The most widely used technique in diagnosing AD is the clinical screening methods, such as brain imaging. At times, the clinical screening methods provide inaccurate results due to technical errors, which eventually delays the treatment. Hence, the research is gradually moving towards molecular data, for instance, microarray data. In the process of finding out differentially expressed genes, thousands of genes are captured and monitored to evaluate the effects of a disease or a treatment (Fung and Stoeckel, 2007). For detecting the expression of hundreds and thousands of genes simultaneously, microarray technology is used widely. In microarray, thousands of genes or DNA sequences are printed in already defined positions. The DNA microarray datasets have vast volumes of genes captured, which might not be relevant to the undertaken domain (treatment/disease) (Huang et al., 2018).

Considering the huge volume of features involved, machine learning-based methods help greatly in classifying AD patients from healthy individuals. Machine learning is a continuously growing area of research, advantageous in many domains, mainly in healthcare. Machine learning algorithms are trained on a set of data, learn from the data, find out the patterns, and predict the future possibilities without much human intervention (Orimaye et al., 2017). It is a part of Artificial Intelligence, assists in data analysis, and automates model building. There are three categories of machine learning algorithm based on the dataset used (Hutter et al., 2019): supervised learning, when the data are structured and attributes are labeled; unsupervised learning, when the data are unstructured and the attributes are unlabeled; and semi-supervised/semi-unsupervised learning, when the data are a combination of supervised and unsupervised categories. Although machine learning algorithms offer great assistance in finding patterns and classification, it is not suitable when the ratio of sample to feature is largely different. In that case, machine learning algorithms will have an overfitting problem.

Artificial Intelligent models have been widely deployed in genetics research (Mahendran et al., 2020). Deep learning approaches remove certain data pre-processing, which is usually deployed in machine learning (Srinivasan et al., 2017; Agarwal et al., 2018; Chakriswaran et al., 2019; Khan et al., 2021a; Khan et al., 2021b; Khan et al., 2021c) (Sanchez-Riera et al., 2018; Srinivasan et al., 2020; Afza et al., 2021; Ashwini et al., 2021; Attique Khan et al., 2021; Khan et al., 2021d; Mamdiwar et al., 2021; Srinivasan et al., 2021). AD is a neurological disorder identified through brain imaging, and there are many works focused on classifying AD through brain images with the help of machine learning or deep learning techniques. For instance, Convolutional Neural Network (CNN) and LeNet architecture is applied on the MRI data to classify AD (Sarraf and Tofighi, 2016a). There are many such works focused on classifying AD through the brain images (Sarraf and Tofighi, 2016b; Farooq et al., 2017; Ji et al., 2019; Ramzan et al., 2020; Tufail et al., 2020), though the imaging data provide inaccurate results at times. Thus, the focus recently is shifted to the molecular dataset such as the Gene Expression and DNA Methylation data, though the problem with such data is the dimensionality. There is a huge number of features, yet very small sample size.

Therefore, the research is focused more on the gene selection techniques to select the relevant features in classifying the AD. For instance, Park et al. (Park et al., 2020) implemented machine learning-based gene selection and a deep learning classifier combining the gene expression and DNA Methylation datasets. Also, the gene pair interaction-based research is done to identify the biomarkers accurately to classify the AD (Chen et al., 2019). Furthermore, there are approaches implemented to detect the possible progression of a dementia to AD with the help of machine learning techniques (Martínez-Ballesteros et al., 2017; Miao et al., 2017). Also, the artificial intelligence approaches are adopted in precision medicine to validate the drugs for AD.

There are four mainly used feature selection techniques, Filter, Wrapper, Hybrid, and Ensemble (Bashir et al., 2019). Filter-based techniques are independent of the classifier model and computationally efficient at times (Acharya et al., 2019). The search for relevant features is isolated completely from the classifier model. The features with the lowest relevance score are eliminated. The filter methods are further classified into univariate and multivariate filters, where univariate treats and evaluates the features individually and multivariate evaluates the feature dependencies. The wrapper methods are implemented as a part of the classification model (Zhou et al., 2018). The feature subsets selected are validated through training and testing datasets. The features with maximum evaluation score are selected for the final classification. The wrapper method’s major drawbacks are as follows: it demands high computational time, it is classifier dependent, and overfitting (Mirzaei et al., 2018).

