Enhancing Autism Spectrum Disorder Classification with Lightweight Quantized CNNs and Federated Learning on ABIDE-1 Dataset

Abstract

Autism spectrum disorder (ASD) is a complex neurodevelopmental condition that presents significant diagnostic challenges due to its varied symptoms and nature. This study aims to improve ASD classification using advanced deep learning techniques applied to neuroimaging data. We developed an automated system leveraging the ABIDE-1 dataset and a novel lightweight quantized one-dimensional (1D) Convolutional Neural Network (Q-CNN) model to analyze fMRI data. Our approach employs the NIAK pipeline with multiple brain atlases and filtering methods. Initially, the Regions of Interest (ROIs) are converted into feature vectors using tangent space embedding to feed into the Q-CNN model. The proposed 1D-CNN is quantized through Quantize Aware Training (QAT). As the quantization method, int8 quantization is utilized, which makes it both robust and lightweight. We propose a federated learning (FL) framework to ensure data privacy, which allows decentralized training across different data centers without compromising local data security. Our findings indicate that the CC200 brain atlas, within the NIAK pipeline’s filt-global filtering methods, provides the best results for ASD classification. Notably, the ASD classification outcomes have achieved a significant test accuracy of 98% using the CC200 and filt-global filtering techniques. To the best of our knowledge, this performance surpasses previous studies in the field, highlighting a notable enhancement in ASD detection from fMRI data. Furthermore, the FL-based Q-CNN model demonstrated robust performance and high efficiency on a Raspberry Pi 4, underscoring its potential for real-world applications. We exhibit the efficacy of the Q-CNN model by comparing its inference time, power consumption, and storage requirements with those of the 1D-CNN, quantized CNN, and the proposed int8 Q-CNN models. This research has made several key contributions, including the development of a lightweight int8 Q-CNN model, the application of FL for data privacy, and the evaluation of the proposed model in real-world settings. By identifying optimal brain atlases and filtering methods, this study provides valuable insights for future research in the field of neurodevelopmental disorders.

1. Introduction

Autism spectrum disorder (ASD) is a neurodevelopmental condition characterized by a range of social, communicative, and behavioral challenges that vary in severity among individuals [1]. The heterogeneity of ASD symptoms is often complicated by comorbidities, resulting in 88.5% of children additionally having diagnoses such as Attention Deficit Hyperactivity Disorder (ADHD), intellectual disability, or developmental coordination disorder, further complicating the diagnostic process [2,3]. This emphasizes the critical need for early diagnosis, which can greatly improve outcomes for individuals with ASD.

Advancements in neuroimaging techniques, particularly functional Magnetic Resonance Imaging (fMRI), have provided significant insights into the neural underpinnings of ASD [3,4]. fMRI, with its non-invasive nature and high spatial resolution, has emerged as an efficient approach for examining brain function and connectivity in psychiatric disorders, including ASD [4,5]. fMRI studies have revealed abnormal patterns of brain connectivity in individuals with ASD, which underlies the social and communicative deficits associated with the disorder [1,6]. However, traditional diagnostic procedures for ASD rely heavily on behavioral assessments and clinical observations, which are time-consuming and often subject to variability among clinicians [7]. Consequently, there is a growing demand for Computer-Aided Diagnosis (CAD) systems that can aid in the accurate and timely diagnosis of ASD [1].

In recent years, machine learning, deep learning, and multi-feature based network-based techniques have shown promise in the medical field, processing large, complex datasets to identify patterns that may not be discernible through traditional analysis and achieving acknowledgment by the trained specialists in diagnostics tasks [8,9,10,11]. Specifically, Convolutional Neural Networks (CNNs) have been employed to analyze fMRI data, offering a powerful tool for detecting ASD-related neural patterns [7,12]. Furthermore, Quantized CNNs (Q-CNNs) have been introduced in various recognition tasks [13,14] to make the models more lightweight and sustainable. This study introduces an automated approach utilizing the ABIDE-1 dataset and int8 quantized 1D CNN model to detect ASD from fMRI data (See Figure 1). The NeuroImaging Analysis Kit (NIAK) pipeline is employed using the Craddock 200 (CC200), Craddock 400 (CC400), Automated Anatomical Labeling (AAL), Dosenbach160 brain atlases, and four different filtering methods, namely filt-global, filt-noglobal, nofilt-global, and nofilt-noglobal. Before the model training process, the Regions of Interest (ROIs) of each atlas are converted to feature vectors utilizing the tangent space embedding. This study proposes a novel 1D-CNN model equipped with an input layer, flatten layer, eight dense layers, and a dropout layer. Furthermore, the CNN model is quantized by utilizing Quantize Aware Training (QAT) to reduce the execution time, power usage, and storage consumption. The proposed Q-CNN model utilizes int8 quantization; therefore, the model is very lightweight and efficient to deploy on any edge devices. The int8 quantization is performed to reduce the dependency on high-end systems for classification tasks. This method was chosen because it strikes an optimal balance between reducing model size and computational load while maintaining a high level of accuracy. Compared to other quantization methods, int8 quantization significantly decreases the memory footprint and power consumption, which is especially important for deployment on resource-constrained devices like the Raspberry Pi. Additionally, int8 quantization is widely supported by hardware accelerators, further making it a practical choice for efficient inference on edge devices, where computational resources are limited. As the motivation is for this model to be used effectively in real-world environments, the need for a privacy preservation system for the healthcare center is a primary concern. To address the issue, a federated learning (FL)-based training framework is introduced to maintain the privacy of the data centers, where their provided dataset will be trained in each data center’s or hospital’s local machine (considered as a client server) while keeping the datasets decentralized. For the FL training, we have 10 clients splitting the overall dataset into two parts for each client. The iterative training process of the FL framework may be particularly effective for the imbalance dataset as the classes are trained locally in multiple different local machines and the training weights are aggregated in a global server. There is a chance that if any class is left under-trained in any client server that the training may be perfectly performed in another client server. Therefore, the overall global server’s weight aggregation process is not compromised. As a result, by introducing an FL-based Q-CNN model, this study provides an efficient framework for the ASD classification task. This study explores the optimal atlases for ASD classification utilizing all the filtering methods within the NIAK pipeline. The Q-CNN model’s training and testing are conducted separately for each of the filtering methods with four atlases.

To evaluate the proposed FL-based Q-CNN framework’s performance in a real-world setting so that in the future it can be accessible for anyone from urban to rural areas, it is further employed in an embedded system, e.g., Raspberry Pi 4. The model is implemented in Python language and the inference was TensorFlow 2.6. The major contributions of this study are:

• A lightweight Q-CNN model is introduced through the utilization of int8 quantization technique.
• An FL-based framework is incorporated for the classification to preserve the privacy of healthcare centers and make the proposed approach more effective for real-world usage.
• The most effective atlas for ASD classification can be identified using the four filtering steps within the NIAK pipeline, with the CC200 brain atlas being found optimal.
• The proposed FL-Q-CNN model is implemented in the Raspberry pi 4 to evaluate its performance in real-world settings.
• A comparative analysis is carried out integrating the CNN model, float 16 quantization model, and proposed int8 Q-CNN model in the Raspberry Pi 4 by calculating the lowest inference time, flash occupancy, and power usage to demonstrate the effectiveness of the proposed framework.

