The basic architecture of the proposed work is shown in Fig. (1). The proposed work consisted of three models. Firstly, the pre-trained AlexNet model was trained on MRI scans of different diseases related to the brain, like dementia, tumor, encephalitis, Parkinson’s, Alzheimer’s, etc. This was done due to the lack of training datasets available to train our machine. In the second phase, the features of the existing pre-trained model were transferred to a new AlexNet model. In the third phase, images were taken from the ADNI dataset to train and fine-tune our model, which has been designed specifically for Alzheimer’s disease prediction. The process is described in detail in the latter part of the paper.

In this study, the convolutional neural network (CNN) classifier has been built using the MRI images from the Alzheimer's Disease Neuroimaging Initiative (ADNI) [1]. ADNI is actually an ongoing study that was started in 2004. It aims at comprehending the diagnostic and prognosticative terms of Alzheimer's disease-specific biomarkers. The information enclosed an overall 715 structured MRI scans out of both ADNI1 as well as ADNI2 phases, having 320 AD cases and 395 normal controls. Then, the data were acquired for the dataset with the previously mentioned description in the DICOM MRI format. For further investigation of the information, it was required to convert the data into NIfTI format so that we can further work on it and provide it to the accessible neuroimaging toolbox, where further preprocessing will be applied to the data.

The raw image data require preprocessing, and for that, statistical parametric mapping (SPM) is used. SPM is basically a statistical technique utilized for evaluating cognitive activities documented throughout neuroimaging tests. The statistical parametric mapping software system is additionally used for spatial standardization, smoothing, and statistical analyses of the parametric images. The original magnetic resonance images were initially stripped of the skull and segmented using the segmentation algorithm based on the probability mapping and then standardized using affine registration on the International Brain Mapping Template. The setup comprised bias, noise, and overall intensity calibration. The traditional way of preprocessing would have created image records having 122X145X122 standardized size. The removal of the skull and normalization offered equivalence within the images by simply adjusting the brain's initial image into normal image space and positioning the same brain substructures with the image's coordinates alongside similar images of different participants. Fig. (2) presents the preprocessing of MRI skull images.

Fig. (1). System architecture.

Fig. (2). Image pre-processing; (a) skull stripping, (b) template matching, (c) white matter, grey matter, CSF extraction and selection.

In this research, AlexNet architecture has been used as a CNN classifier. AlexNet is a popular and precise CNN architecture that has made its name in machine learning and AI, notably in image processing. The basic advantage of this architecture is that it has a pooling layer after every convolutional layer, and we can modify the convolution layer as it does not have a fixed size, which gives us more control over the CNN. It consists of 11X11, 5X5, and 3X3 convolutions, max pooling, dropout, data increase, activation of ReLU, and dynamic SGD. After each convolutional and fully connected layer, ReLU activations are attached.

We looked at two different architectures, AlexNet and GoogleNet, because they have been found to be successful for similar issues [10, 11]. AlexNet was at par with GoogleNet. In both of the trained architectures, 25000 random images of the test dataset were used to compare the accuracy of the two architectures. Then the confusion matrices and the accuracy for each test dataset were calculated for both the architectures.

AlexNet's input is a 224x224x3 RGB image that passes through the first convolution layer with 96 feature maps or filters with a size of 11X11 and a 4 stride. The image is now 55x55x96 in size. The AlexNet then performs a maximum layer of pooling or sub-sampling using a 3 subterranean filter and a 2-step process. The final image will be smaller, measuring 27x27x96 in dimensions. The primary variation in our AlexNet versus the standard AlexNet comes in the second layer. The second convolution layer receives data coming from the first convolution layer, and then screens it with 256 feature maps of dimension 5X5X64. Subsequently, the next convolution layer is connected to the data coming from the second convolution layer by 384 feature maps of dimension 3X33X192. The next layer of convolution has 384 feature maps of dimension 3X3X84, and the fifth layer of convolution has 256 feature maps of dimension 3X3X56, as shown in Fig. (3). These are the ideal dimensions for feature extraction purposes in these types of images to train them properly. In the sixth layer, the output is flattened through a fully connected layer in order to accommodate all the data coming from AlexNet architecture; in our system, we have done some minute adjustments, i.e., a fully connected layer is included with 985 neurons in the base model with a softmax layer to deal with negative loss.

Fig. (3). AlexNet architecture.

Fig. (4). Different activation functions.

An artificial neuron's activation function is the part of the neuron that produces an output in response to inputs. In AlexNet, ReLU is used as an activation function instead of Tanh and sigmoid. The ReLU activation function is used to add non–linearity and different activation functions, as shown in Fig. (4).

The hyperbolic tangent function is defined in Eq. (1):

(1)

The sigmoid function is defined in Eq. (2):

(2)

These functions are slow to train. Because the ReLU does not activate all the neurons at once, it has an advantage over other activation mechanisms. It means that in the ReLU operation, if the input is negative, it converts it to zero and, therefore, the neuron does not get activated. Rectified linear unit (ReLU) is faster to train, and can be done using Eq. (3):

(3)

It enhances the training speed at the same accuracy by 6 times.

