GAN is a fundamental architecture in machine learning, composed of two primary components: the Generator G(z) and the Discriminator D(x), as shown in Figure 1. The GAN framework is designed for generative tasks, aiming to produce synthetic data that closely resembles real data distributions. The Generator G(z) is responsible for creating new data samples. It takes random noise N(z) as input, typically drawn from a uniform or normal distribution. Through a learned transformation process, the Generator generates data that mimics real training data. This process relies on adjusting internal parameters to produce data samples that are increasingly realistic.

The Discriminator D(x) acts as an adversary to the Generator. Its primary role is to differentiate between genuine data from the training set and data generated by the Generator. The Discriminator evaluates each input and assigns a probability score, indicating the likelihood of the input being real. If an input is genuine, D(x) approaches 1, whereas if it is generated, D(x) tends toward 0. The GAN operates as a two-player minimax game, optimizing the value function V(G, D). The objective function is given in Equation 1:

Here, D(·) provides the probability that a given sample belongs to the training data X. The Generator aims to minimize log(1−D(G(z))), making D(G(z)) as high as possible, essentially fooling the Discriminator into considering G(z) as real data. Conversely, the Discriminator seeks to maximize D(X) and 1−D(G(z)), driving its optimal state toward P(x) = 0.5. In practice, GANs continually refine the Generator to produce data that is indistinguishable from real data, representing a powerful framework for generating synthetic data in various domains.

The architecture of our proposed GAN model for AD detection is illustrated in Figure 2. This model is carefully designed to effectively utilize cognitive features in the detection process. The Generator component of our model is based on an encoder-decoder framework, optimized for processing cognitive features as inputs. The encoder in our model is designed to extract meaningful features from the input data through a series of convolutional layers. The encoder comprises five 2-D convolutional layers, strategically placed to extract local correlations within the input features. A reshape layer is employed to appropriately format the encoded features. These layers progressively downsample the input, capturing local correlations and essential patterns. Each convolutional layer is followed by batch normalization and Leaky Rectified Linear Unit (ReLU) activation functions to stabilize training and introduce non-linearity. Positioned in the middle of the Generator architecture, the BiGRU layers are crucial for capturing long-term dependencies and temporal dynamics in the cognitive features. Each BiGRU layer consists of 2,048 units (1,024 in each direction), enabling the model to learn bidirectional temporal patterns that are significant for early Alzheimer's detection.

The decoder mirrors the encoder's structure but performs the inverse operation. It utilizes deconvolutional (transposed convolution) layers to reconstruct the input data from the encoded features. The skip connections between corresponding layers of the encoder and decoder facilitate fine-grained feature integration, enhancing the model's ability to preserve important information during reconstruction. The Generator's primary function is to produce synthetic data that closely resembles the real cognitive feature data. By transforming random noise inputs through the encoder-BiGRU-decoder pipeline, the Generator learns to create realistic data samples that help augment the training set and improve the robustness of the Discriminator. The input to our DeepCGAN model consists of cognitive features derived from the ADNI dataset. The input to the model is a three-dimensional tensor with a batch size of 32, 50-time steps, and 128 features. Thus, the input shape is [32, 50, 128], specifically tailored to capture the temporal and cognitive aspects critical for Alzheimer's detection.

The data preprocessing steps include normalization and sequence padding to ensure uniform input dimensions. The preprocessing steps include: Normalization: The cognitive features are normalized to ensure consistent scales and improve model training stability. Padding: Sequences are padded to a fixed length (e.g., 50 time steps) to ensure uniform input dimensions across different samples. Handling Missing Values: Features with more than 40% missing values are removed. For the remaining features, missing values are imputed using appropriate statistical methods (e.g., mean imputation). In addition, two BiGRUs layers are thoughtfully inserted in the middle of the Generator architecture, which enhances the model's ability to capture long-term temporal cues from the cognitive data. This integration addresses a critical gap in existing models that primarily focus on neuroimaging data, thereby improving the detection of early AD. The decoder of our model mirrors the encoder's structure and consists of five 2-D deconvolutional layers, also known as transposed convolution layers. Batch normalization is consistently applied following each convolutional and deconvolutional operation. ReLU functions are used as activation functions within the hidden layers, while a sigmoid activation function is applied to the output layer. To facilitate fine-grained feature integration, we have incorporated skip connections within the Generator. These skip connections concatenate the outputs of each convolutional layer in the encoder with the corresponding inputs of the deconvolutional layers in the decoder. This design element enhances the model's ability to capture intricate feature cues effectively.