2. Related Works

To investigate the severity of brain disorders, Task-based functional Magnetic Resonance Imaging (TfMRI) is a widely used brain imaging method that shows the functional activity of the brain. Using TfMRI data, Reem Haweel et al. [15] implemented discriminant TfMRI feature extraction methods using a CNN model for global ASD diagnosis. They proposed a three-stage feature extraction and reduction pipeline that is both temporally and spatially oriented. The final stage uses a deep learning 1D CNN model to classify individuals as either generally developing or having ASD. With 4-fold cross-validation, preliminary results on 66 TfMRI datasets obtained 77.2% correct global classification. A new diagnosis method was proposed by Magdiel Jiménez-Guarneros et al. [16] utilizing a lightweight 1-D CNN architecture with the maximal overlap discrete wavelet transform to identify mechanical and electrical defects and related conjunction, in IMs powered by Adjustable Speed Drives (AdSDs). Several specific single and combined faults were examined: phase-to-ground short circuit (electrical), turn-to-turn short circuit (turn-to-turn mechanical), and outside raceway bearing (mechanical). The proposed diagnostic approach achieves an accuracy rate of above 99%. Qaysar Mohi-ud-Din et al. [17] employed a 1D CNN model to detect ASD using Electroencephalography (EEG) signals. The authors trained a multilayered CNN model to classify autism and normal subjects. With this model, they achieved 92.2% accuracy. To improve the inconsistent results of machine learning in ASD classification, Aythem Khairi Kareem et al. [18] proposed a 1D CNN model with three publicly available time-series datasets (children, adults, and adolescents). This approach shows an improved accuracy with 99.45%, 98.66%, and 90% in the three datasets for ASD screening. Using CNN deep networks, a novel CAD framework was proposed by Reem Haweel et al. [19] for classifying 50 children with ASD and 50 developed toddlers with generally developed brains. The integrated global diagnosis attains an 86% accuracy rate, accompanied by 82% sensitivity and 92% specificity. Personalized diagnosis and treatment approaches are made possible by the creation of a brain map that shows the severity of each ASD for each area of the brain. CNN techniques can be applied to identify children who are autistic and those who are not. Another CNN method was used by Narinder Kaur et al. [20] to categorize children into those with autism and those without. Images of children between the ages of four and eleven were utilized. The proposed strategy achieves a quick response time. As a result, by using the proposed strategy, they might greatly reduce the time needed for diagnosis and enable ASD diagnosis at a lesser cost. Using a DSM-V-based dataset, Vikas Khullar et al. [21] proposed an ASD diagnosis system by applying CNN techniques like the Multilayer Perceptron (MLP) and Long Short-Term Memory (LSTM). In this research, comparative analysis showed that when compared to other Artificial Intelligence (AI) algorithms like CNN and MLP, LSTM produced better findings for ASD diagnosis since it demonstrated stabilized outcomes and achieved maximum accuracy. Wentao Lv et al. [22] classified ASD cases using a multisite anti-interference neural network. The findings indicate that ten-fold cross-validation has an average accuracy of 75.56%, which is higher than previous studies. Introducing deep learning-based autism spectrum disorder prediction (DeepASDPred), by Yongxian Fan et al. [23], is a deep learning-based ASD risk Ribonucleic Acid (RNA) prediction tool. The RNA transcript sequences are first feature encoded using K-means, and a feature matrix is created by fusing the feature-encoded sequences with the associated gene expression levels. They input the best feature subset—selected using a combination of the chi-square test and logistic regression—into a binary classification prediction model built using a CNN and LSTM for both training and classification. Ten-fold cross-validation findings showed that our approach performed better than state-of-the-art techniques. To minimize the size and computational complexity of the model, Q-CNNs are a specific type of CNN where the weights and, frequently, the activations are quantized. Ailing De et al. [24] proposed an innovative unsupervised 3D Deep Embedding Clustering (3D-DEC) network and an effective memory reserving-and-fading strategy for their Vector Quantization (VQ)-based 3D segmentation method. Sean I. Young et al. [25] and Muhammad Ilham Rizqyawan et al. [26] compressed CNN weights through quantization. However, utilizing all of the Deep Neural Network (DNN) capabilities for clinical diagnosis is not possible concerning medical images because of serious security and privacy concerns about sharing local medical data between medical establishments. Sajid Nazir et al. [27] explore the uses of federated learning in medical image analysis using DNNs, focus on security issues, discuss various attempts to enhance FL model performance, and outline the difficulties and potential research areas. Rui Yan et al. [28], Aaisha Makkar et al. [29], and Meirui Jiang [30] proposed CNN models with an FL framework to ensure the privacy of medical data and showed a secure connection between the client and server side. Rui Yan et al. [28] presented an entirely novel transformer-based self-supervised pre-training paradigm that uses masked image modeling to pre-train models directly on decentralized target task datasets. This approach enables more reliable representation learning on heterogeneous data and efficient knowledge transfer to downstream models.

Table 1. Summary of state-of-the-art methods for ASD diagnosis and related works.

Reference	Techniques	Dataset	Results	Limitations
[15]	1D CNN	Sixty-six TfMRI datasets	77.2%	Small sample size, limited to TfMRI
[16]	1D CNN	Mechanical and electrical faults in IMs	99.78 ± 0.14%	Limited to fault detection in specific machines
[17]	Multilayered 1D CNN	EEG signals for ASD diagnosis	92.2%	Limited to EEG data, lacks generalizability
[18]	1D CNN	Public time-series datasets	99.45%	Does not consider data from all age groups equally
[19]	CNN	One hundred subjects	86%	Small dataset, limited generalization
[20]	CNN	Images of children aged 4–11 years	99.54%	Limited to images, lacks functional data
[21]	CNN, MLP, LSTM	DSM-V dataset for ASD diagnosis	100%	Needs more data diversity, limited to DSM-V data
[22]	NN	Multisite ASD datasets	75.56%	Lower accuracy, limited robustness
[23]	DeepASDPred	RNA transcript sequence datasets	93.8%	Specific to RNA data, lacks generalizability to other types of data
[24]	3D-DEC	Three-dimensional segmentation dataset	Dice score 91%	Limited application scope, complexity in 3D segmentation
[25]	CNN	Medical images	93%	Not addressing privacy/security concerns
[27]	FL + DNN	Medical image datasets	-	High communication overhead in FL setup
[28]	FL	Decentralized medical datasets	91.47%	Computational complexity and training time
[29]	CNN + FL	Medical datasets	94.4%	Data heterogeneity affects model performance
[30]	CNN + FL	Medical datasets	For MRI 88.31%	Security risks still exist in FL models
Proposed	1D CNN	ABIDE 1	98%	Need to explore ABIDE-II dataset and decentralized FL

shows the summary of the state-of-the-art methods for ASD diagnosis and related works.

3. Background Knowledge

3.1. NeuroImaging Analysis Kit (NIAK) Pipeline

The NIAK is software that has been developed since 2008. It is free and open source, and it is used for preprocessing and data mining of large functional neuroimaging samples. This software is compatible with both the GNU Octave and Matlab programming languages. Created by the Functional Neuroimaging Unit (FNU) of the Montreal Neurological Institute (MNI), the software provides a versatile system for preparing fMRI data, with a specific emphasis. The NIAK plays a pivotal role in facilitating the analysis of complex neuroimaging data. When applied to the Autism Brain Imaging Data Exchange (ABIDE) dataset, NIAK enables researchers to delve deeply into the neural underpinnings of ASD, promoting a better understanding and early detection of the disorder. This chapter explores the capabilities, applications, and significance of NIAK within the context of the ABIDE dataset.

3.2. Brain Atlas

Automated Anatomical Labeling (AAL): The AAL atlas was created using an automated process that segmented the high-resolution T1 volume of a single patient, which was provided by the MNI. This atlas contains 116 ROIs that capture signals from specific brain areas, such as the frontal gyrus, rolandic operculum, supplementary motor area, olfactory cortex, precentral gyrus, gyrus rectus, posterior cingulate gyrus, anterior cingulate and paracingulate gyri, median cingulate and paracingulate gyri, hippocampus, parahippocampal gyrus, amygdala, calcarine fissure and surrounding cortex, cuneus, lingual gyrus, insula, occipital gyrus, fusiform gyrus, and more [31,32,33]. The AAL atlas was shared using the AAL toolbox and segmented with a functional resolution of 3 × 3 × 3 mm³ [34] using nearest-neighbor interpolation.