The ensemble methods simultaneously build different feature subsets and combine the results using standard aggregate methods, such as majority voting, sum rule, mean rule, and weighted voting (Pes, 2019). The exponential growth of technologies across all the domains created a data explosion, which is continuously spreading at an unprecedented speed. The previously mentioned feature selection methods are not suitably designed for a dataset with HDLSS problem and unstable and not robust with changing inputs. Thus, ensemble methods are designed aiming to bring more robustness and stability to the model (Neumann et al., 2017). The main goal of the ensemble model is to attain a better trade-off between stability and predictive performance. The ensemble methods are generally grouped under homogeneous and heterogeneous methods. The homogeneous algorithms use selection algorithm with the varying dataset, for instance, boosting or bagging. The homogeneous ensembles handle the stability issues better. The heterogeneous ensembles implement different selection algorithms with the same dataset. In both cases, the output will be combined to a single feature set, which probably provides an optimal solution (Pes, 2019). Apart from homogeneous and heterogeneous methods, there is another group called the hybrid, which uses different selection algorithms with other datasets.

Though these three feature selection methods are needed, there are various reasons that make them unreliable, unstable, and sometimes ignore the algorithms’ stability. However, there is a fourth method that is focused on much these days, the hybrid method. To solve the issues with respect to filter and wrapper methods, a hybrid method is introduced. It combines two or more feature selection techniques and produces a new method with added benefits. In most cases, wrapper and filter methods are made hybrid by combining their advantages (Hoque et al., 2018; Kollias et al., 2018; Thavavel and Karthiyayini, 2018). This study implemented a feature selection pipeline for selecting relevant genes from the raw Alzheimer’s gene expression dataset. The filter method is simple and ignores the feature dependencies most of the time and also occasionally includes the redundant features. Wrapper methods are at high risk of overfitting and are stuck in the local optima. It is also computationally intensive. Ensemble methods are better than filter and wrapper; however, on the dataset with the High Dimensional and Low Sample Size (HDLSS) issue, it does not perform well. Thus, we desired to implement a feature selection method catering to the HDLSS issue. Hybrid methods are flexible and robust upon high-dimensional data. Also, they offer higher performance and better computational complexity than the filter and wrapper methods. The pipeline consists of a filter method, wrapper method, and unsupervised gene selection method.

mRmR is the most widely used practical statistical approach for feature selection. It was proposed by Peng et al. (Ding and Peng, 2005) initially for classifying patterns. The mRmR method strives to choose the feature subset that is highly relevant to the outcome (target class) and minimally redundant. In simple terms, the features are highly similar to the outcome class (relevance) and dissimilar among themselves (redundancy). The feature selection process in mRmR is carried out by adding the features with the highest feature importance to the feature list at each step (El Akadi et al., 2011; Billah and Waheed, 2020).

The aim of mRmR in gene selection is to select a gene subset, G_s, with {X_m} features that are highly correlated with the target class T (output class). The mRmR involves three steps, finding the relevance, finding the redundancy, and combining the two to get the mRmR feature set.

Step 1

Maximum Relevance

The maximum relevance is calculated using the mean of Mutual Information of all the features in Xm with target class T. The Mutual Information between R and S random variables can be calculated by M I ( R , S ) =   ∑ r ∈ Ω R ∑ s ∈ Ω S p ( r , s ) l o g p ( r , s ) p ( r ) p ( s ) (1) Where.

R—response variable.

S—number of features.

ΩR and ΩS—sample spaces with respect to R and S,

p (r, s)—joint probability density, and

p ()—marginal density function.

The maximum relevance is given by R e l e v a n c e ( G s ) =   1 | G s | ∑ X m ∈ G s M I ( T , X m ) (2) Where MI(T, X_m)—Mutual Information of feature X_m with class T.

Step 2

Minimum Redundancy

The minimum redundancy is calculated with the formula R e d u n d a n c y ( G s ) = 1 | G s | 2 ∑ X i , X j ∈ G s M I ( X i , X j ) (3)

Step 3

Combining the above two constraints

The maximum relevance and minimum redundancy are combined to form the mRmR using the formula max α [ Relevance ( G s ) , Redundancy ( G s ) ] (4) Where α = (Relevance (G_s) − Redundancy (G_s))

PSO is a stochastic, metaheuristic algorithm inspired by the birds’ swarming behavior. From the birds’ flocking behavior, it is understood that each individual is affected by the leader or the global optima and the personal performance or the local optima (Deepthi and Thampi, 2015). The PSO is an optimization technique based on population proposed by Eberhart and Kennedy (Kennedy and Eberhart, 1995), successfully applied in many global search problems. It is considered in many feature selection problems as it is easy to implement, and has reasonable computational time, global search, and fewer parameters.