The Discriminator component, denoted as D, shares a similar structure with the encoder of the Generator. However, a flattened layer is introduced after the fifth convolutional layer to streamline feature processing. Finally, a fully connected dense layer with softmax activation is integrated into the Discriminator to enable classification tasks. Notably, the Discriminator provides two types of outputs, D(y) and Dk(y), with D(y) representing sigmoidal output and Dk(y) signifying linear output, linked by the sigmoid non-linearity function λ(Dk(y)) = D(y). The proposed GAN model for AD detection leverages cognitive features and exhibits a sophisticated architecture, comprising convolutional, deconvolutional, and recurrent layers, skip connections, and a dual-output Discriminator. These design innovations collectively contribute to the model's efficacy in AD detection. Most AD detection models predominantly focus on neuroimaging data, neglecting cognitive features. Our model efficiently incorporates and exploits these underutilized data sources. By including BiGRUs, our model accounts for long-term temporal cues, a crucial aspect often overlooked in AD progression analysis. The Discriminator's architecture, featuring dual output types and skip connections, introduces novel enhancements to improve the model's performance in distinguishing real and synthetic data.

The Discriminator is designed to differentiate between real and synthetic data. It shares a similar structure with the encoder and includes an additional fully connected layer with softmax activation for classification. The dual outputs of the Discriminator, D(y) and Dk(y), provide sigmoidal and linear outputs, respectively, enhancing the model's ability to distinguish between genuine and generated data. The DeeCGAN model is specifically tailored for Alzheimer's detection by focusing on cognitive features and temporal information, which are often underutilized in traditional models. By leveraging the strengths of DeeCGANs in generating realistic synthetic data and incorporating bidirectional GRUs for temporal analysis, our model is able to achieve high accuracy in early Alzheimer's detection.

In the realm of GANs, choosing appropriate loss functions plays a pivotal role in achieving stable training and optimal performance. Our proposed GAN model incorporates and thoroughly investigates two distinct loss functions to determine the one that yields superior results.

We utilized the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset (20), consisting of three distinct stages. The ADNI dataset encompasses cognitive test scores and records of 5,013 instances, corresponding to 819 different AD patients. The cognitive features selected for this study include memory recall tests, attention assessments, and executive function evaluations, which are clinically relevant as they have been shown to be significant indicators of early cognitive decline associated with AD. Patients visited the clinic multiple times during clinical trials, resulting in new cognitive test scores generated and stored as additional records in the dataset for each visit. Among these records, there are 1,643 belonging to cognitively normal individuals and 3,370 related to AD patients. However, the dataset exhibited missing values and underwent initialization through an Iterative Imputer technique to impute the missing values using a round-robin method. This ensures that the most clinically significant features are retained and accurately represented in the dataset. The irrelevant features were removed during the data cleaning and preprocessing.

In the ADNI1 dataset, each record comprises 113 features. The data includes various cognitive assessments (e.g., MMSE scores, ADAS-Cog scores), biomarkers (e.g., cerebrospinal fluid biomarkers, amyloid-beta levels), and potentially neuroimaging features (e.g., MRI and PET scan data). These features are chosen for their relevance in assessing cognitive decline and AD progression. The input data is organized as a temporal sequence, capturing changes in cognitive features over time. This is crucial for modeling the progression of AD, which involves gradual cognitive decline. The dataset was divided into 80% for training and 20% for testing, resulting in 5,000 samples for training and 1,250 samples for testing. Some of these features had excessive missing values, prompting the removal of those with more than 40% missing values. The remaining features underwent initialization through an Iterative Imputer technique to impute the missing values using a round-robin method. After preprocessing, the final dataset comprised 4,500 samples. Additionally, the dataset contained features with varying value ranges, which were normalized to a range of 0–1 using the min-max scaling method. Primary filtering of cognitive features was performed using Pearson's correlation coefficient to identify those most correlated with AD diagnosis. Features with a correlation coefficient above a predefined threshold were selected for further analysis. Performance evaluation utilized metrics including Accuracy, Sensitivity, and F1-Score, which are computed by Equations 9, 10, and 11, respectively.