Craddock 200 (CC200): The CC200 atlas was created by utilizing normalized cut spectral clustering on fMRI data collected from a diverse group of 41 individuals, ranging in age from 18 to 55 years (with an average age of 31.2 and a standard deviation of 7.8), which included 19 females [35]. This method breaks down the brain into 200 regions that share similar functional activity and spatial limitations. The ROIs were labeled by overlapping them with various atlases, including AAL, Eickhoff–Zilles (EZ), Harvard–Oxford (HO), and Talairach and Tournoux (TT).

Craddock 400 (CC400): The CC400 atlas includes 392 regions, developed using a methodology that closely resembles that of the CC200 atlas, guaranteeing a reliable and uniform functional brain parcellation.

Dosenbach 160: The Dosenbach 160 atlas consists of 161 spheres, each with a radius of 4.5 mm, positioned at coordinates provided by Dosenbach et al. [36]. This atlas was included with the Data Processing Assistant for Resting-State fMRI (DPARSF)/Data Processing and Analysis for Brain Imaging (DPABI) toolbox [37]. The brain regions listed here cover a wide range of areas, including the frontal cortex, thalamus, insula, parietal cortex, temporal gyrus, cingulate gyrus, angular gyrus, cerebellum, and occipital cortex [34].

3.3. Filtering Methods

In our research, we utilized four atlases—AAL, CC200, CC400, and Dosenbach160—to explore their effectiveness in conjunction with the NIAK pipeline on the ABIDE-1 dataset. To assess the impact of different preprocessing strategies on functional connectivity, we analyzed four techniques: filt-global, nofilt-global, filt-noglobal, and nofilt-noglobal. These techniques involve variations in the application of filtering and global signal regression (GSR). Each technique offers a different approach to preprocessing fMRI data, with specific advantages and potential drawbacks:

• Filt-global: Aims to enhance signal quality by combining temporal filtering and global signal regression.
• Nofilt-global: Focuses on removing global artifacts while retaining the full frequency spectrum.
• Filt-noglobal: Aims to preserve neural signals within the frequency range of interest, without removing the global signal.
• Nofilt-noglobal: Provides a baseline with no preprocessing, retaining all raw data components.

3.4. Quantization

Quantization is an essential technique in deep learning, converting neural networks from using high-precision floating-point values to lower bit-width integers. This process optimizes models by reducing both the model size and inference time, making it particularly valuable for deployment on resource-constrained IoT devices. By utilizing low-precision integer operations, quantization leverages hardware acceleration for integer calculations, thereby enhancing computational efficiency with minimal accuracy loss.

Our approach focuses on int8 quantization, a method that performs computations entirely in the integer domain, particularly during convolutions and matrix multiplications. This technique is well-suited for edge devices like microcontrollers, which often have limited RAM, flash memory, and processing power. By using high-throughput integer instructions, int8 quantization improves both inference latency and throughput.

The process involves two main steps: defining the range of real numbers for quantization and converting these values into integers through rounding. The primary operations in this context are quantization, which maps floating-point numbers to integers (e.g., float32 to int8), and dequantization, which reverses this mapping back to floating-point values. For example, a real number range $[\beta ,\eta ]$ is mapped to an integer range $[-2^{b-1},2^{b-1},-1]$, where b represents the bit-width. Out-of-range values are clipped to the nearest boundary. In scale quantization, particularly in its symmetric form, both the input and integer ranges are centered around zero. This method uses the integer range [−127, 127] for int8 quantization, excluding −128 to maintain symmetry. Although this exclusion results in losing one representable value out of 256, the benefits of symmetry become more pronounced with lower bit-width quantization. Equations (1) and (2) demonstrate the translation of a real value r into b-bit number $r_q$ using a spectrum $[-\eta ,\eta ]$.

$$p={\displaystyle \frac{2^{b-1}-1}{\eta }}$$

(1)

$$r_q=quantize(r,b,p)=clip(round(p.r),-2^{b-1}+1,2^{b-1}-1)$$

(2)

Although both affine and scale quantization enable the use of integer arithmetic, scale quantization is particularly advantageous for computational efficiency during inference [38]. Equation (3) demonstrates the dequantization process associated with scale quantization.

$$\overline{\tau }=dequantize(r_q,p)={\displaystyle \frac{1}{p}}\times r_q$$

(3)

Overall, uniform quantization enables efficient hardware resource utilization, making it a practical solution for deploying deep learning models on devices with limited computational capabilities without significantly compromising performance.

4. Dataset Description

This work utilizes the data of the ABIDE dataset [39]. This dataset fundamentally works as a cooperative endeavor between carefully collected fMRI data and associated phenotypic data from eighteen research sites worldwide. There were 539 individuals with an ASD diagnosis and 573 control participants out of the original 1112 scans in the sample. Still, some of the data did not meet the strict Quality Assessment Protocol (QAP) metrics requirements set forth by the Preprocessed Connectomes Project (PCP) community (http://preprocessed-connectomes-project.org) (accessed on 11 July 2024). The dataset was updated to include 866 people in total, 402 of whom had been diagnosed with ASD, and 464 of whom were control subjects. To obtain a thorough understanding of the individual sites included in this study, please see

Table 2. Summary of the phenotypic data for the participants in the ABIDE dataset.

Site	Count			Age Range
	ASD	Control	Total
Caltech	5	10	15	17–56
CMU	6	4	10	19–40
KKI	12	20	32	8–13
LEUVEN	26	30	56	12–32
MAX_MUN	19	27	46	7–58
NYU	74	98	172	6–39
OHSU	12	13	25	8–15
OLIN	14	14	28	10–24
PITT	24	26	50	9–35
SBL	12	14	26	20–64
SDSU	8	18	26	9–17
Stanford	12	13	25	8–13
Trinity	19	25	44	12–26
UCLA	48	37	85	8–18
UM	46	73	119	8–29
USM	43	24	67	9–50
YALE	22	18	40	8–18
Total	402	464	866	6–64

, which presents a detailed analysis of the phenotypic data.

The preprocessed pipeline data (CPAC, NIAK, CCS, and DPARSF) were obtained via PCP pipelines (http://preprocessed-connectomes-project.org/abide/Pipelines.html) (accessed on 7 March 2024). These pipelines include all the necessary methods for preparing data from neuroimaging. Slice timing inconsistencies, motion artifacts, intensity leveling, and the removal of unwanted signals are all addressed by the preprocessing techniques. These nuisance signals include, among other things, those pertaining to breathing, pulse, global mean data regression, low-frequency scanner shifts, and head movement. Following preprocessing, bandpass filtering was applied to the functional data, namely in the 0.01 to 0.1 Hz frequency range. This was then followed by spatial registration to align it with the MNI1523 template space, and to achieve a more thorough comprehension of the methods, strategies, parameter setups, and software tools utilized in this procedure.

5. Proposed Method

The classification task’s workflow is divided into four distinct segments (refer to Figure 1). Initially, the ABIDE dataset’s four distinct filtering methods are employed to extract ROIs from the preprocessed data of the CC200, CC400, AAL, and Dosenbach160 brain atlases, from the NIAK pipeline [39]. Consequently, a connectivity matrix is created, which is a pairwise relationship or connection between various brain regions, as determined by fMRI data. Subsequently, the connectivity matrix is converted into a feature vector. Finally, the classification task is executed using a 1D CNN network after the lower triangular data of the connectivity matrix has been flattened. The subsequent subsections offer a comprehensive examination of these 4 segments, including a sequential description of each.