The optimizer we tended to use was the Adam optimizer; one of the algorithms that work well across a wide variety of deep learning architectures is the adaptive moment estimation or Adam optimization algorithm. Adaptive moment estimate (Adam) [14] calculates for each parameter the adaptive learning rates. It is also referred to as a solver. The falling averages of the past and past square gradients, mt and vt, can be calculated using Eqs. (4 and 5):

(4)

(5)

The method's names, mt and vt, represent estimates of the gradients' first moment (the mean) and second moment (the uncentered variance), respectively. They balance out these biases by computing bias-correction, first, and second moment estimates using Eqs. (6 and 7):

(6)

(7)

We used these to update the parameters in order to give the update rule for Adam, as presented in Eq. (8):

(8)

As we know that the network's end layers tend to be much more precise to the class features in the initial dataset and that the pretrained AlexNet dataset varies from the initial dataset, to tackle this situation, we have to replace the last classifying layer and also calibrate all the classifiers. To solve this problem, first, the fully connected layer is back propagated and its weights are kept in the earlier convolution layer.

The final layer of convolution and the classifiers formulated are calibrated on the observation that the network’s end layer contains more precise characteristics for the dataset. We, however, cannot discover that only calibrating it for the fully connected layer will solve all the problems. Subsequently, we have carried out some trials to adjust the final output layer by the use of the last convolution layer. Mainly because contorting the initial parameters can be disastrous for the network, in our research, the learning rate or we can say the weight-controlling parameter that we have used was 1e−4; the learning rate was increased for enhanced learning and fine-tuning, which showed better performance than the standard learning rate.

In our experiment, with learning rate 1e-3, the max validation accuracy achieved was 80% and the max training accuracy was 85%, as shown in Fig. (5a), and when we increased the learning rate to 1e-4, we achieved max validation accuracy as 82% with corresponding training accuracy as 96.5%, as shown in Fig. (5b).

Fig. (5). Analysis of learning rate; (a) with learning rate 1e-3, (b) with learning rate 1e-4.

Additionally, as mentioned earlier, the improper initialization of the network parameter could impact the performance of the network. But to set the initial parameter uniformly, there are various algorithms available, and we have used the Xavier initialization algorithm based on some research. Support vector machine (SVM) was used for the final classification and AlexNet as an extractor.

A small dataset limits the use of a complex neural network as it would overfit the training data, while transferring learning shows good performance by using a pre-trained network (e.g., AlexNet) to extract features or fine-tune parameters. After finishing AlexNet's higher layer, we achieved 86 percent accuracy in the AD/normal classification. We ensured that the weights were not too small as well as not too large to accurately propagate the signals. Initialization is important for a small network with a limited number of layers; thus, a significant variance can be there while initializing the weights for distribution having zero mean and variance using Eq. (9):

(9)

Where, n_in and n_out are, respectively, the numbers of inputs and outputs in the layer.

For the evaluation metrics, the F1 score, accuracy, precision, recall, and false negative scores are used, in addition to the confusion matrix. True positive and true negative values are stored in a form that resembles a table in a confusion matrix. There are four parts to it; in the first scenario, also known as true positive (TP), the data are verified to be accurate. The second type is a false positive (FP), which involves the values that have been found to be false but are actually true. False negatives (FN) constitute the third category, in which the value actually being positive is found. The fourth one, true negative (TN), genuinely determines the negative value.

Eq. (10) defines accuracy as the proportion of cases that meet the criteria for the dataset divided by the total number of occurrences.

(10)

Precision is defined as the average likelihood of obtaining pertinent data in Eq. (11).

(11)

Recall is defined as the typical condition likelihood of full recovery and is represented by Eq. (12).

(12)

After determining the precision and recall of the classification problem, the F-measure was calculated by combining the two scores. The traditional F-measure computation is shown in Eq. (13).

(13)

To perform classification using SVM, we performed the experiment using different layers of output features. Previous studies [11-13] have suggested that generic characteristics are usually extracted from lower layers. Our results have indicated that these generic features are not good for SVM classification (the accuracy is 55%), while the features in the higher layers contain more specific characters that can be distinguished by a linear SVM (the accuracy is 85%). Table 1 presents performance parameter values for different datasets. Table 2 compares the suggested method with current methods in a comparative analysis. Our method has yielded superior outcomes to those already achieved. The effectiveness of the proposed model has also been compared to current models, as shown in Table 2, and the suggested model has outperformed the existing models in terms of accuracy. Table 2 illustrates how our model's accuracy compares to that of the models proposed earlier [25-28] at 82.22%, 81%, 74% and 86.47%, respectively. Fig. (6) displays the graphical comparison of the proposed method with state-of-the-art methods.

We have presented two basic CNN architecture models, 2D-CNN and 3D-CNN, for the application of multi-class and binary medical image classification algorithms. These models have been assessed based on the accuracy measure by contrasting their performance to other cutting-edge models, as indicated in Table 1, and a comparison of the proposed work with state-of-the-art methods is tabulated in Table 2.

Fig. (6). Visual comparison of the suggested approach to the state-of-the-art methods.

Fig. (7). The confusion metric and normalized confusion metric for the proposed models.

The number of patients diagnosed with NC and AD and the number of patients diagnosed with MCI are all depicted in the confusion matrix. It shows the number of patients diagnosed as MCI as well as others. The model has also been accompanied by the numerical, reciprocal, and normalized confusion matrices, as depicted in Fig. (7).