Here, TP represents True Positives, TN stands for True Negatives, FP is False Positives, and FN represents False Negatives.

The DeepCGAN model architecture for AD detection incorporates carefully chosen parameters to optimize performance across multiple metrics. The feature maps in the Generator's encoder are structured with fixed sizes of 16, 32, 64, 128, and 256 in successive convolutional layers, with specific kernel sizes and strides tailored to enhance feature extraction efficiency. The kernel size is set to (1,3) for the first 2D-Conv layer and (2,3) for subsequent layers, all with a stride of (1,2). Convolutional layers are utilized for their strength in extracting local patterns and hierarchical features from the cognitive data, which are essential for distinguishing subtle differences between normal and AD-affected individuals.Similarly, the BiGRU layers are configured with 2,048 units, with 1,024 units in each direction, split into forward and backward directions, operating over a fixed time step of 50. The BiGRUs were selected for their ability to capture long-term dependencies and temporal patterns in cognitive data, which are crucial for accurately modeling the progression of AD over time. For the Generator's decoder, these parameters are inversely set to reconstruct the input features faithfully. Moreover, the Discriminator (D) employs deconvolutional layers with gradually increasing feature maps from 4 to 64, designed to discriminate between real and generated samples effectively. The proposed AD detection models, incorporating these two distinct losses, undergo training and optimization using the Adam optimizer for 1,000 epochs, with a learning rate of 0.005 and a batch size of 32 samples. The combination of convolutional layers and BiGRUs in the DeepCGAN architecture leverages both spatial and temporal features, providing a robust framework for early AD detection by capturing complex patterns in cognitive data that simpler architectures might miss. This setup ensures robust optimization and convergence of the DeepCGAN model. To assess the performance of our proposed model, we conducted a comprehensive comparison with several other models, including DeciTree, RanForest, KNN, Linear Regression (LR), SVM, DNN, AdaBoost, and Adaptive Voting, utilizing various metrics such as Accuracy, Precision, Recall, and F1-Score.

Table 1 displays the results obtained from our proposed DeepCGAN model along with other DL models trained on similar cognitive features for detecting cognitive normal and AD. We measure the model's performance using Accuracy, Precision, Recall, and F1-Score as evaluation metrics. Notably, the results demonstrate that our proposed DeepCGAN outperforms all other competing models in terms of these metrics. The DeepCGAN achieved an Accuracy of 97.32%, Precision of 95.31%, Recall of 95.43%, and F1-Score of 95.61%, respectively. In contrast, the lowest-performing model, linear regression, achieved only 82.05% Accuracy, 81.83% Precision, and 81.45% F1-Score.

To highlight the improvements made by our proposed model, we chose linear regression as a reference model. DeepCGAN substantially improved Accuracy by 15.27%, Precision by 13.48%, and F1-Score by 14.16% compared to linear regression. Moreover, when compared to the second-best model, Adaptive Voting, DeepCGAN showed a 3.40% improvement in Accuracy. It also outperformed DNN and Random Forest by 6.79 and 6.99% in Accuracy, respectively, which is a significant performance gain. Furthermore, our DeepCGAN model demonstrated substantial improvements in Recall and F1-Score compared to competing models. The Recall increased from 88.93% (DeciTree) to 95.43% with DeepCGAN, and the F1-Score increased from 86.31% (AdaBoost) to 95.61%. These results signify the superior ability of DeepCGAN to correctly identify AD cases while minimizing false negatives. The errors are vastly improved over other models. To highlight the effectiveness of the proposed model, we present the overall improvements depicted in Figure 3. The linear regression is the reference model that has achieved the lowest performance among DL models. Figure 3 indicates the best performance of the proposed DeepCGAN.