5.1. Extraction of ROI

AAL, Dosenbach160, CC200, and CC400 functional brain atlases are employed to derive ROIs from the NIAK pipeline. These four atlases contain 200, 400, 116, and 160 unique ROIs, respectively, which were obtained through normalized cut spectral clustering. Initially, the 4D fMRI data are specified by their dimensions $(\iota ,\delta ,\nu ,\omega )$, which represent height, width, depth, and time points, respectively. These data are then converted to 2D data with dimensions $\omega$ × $\psi$, where $\psi$ is the number of ROIs. Each row of the matrix $\omega$ × $\psi$ corresponds to specific time points, while each column represents unique properties that have been derived from fMRI data. The computationally intensive process of extracting mean time-series signals by applying a brain atlas to preprocessed fMRI data can place a strain on computational resources. This investigation employed pre-extracted time-series data to circumvent hardware and memory constraints. For the brain atlases, the mean time-series signals were directly obtained from the PCP.

5.2. Formation of the Functional Connectivity Matrix

After the ROIs are extracted, the final stage is to convert them into a functional connectivity matrix, which is also referred to as a functional connectome. This matrix is represented by the dimensions $(\psi ,\psi )$. The brain atlas determines the associations between specific regions of interest in the brain, which are measured by the functional connectome, a comprehensive representation. The essential data pertinent to the correlation of Blood Oxygen Level-Dependent (BOLD) signal time series between each pair of ROIs are the fundamental purpose of a functional connectivity matrix, as defined by a specific brain atlas. The method is implemented on an individual basis for each participant. To develop functional connectomes, an intricate methodology was implemented. Utilizing the default Ledoit–Wolf regularized covariance estimator [34] necessitated the implementation of a tangent-embedded parametrization technique. To robustly characterize replicable connection patterns at the group level, the tangent space embedding method efficiently employs both partial correlations and correlations. In addition, it effectively depicts individual connections as deviations from the group’s average, thereby facilitating the identification of subtle differences at the individual level. The embedded connectome in Figure 2 illustrates the functional connectivity matrices, which demonstrate the complex connections between various brain regions. A representative group of individuals diagnosed with autism spectrum disorder and a control group are effectively represented in the graphic that is presented, which illustrates the substantial differences in functional connectivity observed in various brain regions. In every cell of the correlation matrix or connectome, the correlation coefficient is present, which quantifies the magnitude of a linear relationship between two regions. From −1 to 1 is the range of the correlation coefficient. When the correlation coefficient is 1, a perfect positive linear relationship is observed. Conversely, a correlation coefficient of −1 indicates a complete negative linear association, which means that when one region experiences an increase, the other region experiences a corresponding decline. The absence of a linear relationship between the variables is demonstrated by a correlation coefficient of 0.

5.3. Conversion of Correlation Matrix to 1D Feature Vector

This section represents the process of converting the ASD features of atlases into a 1D feature vector. A symmetrical functional connectivity matrix is obtained from the tangent space embedding where the upper triangular value repeats the lower one. Then, the dimensionality is reduced through only retrieving the lower triangular value and removing the upper one including the diagonal. A further procedure is conducted utilizing this lower triangular part where it has been flattened to a 1D vector. The size of the 1D vector is calculated as shown in Equation (4).

$$Size={\displaystyle \frac{\psi \times (\psi -1)}{2}}$$

(4)

Here, $\psi$ defines the number of ROIs. Using Equation (4), we can obtain the feature vector sizes of each atlas, 19,900, 76,636, 6670, and 12,880 for CC200, CC400, AAL, and Dosenbach160, respectively. These feature vectors are then fed into the FL-based Q-CNN.

6. Proposed Model

This section presents the architectural description of our proposed model. Initially, a CNN model is built, which is quantized to build the Q-CNN model. Additionally, to make the Q-CNN model more lightweight, int8 quantization is performed. Lastly, the int8 Q-CNN model is incorporated into the FL framework to maintain the proposed system’s privacy. The overall procedure is described accordingly. We have made the experimental source code publicly available for further verification and replication of our results (https://github.com/RashikRahman/Enhancing-ASD-Classification-with-Lightweight-QCNNs-and-FL) (accessed on 19 May 2024).

6.1. CNN Model

The proposed CNN architecture includes an input layer followed by a flatten layer, where the 1D feature vectors are flattened and pass through seven dense layers with the sizes of 128, 64, 32, 16, 16, 8, and 8. A kernel regularizer of 0.0026 is incorporated in the dense layer with a filter value 32. Each dense layer consists of a Rectified Linear Unit (ReLU) activation function. A dropout layer of 0.4 is used to drop a certain percentage of neurons during training, reducing the risk of overfitting. In the final dense layer, to convert the overall output into probability scores, the SoftMax activation function is used. Let us consider a hidden layer of h, where each neuron of the hidden layer receives an input and bias value of $p_h$ and $b_h$, respectively. The connection between two subsequent hidden layers of h and $h+1$ is connected through the weight vector $w_h$. After the connection, the $h+1$ hidden layer is activated using Equation (5).

$$A_{h+1}=f(w_h{p}_h+b_h)$$

(5)

Here, A denotes the activation of the $h+1$ hidden layer, and the ReLU activation function is defined as f. The equation for the ReLU activation function is represented in Equation (6).

$$f\left(p\right)=max(0,p)$$

(6)

The ReLU activation function generates output with a $[0,inf]$ range. Then the SoftMax function for output prediction is defined in Equation (7).

$$\sigma {(\stackrel{p}{\to })}_i={\displaystyle \frac{e^{p_i}}{{\sum }_{j=1}^n{e}^{p_j}}}$$

(7)

Here, the SoftMax function is defined as $\sigma$ and $\stackrel{p}{\to }$ represents the input feature vector. $e^{p_i}$ and $e^{p_j}$ denote the standard exponential function for the input and output, respectively. The number of classes is represented by n. The categorical cross entropy as the loss function and Adam as the optimizer are used in the proposed model. The categorical cross entropy $\left(X_{c}ce\right)$ can be calculated using Equation (8),

$$X_{cce}={\displaystyle \frac{1}{k}}\sum _{w=1}^n\sum _{k=1}^n{y_k}^w\times log\left(h_w(p_k,n)\right)$$

(8)

where K denotes the number of training examples and the target label for a class n is ${y_k}^w$. The CNN architecture is demonstrated in Figure 3.

6.2. Proposed Q-CNN

In this section, the quantization technique applied to the 1D-CNN model is described. Here, quantized values are denoted as q and real numbers as R. The method incorporates both integer and floating-point computations for training and inference to ensure close alignment between the two approaches. Generally, quantized networks are trained using floating-point precision before the resulting weights are converted into a quantized format.

Algorithm 1 outlines the quantization training process, as illustrated in Figure 4. The process begins with the model accepting an input feature vector X and its corresponding labels y. The CNN-based architecture, initially designed for floating-point inference, is utilized to predict outputs from the input feature vectors, as depicted in Figure 3. Figure 4 demonstrates the transformation of the dense layer’s pre- (see Figure 4a) and post-quantization (see Figure 4b). As in Equation (9), both input and output are represented as 8-bit integers, using a 32-bit integer accumulator and Figure 4b illustrates the dense layer’s training using simulated quantization. Throughout this process, all variables and computations are executed with 32-bit floating-point arithmetic. To replicate the effects of quantization on variables, weights, and activation functions, quantization endpoints are incorporated into the computational graph. This graph simulates integer-only computation while remaining trainable by standard optimization techniques for floating-point models.