In PSO, the population is initialized with particles, each having its own position and velocity. The quality of the particles is estimated at each iteration with the help of a fitness function. Every particle in the search space will carry the present position (x_ppos), present velocity (v_pvel), and personal best (y_pbest). After every iteration, the velocity can be updated by v p v e l ( n e w ) = i w v p v e l ( o l d ) + a c 1 r 1 ( y p b e s t − x p p o s ( o l d ) ) + a c 2 r 2 ( y ^ g b e s t − x p p o s ( o l d ) ) (5) Where.

i_w—inertia weight,

a_c1 and a_c2—acceleration constants,

r₁ and r₂—random numbers (range [0, 1]),

v_pvel (old)—present best solution of the particle,

y_pbest—personal best solution of the particle, and

ŷ_gbest—global best solution.

The new position of the particle can be determined by x p p o s ( n e w ) = x p p o s + v p v e l ( n e w ) (6)

The positions and the velocity of the particle are updated at every iteration using the formulas given. The process is stopped when certain minimized fitness function criteria are achieved or a particular predefined iteration is reached. For position and velocity updates, the particles use the knowledge of their own and that of other neighboring particles. The final output represents the optimal feature set. We implemented a wrapper-based PSO with the k-means algorithm as the wrapper method. This wrapper method will aid in overcoming the problem of reaching local optima.

The fitness function for each subset is calculated using the below equation, S u m   o f   S q u a r e d   E r r o r = ∑ x = 1 k ∑ i ∈ C x d 2 ( c x , i ) (7) Where.

k—number of clusters,

i—object in the cluster,

c_x—cluster centroid, and

d—Euclidean distance.

Autoencoder is an artificial neural network with feed-forward processing. The autoencoder consists of input and output with one or more hidden layers, where the number of neurons (features) in the input and output layer is the same (Chicco et al., 2014). The autoencoder’s main aim is to reconstruct the inputs such that the difference between the input and the output is minimized. The learning in autoencoder is compressed and distributed (encoding) (Ferri et al., 2021). The training of autoencoder involves three steps:

1. If “x” is the input and “x̂" is the output, the feed-forward pass is done to estimate the values of all the nodes in the hidden layers after applying the activation function. For an autoencoder with a single hidden layer, the hidden unit vector h_u is given by h u = a f u n c ( W e . x + b i a s e ) (8) Where.

h_u—hidden unit,

a_func—activation function.

W_e—parameter matrix (encoding),

x—input, and

bias_e—bias parameter vector (encoding).

2. Map the hidden representation into the space “x” with the help of the decoding function. The decoding function is given by x ^ = a f u n c ( W d . h u ,   + b i a s d ) (9) Where.

W_d—parameter matrix (decoding) and

bias_d—bias parameter vector (decoding).

3. Calculate back propagation error using the formula M S E ( x , x ^ ) = ‖ x − x ^ ‖ 2 2 = ‖ x − ( W d . h u + b i a s d ) ‖ 2 2 (10)

In Deep Belief Network (DBN), the Restricted Boltzmann Machines are stacked together to form a network (An et al., 2020). RBMs are energy-based generative models with two layers, visible and hidden. Both the layers have nodes connected to each other (Mahendran et al., 2020; Sureshkumar et al., 2020). The major components in RBMs are bias, weight, and activation function (Le Roux and Bengio, 2008; Sekaran and Sudha, 2020). The output is produced after processing with the activation function. We implemented an IDBN with stopping criteria. We chose the hyperparameters using the Bayesian Optimization technique. The Bayesian approach for tuning the hyperparameter keeps past records and verifies the probability to select the next set of parameters. It takes informative decisions in choosing the parameters. The final values for the hyperparameters in IDBN are as follows: learning rate = 0.01, hidden layers = 9, number of nodes per layer = 342, and dropout rate = 0.85. We used the Rectified Linear Unit (RLu) as the activation function. To avoid the overfitting problem, we introduced a stopping criteria strategy. After every 40 epochs, the test accuracy of the last 10 epochs will be compared and checked for convergence, and the training accuracy will also be checked. If both the conditions are satisfied, the learning is ended.

For evaluating the results of the proposed model, we have used the standard evaluation metrics such as Accuracy, Sensitivity, Specificity, and FMeasure.

• Accuracy: It is a simple ratio between the correctly classified as AD and non-AD to the total number of samples.