Our DeepCGAN model was trained and optimized using two different loss functions: Wasserstein and Relativistic loss. The Wasserstein loss function was chosen for its ability to provide a smoother gradient, thereby stabilizing the training process. This stability is particularly important for AD detection, where the model must accurately learn from subtle variations in cognitive data. Figure 4 presents the confusion matrices for both losses, revealing that the Wasserstein loss function results in better performance. Figure 4A illustrates the predicted labels when trained with Wasserstein loss, while Figure 4B shows the outcomes with Relativistic loss. It is evident that the model trained with Wasserstein loss provides more accurate predictions.

To further assess the performance, we compared the model's Accuracy on training and validation data. The Wasserstein loss outperformed the relativistic loss by a significant margin, indicating faster convergence and better Accuracy. Figure 5 displays the loss curves over 1,000 epochs, illustrating the superior performance of the DeepCGAN model in achieving its detection task. We also evaluated the Area Under the Curve (AUC), which measures the model's ability to differentiate between labels. DeepCGAN exhibited higher AUC values compared to models trained with relativistic loss, further confirming its superior discriminatory capability. Figure 6 illustrates the AUC curves for both loss functions.

In this subsection, we compare our proposed DeepCGAN model with state-of-the-art (SOTA) models in the literature, including AlexNet (31), VGG-16 (32), GoogleNet (33), and ResNet (34), using cognitive features from the ADNI dataset. This comparison aims to benchmark the performance of DeepCGAN under similar experimental settings and datasets. Table 2 presents the results in terms of Accuracy, Precision, Recall, F1-scores, and AUC.

DeepCGAN surpassed all SOTA models in terms of Accuracy, achieving an Accuracy of 97.32%, which is a 5.59% improvement over GoogleNet. Similarly, Precision improved from 90.20% (GoogleNet) to 95.31%, reflecting a 5.11% boost in Precision. When compared to AlexNet, DeepCGAN demonstrated a 3.57% increase in Accuracy. Furthermore, DeepCGAN achieved the highest AUC among all models, with a 99.51% AUC, outperforming ResNet by 4.53% and VGG-16 by 4.55%, highlighting its superior discriminatory power. Regarding Recall, DeepCGAN exhibited substantial improvements over SOTA models except for ResNet, where the results were marginally lower. Specifically, the Recall increased from 92.28% (AlexNet) to 95.43% with DeepCGAN. The F1-Score achieved with GoogleNet was 91.82%. DeepCGAN's superior performance can be attributed to its novel architecture, which combines convolutional layers for effective feature extraction and BiGRUs for capturing temporal dependencies. This dual approach enables the model to detect subtle changes and patterns in cognitive data more accurately than models that rely solely on neuroimaging data or simpler architectures. Additionally, the use of GANs for data augmentation increases the dataset's size and diversity, enhancing the model's generalizability and robustness. The core innovation lies in expanding the cognitive features dataset and enhancing its diversity through GANs.

DeepCGANs significantly enhance Alzheimer's detection due to their ability to generate realistic synthetic images, crucial for augmenting limited MRI and PET scan datasets. Their deep convolutional layers extract complex features, improving diagnostic accuracy by capturing subtle disease indicators. Adversarial training refines synthetic images iteratively, ensuring they closely resemble real patient data. DCGANs' adaptability across imaging modalities and superior performance in comparative evaluations underline their transformative role in improving diagnostic accuracy and clinical outcomes for AD.

In this section, we compare our proposed DeepCGAN model with a recently reported technique by Gill et al. (35) that used cognitive features for AD detection. Both studies utilized the same ADNI dataset, and the results are presented in Table 3. Our proposed DeepCGAN model outperformed the model proposed by Gill et al. (35) and Adaptive Voting using cognitive features from the ADNI dataset. DeepCGAN achieved the highest Accuracy of 97.32%, representing a 15.52% improvement over Adaptive Voting and a 3.4% improvement over Gill et al.'s technique for early AD detection. This improvement is due to its ability to generate synthetic data that closely resembles the actual cognitive features, thus reducing overfitting and improving the model's ability to generalize to new, unseen data.