Algorithm 1 Quantization Training Process

1: Input: Feature vector X, Label y  2: Initialize a floating-point model graph M  3: Compile the model M  4: Quantize the compiled model M:  5:    Reduce tensor precision for inference (as per Equation (9))  6: Train the quantized model M using X and y:  7: for each epoch do  8:     Perform forward pass through model M  9:     Compute loss using predicted and true labels 10:     Backpropagate to update model parameters 11:     Quantize weights and activations during training 12: end for 13: Optimize the quantized model M for inference 14: Perform predictions on new input data using trained quantized model M

• Prior to performing convolution operations with the input, the weights were quantized. When batch normalization was applied, the batch normalization parameters were incorporated into the weights $\widehat{w}$ before quantization. This integration was achieved using Equation (9). Here, $\lambda$ represents the scale parameter from batch normalization, ${\sigma }_B^2$ is an estimated moving average of the variance of the convolutional results over the batch, w is the original weight, and $ϵ$ is a small constant for numerical stability.

  $$\widehat{w}={\displaystyle \frac{\lambda \times w}{{({\sigma }_B^2+ϵ)}^2}}$$

  (9)
• Activation quantization was performed at specific points during inference, ensuring accurate approximation of activations. The quantization process for each layer was defined by several parameters, including the number of quantization levels and the clipping range. The quantization function q is shown in Equation (10).

  $$\begin{array}{cc}\hfill \mathrm{clip}(R,q,r)& =min(max(x,z),r)\hfill \\ \hfill p(q,r,N)& ={\displaystyle \frac{r-q}{N-1}}\hfill \end{array}$$

  $$\begin{array}{cc}\hfill q(R,q,r,N)& =\left({\displaystyle \frac{\mathrm{clip}(R,q,r)-q}{p(q,R,N)}}\right)·(p(q,R,N)+q)\hfill \end{array}$$

  (10)

Here, the quantized real value is represented as $R,$ and $(q,r)$ denotes the quantization spectrum. The number of quantization levels is denoted as N. For the 8-bit quantization, the N will be $N=2^8=256$. There are different methods for activation and weight quantization within defined quantization ranges. Activation quantization depends on the network’s input. To estimate this range, $(q,r)$ values observed during training are collected. These values are then merged using exponential moving averages with a smoothing parameter close to 1, resulting in a smoothed spectrum. Due to the significant latency in updating activation ranges, which can frequently change, it was found beneficial to initially disable activation quantization during the training phase. This allows the network to reach a more stable state, ensuring that the activation quantization ranges do not exclude a substantial proportion of possible values. Conversely, for weight quantization, the method involves setting q as the minimum value and r as the maximum value of the weights. When converting these weights to the int8 format, an adjustment is made to ensure they fall within the range of [−127, 127], deliberately excluding the value 128 to capitalize on an optimization opportunity. The limits $(q,r)$ are adjusted to ensure that the value 0.0 can be precisely represented as an integer upon quantization for both instances. Thus, the learned quantization parameters correspond to the scale S and zero-point Z as described in Equation (11),

$$R=S(q-Z)$$

(11)

6.3. Federated Learning Framework

The federated learning setup consists of one server, with x number of clients over a series of training rounds [40]. The clients hold a constant part of the full dataset. A global model is initialized by the server, the clone of model $\Delta M$ is sent to each client x, and $M_x$ receives data from client x. After receiving the data into the clone of the global model, the training round is started. In each training round, the clone of the model compiles the data using a customized data generator on the specific dataset provided by the client. After the training process, the updated model weights are sent to the global server, where the received weights are aggregated, and the global model is updated accordingly. The aggregated weight of the global model is again sent to the client and this federated training loop continues until k federated rounds are completed. This training round is called the communication round [41]. In the weight aggregation algorithm, the weighted arithmetic mean $\delta M_x$ is calculated, which ensures that all training results of the model are included in the global model.

The proposed FL framework defines a client as an individual acquisition site of the database, with each client representing a distinct location where fMRI data are collected independently. Instead of sharing raw data, the clients train the model locally on their data and only transmit model updates to a central server. This mechanism is crucial for maintaining data privacy and mitigating the risks associated with centralized data storage, particularly when handling sensitive medical information like fMRI data.

In this client–server framework, the fMRI images are initially preprocessed using the NIAK pipeline and then converted into feature vectors. These feature vectors serve as the input for model training. The dataset, now in the form of feature vectors, is distributed across 10 clients, with each client receiving a clone of the global model from the central server. The model is trained locally on each client’s data, and once the training rounds are complete, the results (i.e., model updates) are aggregated and sent back to the global server, which updates the global model. This iterative process continues until the model converges. The aggregation algorithm can be expressed mathematically in Equation (12).

$$w_{t+1}=\sum _{i=1}^N{\displaystyle \frac{n_i}{n}}{w}_i,t+1$$

(12)

In this equation, $w_{t+1}$ is the updated global model weights at round $t+1$. $w_i$, $w_{t+1}$ are the updated model weights from client i at round $t+1$. $n_i$ is the number of data samples on client i. n is the total number of data samples across all clients, as in $n={\sum }_{i=1}^N{n}_i$, and N is the total number of clients. The loss values are calculated using a loss function, which is described in Equation (13).

$$f\left(M\right)=\sum _{j=1}^x{\displaystyle \frac{n_x}{n}}{F}_x\left(M\right),where,F_X\left(M\right)={\displaystyle \frac{1}{n_x}}\sum _{i=1}^{n_k}{f}_i\left(M\right)$$

(13)

In Equation (13), x is the number of clients, $n_x$ is the amount of data from each client, M is the weight vector from the model, and $f_i\left(M\right)$ is the loss function. $F_x\left(M\right)$ defines the local loss function $f_i\left(M\right)$ for a prediction for the Nth client with weight vector M, collectively representing the average loss for all clients $f\left(M\right)$. In Figure 5, an overview of the federated learning framework is presented.

In Figure 5, a global model $\delta M$ is sent to the clients. After training the model $\delta M_x$, the model training weight is sent to the server. The averaging process can be described mathematically by Equation (14).

$$\delta M=\sum _{i=1}^x{\displaystyle \frac{n_x}{n}}\delta M_i$$

(14)

In Equation (14), $\delta M$ represents the aggregate model weight where x represents the client and $n_x$ represents the data presented by each client.

6.4. Raspberry PI Configuration

The Q-CNN model is deployed on a Raspberry Pi 4 embedded system to evaluate its performance in a real-world environment. The python programming language is utilized for the implementation, with inference managed by TensorFlow 2.6. The process starts with the Raspberry Pi taking the feature vector as input. These inputs are then analyzed by the Q-CNN model for predictions. Finally, the results are displayed on a screen connected to the Raspberry Pi via its HDMI port. This setup allows us to assess how effectively the Q-CNN model operates in practical applications. The detailed configuration of the Raspberry Pi 4, including system specifications and computation times, is provided in

Table 3. Raspberry Pi 4 Configuration and Computation Details.

Component	Configuration Details
Model	Raspberry Pi 4 Model B
CPU	Quad-core Cortex-A72 (ARM v8) 64-bit SoC @ 1.5 GHz
RAM	4 GB LPDDR4-3200 SDRAM
Operating System	Raspberry Pi OS (64-bit)
Python Version	Python 3.9.2
Deep Learning Framework	TensorFlow 2.6
Computation Type	CPU (No GPU acceleration)
HDMI Display	Connected to Raspberry Pi via HDMI

.

7. Results

To detect ASD from the ABIDE dataset, four filtering methods, filt-global, filt-noglobal, nofilt-global, nofilt-noglobal, are utilized. From each of the filtering methods, the NIAK pipeline is selected to explore where under every NIAK pipeline there are four brain atlases, namely CC400, CC200, AAL, and Dosenbach 160, that are selected to train and test the model. We analyzed the detailed performance of Base CNN, Quantized CNN, and the proposed Int8 Quantized CNN.

