and Random forest. The particulars of the algorithms are explicated in the subsequent subsections.

3.3.1 K-Nearest neighbors

The KNN method is a supervised machine learning algorithm utilized for addressing classification and regression problems. Its approach involves classifying new data by considering the class of its k-nearest neighbors, selected using the majority voting principle. Specifically, for a given value of k, the algorithm evaluates the classes of the k closest training points to the test data point. The test data point's class is then determined depend on the majority class of the k nearest neighbors. The distance between the training and testing data points can be calculated using Euclidean, Manhattan, or Hamming distances [38]. This work utilizes Manhattan distance.

Eq. (9) for Manhattan distance is

$d(x . y)=\sum_{i=1}^n\left|x_i-y_i\right|$                    (9)

where, $d(x . y)$ represents the distance between point x and point y, ∑ represent cumulative sum of n step.

The KNN algorithm is composed of several fundamental steps, as follows:

Step 1: Determine the value of k, representing the number of nearest neighbors to be examined.

Step 2: Compute the distance between the each of the training data points and new data point, utilizing a distance metric such as Euclidean distance or Manhattan distance.

Step 3: Identify the k nearest data points by selecting the ones with the smallest calculated distances.

Step 4: For classification tasks, determine the majority class among the k nearest neighbors and assign this class to the new data point.

Overall, the KNN algorithm involves a series of computations and decisions based on the value of k and the distance metric used.

3.3.2 Multi-layer perceptron

This work utilized the MLP feedforward ANN model for converting input data sets into appropriate outputs. The MLP consists of fully interconnected multiple layers, with each layer containing neurons with nonlinear activation functions, except for the input layer. One or more nonlinear hidden layers may separate the input and output layers. The error is estimated based on the labels for the initial feed-forward operation using a cost function, which is a term used to describe the error function. The cost function types include cross-entropy, mean absolute error, and mean squared error. For categorization purposes, the cross-entropy cost function is used. The weights are updated using gradient descent through backpropagation, with stochastic gradient descent being commonly employed for this optimization. In this work, the Adam optimizer is utilized for classification. After several training epochs, the model is capable of categorizing the data [39].

The activation function is defined by the following equation,

$f\left(b+\sum_i w_i x_i\right)$                         (10)

where, $f()$ the activation function, b indicates the bias component, $x_i$ signifies the activation values, $w_i$ represents the weight values and b corresponds to the bias component of the model.

3.3.3 Decision tree

The decision tree algorithm is a popular machine learning technique employed for addressing both regression and classification problems. It constructs a tree-like structure to represent a set of decisions and their corresponding results. Each node in the tree like structure represents a decision based on one or more input features, while each leaf node of the tree represents the predicted output. In classification problems, the goal is to forecast the class label of a new instance based on its input features. The algorithm recursively splits the data into smaller subsets based on the input features until each subset is as homogeneous as possible concerning the target variable. At each node of the tree, the algorithm selects the feature that can best separate the data into the most homogeneous subsets using a splitting criterion, such as the Gini index, information gain, or entropy. The Gini index is employed as the splitting criterion in this work.

The formula for the Gini index is defined by Eq. (11),

$Gin \,\,i=1-\sum_{i=1}^j P(i)^2$                    (11)

where, j denotes the number of classes present in the target variable, and let P(i) denote the ratio of observations that have passed in a given node, divided by the total number of observations present in that node.

Decision trees are highly regarded in machine learning due to their interpretability and ability to handle both numerical and categorical data. However, they are susceptible to overfitting, where the tree becomes too difficult and fits the training data too strictly, prominent to poor generalization performance on new data. To overcome this issue, techniques such as pruning, ensemble methods, and regularization can be applied to mitigate overfitting and enhance the performance of decision trees.

3.3.4 Support vector machine

The SVM machine learning algorithm is employed for performing both regression and classification tasks. SVM algorithm is primarily used to determine the optimal hyperplane or boundary that can effectively distinguish between different classes within the feature space. This hyperplane is selected to maximize the margin or the distance between the closest data points of each class. The margin size is indicative of the robustness and generalizability of the model for future predictions.

The equation for the hyperplane in an SVM with two classes is given by Eq. (12),

$w^T x+b=0$              (12)

where, w is the vector perpendicular to the hyper-plane, x is the input data, and b is the bias term or offset of the hyperplane from the origin. The SVM aims to identify the values of w and b that maximize the margin while ensuring that all data points are accurately classified. This is accomplished by resolving a constrained optimization problem in which the norm of w is minimized while satisfying the constraint that each data point is on the correct side of the hyperplane.

3.3.5 Ensemble learning

In disease diagnosis, an ensemble approach involves partitioning the original dataset into smaller datasets to decompose each dataset, thus enabling prediction algorithms to be applied to each decomposed dataset. By leveraging the decomposed dataset as a reference, the individual prediction outcomes are averaged to obtain an overall prediction. Allende and Valle suggest that merging models for disease diagnostic prediction can have several advantages, including the use of appropriate aggregation techniques, which can significantly improve overall diagnostic accuracy; the use of combination strategies as the optimal prediction model is often unknown; and the ability to significantly reduce errors by combining multiple predictions. Furthermore, ensembles are frequently employed for prediction for several reasons, such as improved generalizability, increased tolerance, and decreased model variance concerning data noise.

Bagging ensemble Bagging is a suitable tool for algorithms that are considered weaker or more prone to variances such as KNN or decision trees. Breiman [40] proposed the use of bagging, also known as bootstrap aggregating, as a traditional ensemble method for addressing classification issues. Bagging involves generating several samples from a single dataset using the bootstrap method with replacement, resulting in multiple trees for the same predictor variables that are combined to produce an aggregate estimate. The aggregate estimate is determined through averaging or voting for classification or regression problems, respectively [41]. The advantage of using bagging for ensemble formation is that it reduces the baseline predictor's error and can generate predictive performance estimates that are correlated with test set estimates or cross-validation [42]. However, the trees generated using bagging may lack diversity and share traits, which can limit their predictive power. To address this issue, RF was developed as a modification of the bagging method, with the addition of randomly selecting predictors at each decision tree node [43]. RF also involves choosing the optimal collection of features to describe the data [44]. Its algorithm includes the following steps: (i) generating samples from a training set using the bootstrap method with the number of observations for several predictors and variable responses; (ii) building several trees, with each node containing a subset of the number of predictor variables chosen at random; (iii) using the best subset identified in step (i) to produce a variable response estimate from each tree; and (iv) producing a final estimation by averaging the predictions acquired in step (iii). The main goal of using RF is to enhance tree performance by reducing their variance [45]. Unlike bagging, RF aims to minimize correlation among the sampled datasets by increasing randomization while developing trees. Therefore, RF outperforms bagging models by providing better predictive power due to its reduced correlation among the trees.