7.1. Filt-Global

In this analysis, the classification performances of four atlases, CC400, CC200, AAL, and Dosenbach 160, are analyzed. Classification performance is evaluated using precision, recall, and F1-score metrics, providing a comprehensive understanding of the model’s effectiveness. The classification results for our models are summarized in

Table 4. Classification report for four atlases using Base CNN, Quantized CNN, and TFLite Quantized CNN with the filt-global filtering method.

Atlas	Class	Overall Accuracy (%)	Macro Avg (%)	Weighted Avg (%)
CC400	Base CNN	91.00	92.00	92.00
	Quantized CNN	95.00	95.00	95.00
	Int8 Quantized CNN (Proposed)	97.00	97.00	97.00
CC200	Base CNN	97.00	97.00	97.00
	Quantized CNN	97.00	97.00	97.00
	Int8 Quantized CNN (Proposed)	98.00	98.00	98.00
AAL	Base CNN	95.00	95.00	95.00
	Quantized CNN	95.00	95.00	95.00
	Int8 Quantized CNN (Proposed)	96.00	96.00	96.00
Dosenbach 160	Base CNN	91.00	91.00	91.00
	Quantized CNN	93.00	93.00	93.00
	Int8 Quantized CNN (Proposed)	93.00	93.00	93.00

.

The table presents the performance metrics of three CNN models, Base CNN, Quantized CNN, and Int8 Quantized CNN (proposed). Each model’s performance was evaluated in terms of overall accuracy, macro average, weighted average, and support. For the CC400 atlas, the Int8 Q-CNN achieved the highest overall accuracy at 97%, followed by the Quantized CNN at 95%, and the Base CNN at 91%. In the case of the CC200 atlas, the Int8 Quantized CNN again outperformed the others with 98% overall accuracy, with both the Quantized CNN and Base CNN scoring 97%. For the AAL atlas, the Int8 Quantized CNN reached 96% accuracy, slightly higher than the 95% achieved by both the Quantized CNN and Base CNN. Lastly, for the Dosenbach 160 atlas, the Base CNN showed 91% overall accuracy, while the Quantized CNN and Int8 Quantized CNN achieved 93%. This analysis highlights the superior performance of the Int8 Quantized CNN across all atlases.

For the CC200 atlas, the proposed model achieved the highest overall accuracy at 98%. The confusion matrix for CC200 atlas is shown in Figure 6.

The training and validation loss and accuracy curves for the CC200 atlas provide insightful details about the model’s learning process and performance over epochs. Observing these curves, we can observe how well the proposed model has been trained and validated on the ABIDE dataset. Figure 7 shows the loss and accuracy curves of CC200 atlas.

As CC200 atlas shows the highest accuracy with the Int8 Quantized CNN model, the performance metrics are analyzed in

Table 5. Performance metrics of CC200 atlas with TFLite Quantized CNN model.

Performance Metrics	Results (%)	Performance Metrics	Results (%)
Test Accuracy	98.00	FPR	3.23
Sensitivity	98.36	FDR	3.23
Precision	96.77	FNR	1.64
Specificity	96.77	F1 Score	97.56
NPV	98.36	MCC	95.13

.

The table presents several performance metrics for the proposed model evaluated on the ABIDE dataset using the CC200 atlas. The test accuracy is 98.00%, indicating a high overall correct prediction rate. The sensitivity (recall) is 98.36%, showing the model’s ability to correctly identify true positives, while the specificity is 96.77%, reflecting its capacity to correctly identify true negatives. The precision is 96.77%, indicating the proportion of true positives among the predicted positives. The F1 Score, which balances precision and recall, is 97.56%. The Negative Predictive Value (NPV) is 98.36%, showing the proportion of true negatives among the predicted negatives. The False Positive Rate (FPR) and False Discovery Rate (FDR) are both 3.23%, indicating low rates of false positives and false discoveries, respectively. The False Negative Rate (FNR) is 1.64%, demonstrating a low rate of missed positive cases. Lastly, the Matthews Correlation Coefficient (MCC) is 95.13%, highlighting a strong correlation between the observed and predicted classifications. Overall, these metrics indicate a highly effective and reliable model.

7.2. Filt-Noglobal

In this analysis, the classification performance of four atlases is examined using the filt-noglobal filtering method.

The classification results of our models are summarized in

Table 6. Classification report for four atlases using Base CNN, Quantized CNN, and TFLite Quantized CNN with the filt-noflobal filtering method.

Atlas	Class	Overall Accuracy (%)	Macro Avg (%)	Weighted Avg (%)
CC400	Base CNN	95.00	95.00	95.00
	Quantized CNN	96.00	96.00	96.00
	Int8 Quantized CNN (Proposed)	96.00	96.00	96.00
CC200	Base CNN	96.00	96.00	96.00
	Quantized CNN	97.00	97.00	97.00
	Int8 Quantized CNN (Proposed)	98.00	98.00	98.00
AAL	Base CNN	96.00	96.00	96.00
	Quantized CNN	97.00	97.00	97.00
	Int8 Quantized CNN (Proposed)	97.00	97.00	97.00
Dosenbach 160	Base CNN	92.00	92.00	92.00
	Quantized CNN	93.00	93.00	93.00
	Int8 Quantized CNN (Proposed)	93.00	93.00	93.00

. The table displays the classification performance of three CNN models—Base CNN, Quantized CNN, and the proposed Int8 Quantized CNN—across four different brain atlases, using the filt-noglobal filtering method. For the CC400 atlas, the Base CNN achieved an overall accuracy of 95%, while both the Quantized CNN and the proposed model improved slightly to 96%. The CC200 atlas shows the best results, with the proposed model leading at 98% overall accuracy, followed by the Quantized CNN at 97% and the Base CNN at 96%. The AAL atlas results are similar, with the proposed model and Quantized CNN both reaching 97% accuracy, and the Base CNN slightly lower at 96%. Lastly, for the Dosenbach 160 atlas, the Base CNN achieved an overall accuracy of 92%, while both the Quantized CNN and the proposed Int8 Quantized CNN achieved 93%. This analysis highlights that the CC200 atlas yields the highest overall performance, with the proposed model consistently outperforming or matching the other models across all atlases. The confusion matrix for the CC200 atlas is illustrated in Figure 8 and Figure 9 where the loss and accuracy curves are shown.

As CC200 atlas shows the highest accuracy with the Int8 Quantized CNN model in the filt-noglobal filtering method, the performance metrics are analyzed in

Table 7. Performance metrics of CC200 atlas with TFLite Quantized CNN model in filt-noglobal filtering method.

Performance Metrics	Results (%)	Performance Metrics	Results (%)
Test Accuracy	98.00	FPR	1.64
Sensitivity	96.72	FDR	1.67
Precision	98.33	FNR	3.28
Specificity	98.36	F1 Score	97.52
NPV	96.77	MCC	95.09

. With a test accuracy of 98.00%, the model demonstrated a high percentage of accurate predictions. The model’s sensitivity, also known as recall, is 96.72%, indicating its accuracy in identifying positive cases. With a precision of 98.33%, the percentage of genuine positives among all positive forecasts is shown. With a specificity of 98.36%, the model effectively identifies negative cases. The F1 Score is 97.52%, which weighs recall and precision equally. The accuracy of negative predictions is indicated by the Negative Predictive Value (NPV), which is at 96.77%. Low rates of false positives and discoveries are indicated by the False Positive Rate (FPR) of 1.64% and the False Discovery Rate (FDR) of 1.67%. The percentage of missed positive instances is shown by the False Negative Rate (FNR), which stands at 3.28%. Finally, a significant overall connection between the anticipated and actual classifications is shown by the Matthews Connection Coefficient (MCC), which stands at 95.09%. All of these indicators together point to an outstanding and reliable model performance on the CC200 atlas.

7.3. Nofilt-Global

The nofilt-global filtering method is used in this evaluation to assess the classification performance of four atlases across all filtering methods of the NIAK pipeline. The review offers a comprehensive analysis of the model’s efficacy and focuses on precision, recall, and F1-Score metrics.

Table 8. Classification report for four atlases using Base CNN, Quantized CNN, and TFLite Quantized CNN with the nofilt-global filtering method.

Atlas	Class	Overall Accuracy (%)	Macro Avg (%)	Weighted Avg (%)
CC400	Base CNN	97.00	97.00	97.00
	Quantized CNN	97.00	97.00	97.00
	Int8 Quantized CNN (Proposed)	97.00	97.00	97.00
CC200	Base CNN	95.00	95.00	95.00
	Quantized CNN	96.00	96.00	96.00
	Int8 Quantized CNN (Proposed)	98.00	98.00	98.00
AAL	Base CNN	97.00	97.00	97.00
	Quantized CNN	97.00	97.00	97.00
	Int8 Quantized CNN (Proposed)	97.00	97.00	97.00
Dosenbach160	Base CNN	96.00	96.00	96.00
	Quantized CNN	96.00	96.00	96.00
	Int8 Quantized CNN (Proposed)	97.00	97.00	97.00

provides specifics of the outcomes for each model. With an accuracy of 97% overall, all models performed identically on the CC400 and AAL atlases. The proposed Int8 Quantized CNN fared somewhat better than the other models in the Dosenbach 160 atlas, with an accuracy of 97% as opposed to 96% for the Base CNN and Quantized CNN. Notably, the CC200 atlas showed the best overall performance; the proposed model achieved the maximum accuracy of 98%, outperforming the Quantized CNN’s 96% and the Base CNN’s 95%. For the CC200 atlas, the proposed Int8 Quantized CNN attained the highest overall accuracy of 98% using the filt-noglobal filtering method. The confusion matrix for the CC200 atlas is illustrated in Figure 10 and Figure 11 where the loss and accuracy curves are shown.

As CC200 atlas shows the highest accuracy with the Int8 Quantized CNN model in the filt-noglobal filtering method, the performance metrics are analyzed in

Table 9. Performance metrics of CC200 atlas with TFLite Quantized CNN model in nofilt-global filtering method.

Performance Metrics	Results (%)	Performance Metrics	Results (%)
Test Accuracy	98.00	FPR	3.23
Sensitivity	98.36	FDR	3.23
Precision	96.77	FNR	1.64
Specificity	96.77	F1 Score	97.56
NPV	98.36	MCC	95.13

. The model’s test accuracy for the nofilt-global filtering method on the CC200 atlas reached 98.00%, indicating strong overall performance. Specificity was 96.77%, demonstrating good performance in identifying negative cases, while sensitivity was 98.36%, suggesting successful identification of positive cases. Recall and precision were balanced, with precision at 96.77% and the F1 Score at 97.56%. The model had strong performance, as evidenced by its 98.36% Negative Predictive Value (NPV) and 95.13% Matthews Correlation Coefficient (MCC). Low rates of inaccurate predictions were highlighted by the False Positive Rate (FPR), False Discovery Rate (FDR), and False Negative Rate (FNR), which were all 3.23% and 1.64%, respectively.

7.4. Nofilt-Noglobal

The nofilt-noglobal filtering method is utilized in this evaluation to assess the classification performance. This review provides a detailed analysis of the model’s effectiveness, focusing on precision, recall, and F1-Score metrics.

The results for each model are detailed in

Table 10. Classification report for four atlases using Base CNN, Quantized CNN, and TFLite Quantized CNN with the nofilt-noglobal filtering method.

Atlas	Class	Accuracy (%)	Macro Avg (%)	Weighted Avg (%)	Support (%)
CC400	Base CNN	95.00	95.00	95.00	122
	Quantized CNN	96.00	96.00	96.00
	Int8 Quantized CNN (Proposed)	97.00	97.00	97.00
CC200	Base CNN	97.00	97.00	97.00
	Quantized CNN	97.00	97.00	97.00
	Int8 Quantized CNN (Proposed)	98.00	98.00	98.00
AAL	Base CNN	97.00	97.00	97.00
	Quantized CNN	97.00	97.00	97.00
	Int8 Quantized CNN (Proposed)	97.00	97.00	97.00
Dosenbach 160	Base CNN	96.00	96.00	96.00
	Quantized CNN	97.00	97.00	97.00
	Int8 Quantized CNN (Proposed)	97.00	97.00	97.00

. Using the nofilt-noglobal filtering approach across four atlases, the classification performances of three CNN models—Base CNN, Quantized CNN, and the proposed Int8 Quantized CNN—are presented in the table. Outperforming or matching the other models, the proposed model obtained the highest overall accuracy of 97% on the CC400 and Dosenbach 160 atlases, and 98% on the CC200 atlas. With a 97% accuracy rate, all models functioned similarly for the AAL atlas. All things considered, the suggested model constantly produced better or comparable results across all atlases. The confusion matrix for the CC200 atlas is illustrated in Figure 12 and in Figure 13 where the loss and accuracy curves are shown.

Since the CC200 atlas achieved the highest accuracy with the proposed model using the nofilt-noglobal filtering method, the performance metrics are detailed in

Table 11. Performance metrics of CC200 atlas with the proposed model in nofilt-noglobal filtering method.

Performance Metrics	Results (%)	Performance Metrics	Results (%)
Test Accuracy	98.00	FPR	0.1
Sensitivity	96.72	FDR	0.1
Precision	99.98	FNR	3.28
Specificity	99.98	F1 Score	98.36
NPV	96.83	MCC	96.67

.

The CC200 atlas’s performance metrics with the nofilt-noglobal filtering technique are as follows: The model performed well overall, with a test accuracy of 98.00%. The results showed that the specificity was 99.98%, which demonstrated a good capacity to accurately identify negative cases, and the sensitivity was 96.72%, which indicated a great ability to detect positive cases. Recall and precision were well balanced, with the F1 Score coming in at 98.36% and the remarkable precision of 99.98%. With a Negative Predictive Value (NPV) of 96.83%, it was evident that the prediction of negative cases was reliable. A comparatively low rate of missed positives was shown by the False Negative Rate (FNR), which was 3.28%, and the extremely low False Positive Rate (FPR) and False Discovery Rate (FDR), both of which were 0.1%.

Across the four filtering methods examined, the CC200 atlas consistently achieved the highest accuracy of 98%. This exceptional performance underscores the effectiveness of the CC200 atlas in enhancing model accuracy, particularly when combined with the proposed model. The superior accuracy of CC200 from all filtering methods highlights its suitability for this classification task compared to the other atlases and other models used. Additional analysis of the Flash Occupancy of models in each pipeline of every filtering method shows that, in comparison to Base and Quantized CNNs, the Int8 Quantized CNN significantly lowers memory requirements for all atlases. Each time, the Int8 Quantized CNN shows notably faster prediction speeds in terms of Average Inference Time. In comparison to its counterparts, the proposed model is significantly more energy-efficient, as evidenced by the Average Power Consumption statistics. These results highlight the higher efficiency of memory usage, speed, and energy consumption of the Int8 Quantized CNN model in different atlases. Figure 14 shows the illustration of these metrics. The values of flash occupancy, inference time, and mean power consumption are consistent across all filtering methods, as the parameters of the model differ based only on the pipeline.

7.5. Computational Complexity Analysis of Local Machine

Table 12. Computational performance metrics of different atlases on local machine.

Algorithm (Atlas)	Training Time (s)	Testing Time (s)
Base CNN (CC200)	75	15
Quantized CNN (CC200)	57	11
Int8 Quantized CNN (CC200)	40	8
Base CNN (CC400)	65	13
Quantized CNN (CC400)	45	9
Int8 Quantized CNN (CC400)	30	6
Base CNN (AAL)	70	14
Quantized CNN (AAL)	52	10
Int8 Quantized CNN (AAL)	35	7
Base CNN (Dosenbach 160)	70	14
Quantized CNN (Dosenbach 160)	50	10
Int8 Quantized CNN (Dosenbach 160)	38	7

shows the computational performance measures, specifically, the amount of time for training and testing, for several atlases. The metrics for Base CNN, Quantized CNN, and Int8 Quantized CNN are reported using four different atlases: CC200, CC400, AAL, and Dosenbach 160. Unlike the data shape or model architecture, the filtering method does not influence these results, therefore making the comparison solely dependent on the atlas employed. A consistent pattern is observed from the Base CNN to the Int8 Quantized CNN results in reduced training and testing durations for all atlases. This implies that the optimization of model performance, in relation to computing, is greatly enhanced by the use of quantization techniques, thereby making it more desirable for implementation in situations when computational resources are constrained.

7.6. Computational Complexity Analysis of Raspberry PI

Flash Occupancy: The quantity of memory that the models require is referred to as flash occupancy. All atlases show comparable flash occupancy values for the Base CNN and Quantized CNN. The flash occupancy for the Base CNN and the Quantized CNN in the CC200 atlas is approximately 30,770 KB and 30,881 KB, respectively. The flash occupancy dramatically decreased to 2057 KB via the Int8 Quantized CNN. The Base CNN’s value for the CC400 atlas is 11,117 KB, the Quantized CNN’s is 11,960 KB, and the Int8 Quantized CNN’s is 983 KB. The Base CNN has 10,400 KB, the Quantized CNN has 10,490 KB, and the Int8 Quantized CNN has 872.3 KB according to the AAL atlas. The Int8 Quantized CNN takes 167 KB of storage for the Dosenbach 160 atlas, while the Base CNN and Quantized CNN take roughly 19,920 KB and 20,003 KB, respectively.

Average Inference Times: The average inference time calculates how long it takes the models to provide predictions. The Base CNN and Quantized CNN for the CC200 atlas take about 36,308 ms and 36,439 ms, respectively, while the Int8 Quantized CNN takes much less time—2427 ms. In the CC400 atlas, the Int8 Quantized CNN takes 119.94 ms, the Quantized CNN takes 14,112 ms, and the Base CNN takes 13,118 ms. Inference times of 12,272 ms for the Base CNN, 12,378 ms for the Quantized CNN, and 1029.314 ms for the Int8 Quantized CNN are displayed by the AAL atlas. The Base CNN and Quantized CNN for the Dosenbach 160 atlas take about 23,505 ms and 23,603.54 ms, respectively, whereas the Int8 Quantized CNN takes 197.06 ms.

Average Power Consumption: The models’ average power consumption during inference [42] is shown by this metric. Our proposed end-to-end setup makes use of a Raspberry pi 4 system, and a 2600 mAh battery bank. The energy consumption $\left(E\right)$ for each inference can be calculated using $E=I\times V_{in}\times t$, where we represent the mean consumed current, $V_{in}$ is the supplied voltage, and t is the inference time. Base CNN uses about 162,157 mJ, Quantized CNN uses 163,360.49 mJ, and Int8 Quantized CNN uses 10,819.82 mJ for the CC200 atlas. The Base CNN’s power usage is 58,586.59 mJ, the Quantized CNN’s is 63,268.4 mJ, and the Int8 Quantized CNN’s is 5200.07 mJ, according to the CC400 atlas. The Base CNN has 55,016 mJ, the Quantized CNN has 55,492.1 mJ, and the Int8 Quantized CNN has 4614.467 mJ, according to the AAL atlas. The Base CNN consumed 105,376.8 mJ of electricity, the Quantized CNN 105,815.87 mJ, and the Int8 Quantized CNN 883.43 mJ, according to the Dosenbach 160 atlas.

Table 13. Computational performance metrics of different atlases on Raspberry Pi 4.

Algorithm (Atlas)	Inference Time (ms)	Flash Occupancy (KB)	Average Power Consumption (mJ)
Base CNN (CC200)	36,308	30,770	162,157
Quantized CNN (CC200)	36,439	30,881	163,360.49
Int8 Quantized CNN (CC200)	2427	2057	10,819.82
Base CNN (CC400)	13,118	11,117	58,586.59
Quantized CNN (CC400)	14,112	11,960	63,268.4
Int8 Quantized CNN (CC400)	119.94	983	5200.07
Base CNN (AAL)	12,272	10,400	55,016
Quantized CNN (AAL)	12,378	10,490	55,492.1
Int8 Quantized CNN (AAL)	1029.314	872.3	4614.467
Base CNN (Dosenbach 160)	23,505	19,920	105,376.8
Quantized CNN (Dosenbach 160)	23,603.54	20,003	105,815.87
Int8 Quantized CNN (Dosenbach 160)	197.06	167	883.43

shows the computational performance metrics of different algorithms on Raspberry Pi 4.

8. Limitations and Future Work

While this study demonstrates the potential of the Int8 Quantized CNN model ASD diagnosis, several limitations must be addressed. First, the study relied exclusively on the ABIDE-I dataset, limiting the generalizability of the results to other datasets. Future work could explore the use of the ABIDE-II dataset or other neuroimaging databases to validate the model’s robustness across different populations. Additionally, the study focused solely on fMRI data; integrating other types of neuroimaging data, such as EEG or diffusion MRI, could provide a more comprehensive understanding of ASD-related biomarkers.

Furthermore, although the Int8 Quantized CNN model showed superior performance in terms of accuracy, power consumption, and memory efficiency, it is important to consider that quantized models may sometimes suffer from reduced performance on larger or more complex datasets. Future research should examine the scalability of the model and its ability to maintain high accuracy with larger datasets or in real-time clinical settings. Lastly, while the power consumption and memory footprint of the model were minimized, further optimization could be explored to reduce these metrics even more, especially for deployment on other low-power devices or in edge computing scenarios. Future work could also investigate the potential of decentralized FL to ensure data privacy and security when deploying these models in multi-institutional setups. This approach would address privacy concerns related to sharing sensitive medical data while maintaining high model performance.

9. Conclusions

This study used the NIAK pipeline to preprocess fMRI slices from the ABIDE dataset. After preprocessing, feature vectors were extracted using a tangent function. Four filtering methods were included in the NIAK pipeline: filt-global, filt-noglobal, nofilt-global, and nofilt-noglobal, which were assessed using CC200, CC400, AAL, and Dosenbach 160 brain atlases. Three models were used to evaluate these filtering methods: Base CNN, Quantized CNN, and Int8 Quantized CNN. Using the Int8 Quantized CNN model, in all the filtering methods with the CC200 atlas, produced the maximum test accuracy of 98% in the detection of ASD. Notably, in terms of accuracy, the Int8 Quantized CNN model consistently performed better than the Base CNN and Quantized CNN models across all filtering techniques. In-depth examinations of the average power consumption, average inference time, and flash occupancy were also performed. Per the findings, the Int8 Quantized CNN model outperformed the other models in every metric evaluated including memory efficiency, prediction speed, and energy consumption. This thorough analysis demonstrates how the Int8 Quantized CNN model may achieve great accuracy and efficiency, especially when used in conjunction with the CC200 atlas. The study emphasizes how crucial it is to select the ideal preprocessing strategies and model combinations in order to improve the accuracy of ASD identification from fMRI data. All things considered, the results indicate that the Int8 Quantized CNN model is a viable way to increase diagnostic accuracy while preserving computing economy when combined with the best possible filtering and atlas selection in the detection of ASD.