Predicting Alzheimer's Disease Using a Modified Grey Wolf Optimizer and Support Vector Machine

In this section of the suggested process, the microarray AD data set is loaded in its raw form, among other crucial steps. Then, as shown in Figure 1, Gene selection techniques employ the Min-Max strategy to standardize data, optimization gray wolf optimizer with crossover, and classification with a Support Vector Machine. The Gene Expression Omnibus (GEO: GSE63060 and GSE63061) of the National Center for Bioinformatics (NCBI) was the source of the data, which is publicly accessible. Next, we created the AD dataset by merging two datasets into one. The Alzheimer's disease dataset including 16382 genes and 569 samples, comprising 245 Alzheimer's disease and 142 mild cognitive defect patients (MCI). The microarray usually is used for representing the genetic datasets. In other word, the contents of such datasets are thousands of genes, which not all of them are important or relevant to the classification process [12]. The size of the dataset and the nature of the genes as well effect on the performance of the classification models – i.e., the classification accuracy, and on the time of learning process. Meaning that, these two factors could cause an over-fitting to the training process, which confuses the learning procedures. Therefore, designing an efficient gene selection method is an important preprocessing step, which selects the best minimal number of genes.

The preprocessing for the data is a bit noisy generated by microarray technologies. The dataset needs to be uniform to reduce the variation in expression measurements. The process of normalizing the data collection can be normalized using the min-max method. Gene expression values are calculated so that each gene's lowest value is zero and its greatest value is one.

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Figure 1. Proposed methods (CGWO-SVM)

2.1 Gene selection methods

A set of microarray tests indicates the varied expression from multiple genes in many contexts. A dimensionality of microarray data is an issue because most of the genes are unrelated to the categorization process. As a result, gene selection approaches are effective in the 182 Control Subjects (CTL). Data dimensionality can be reduced by removing redundant and unnecessary genes [13]. The goal of the gene selection approach is to identify the small number from genes that generates good results, which can AD's computational expenses will be reduced, and Its effectiveness will increase categorization. In this study, a variety of gene selection techniques, including Information Gain (IG), were used to find helpful genes that are directly associated with illness diagnosis [14].

A basic purpose from gene selection approaches is to reduce the dataset's dimensionality in computing space. Because genes are frequently unimportant, it is a method for choosing a subset of genes from a larger dataset. Whatever the machine learning techniques, these procedures are normally carried out prior to the use of gene selection based on performance measures and machine learning methods. Gene selection method IG was a technique for identifying a selection of genes used in this study's categorization right away.

2.2 Information Gain (IG)

Genes that are less helpful in creating a solid predictive model could be eliminated through effective gene selection. Also, genes unrelated to the target variable must be eliminated because they may increase computational costs and hinder the model from performing at its best [15]. The most crucial gene using the Information Gain (IG) method. Differences between entropy and conditional entropy can be used to assess how important a gene is in a certain category [16]. The ability of the predictor variable to categorize the dependent variable is determined by the IG, a kind of filter-based gene selection [17]. The information theory-based IG technique determines the statistical dependence between two variables [18]. The IG important in calculates the reduction in entropy from the transformation of a dataset. It can be used for gene selection by evaluating the information gain of each variable in the context of the target variable.

The IG between the two variables X and Z is formulated mathematically, as Eq. (1):

IG (X|Z) = H(X) – H (X|Z)         (1)

H(X|Z) is the conditional entropy for variable X given Z, while H(X) is the entropy for variable X. When determining the IG value for an attribute, the conditional entropies for all possible values of that attribute must be subtracted from the target variable's overall dataset entropy [19]. Along with computing the entropy H(X) and conditional entropy H(X|Z) for the probability distribution P, as Eq. (2), and Eq. (3):

H(X) = − ∑x∈X P(x) log2 (x)           (2)

H(X|Z) = − ∑ x∈X P(x) ∑ z∈Z P(x|z) log2(P(x|z))         (3)

2.3 Grey Wolf Optimizer with Crossover (CGWO)

The four sorts of wolves represent the hierarchy of wolves: alpha, beta, delta, and omega. The top, second, the remaining wolves are referred to as omega, while the third, fourth, and fifth wolves are termed alpha, beta, and delta, respectively [20]. When it comes to hunting or optimization in the GWO, alpha, beta, and delta lead. They point out the best places or areas for searching to the other wolves. The alpha, beta, and delta wolves determine the prey's likely position during the iterative search process. The GWO takes into account the hunting, social hierarchy, and searching habits of grey wolves [21]. Because of its decreased unpredictability and different numbers of participants assigned to the global and local search processes, the GWO method can be easily applied and converges quickly. Data indicates that it performs more efficiently than other bionic algorithms including the PSO method. Because of its improved performance, apps have received more attention [22]. The selections of features and bands, parameter approximation, automatic control, power dispatching, multi-objective optimization, and shop scheduling have all been worked on. However, the typical GWO method was created using the grey wolves' placements, which have equal relevance but lack rigorous conformity with their social order [23]. The binary and multi-objective GWO algorithms are examples of recent advancements in GWO algorithms that tend to blend together and maintain their original form when merged with other algorithms. The GWO algorithm can likely be improved if the grey wolves' search and hunt positions also follow the social hierarchy [24], as shown in Figure 2. Because the proposed GWO gene selection technique seeks to determine the optimal feature subset for medical data, we have chosen to use the GWO in this research.

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Figure 2. Hierarchy of grey wolf [22]

The updated version of the Grey Wolf Optimizer (GWO) algorithm in this study contains a new step, it can be found at the conclusion of every loop. Stated otherwise, the initial iteration of the GWO is implemented, followed by the crossover operator's enhancement of the current optimal solution, or alpha. An enhanced version of Grey Wolf Optimizer (GWO) based on crossover operators for enhancing the local search process. The suggested method is known as "Grey Wolf algorithm with Crossover (CGWO)", which is given as follows:

Inputs: Obtain every parameter needed to solve a certain optimization issue.

Initialization: Using the search space, randomly generate each search agent using an uniform distribution method, which depends on the upper and lower bounds for the objective function. The generating method is as follows, in Eq. (4):

$W_i \cdot Position _j=(U-L) * Rand +L$         (4)

where, W_i represents the i^th search agent, Positions_j represents the j^th dimension in each solution, U and L represent the upper and lower boundaries for the search, and Rand represents a random number in range 0 and 1 . It is worth to mention that that $i$ is in range [1, Size], while $j$ is in range [1, Dim]. The values of U and L depend mainly on the nature of the optimization problem.

Determine $W_{ {Alpha }}, W_{ {Beta }}$, and $W_{ {Delta }}$ : In this step, the solution should be sorted ascending to identify the best wolves. If there is a new solution with fitness better than the previous, then keep it as $W_{ {Alpha }}$, otherwise, keep the previous $W_{{Alpha }}$.

Crossover Operator: In the event that the optimal solution from this iteration is the same as the prior one, then, the alpha is updated via crossover it with the beta as these two solutions are the best two solutions found so far.

The type of encoding used in this study is the real encoding, which means there are specific types of crossover operator to be used. In this study, the Blended Crossover (BLS-a). Is utilized for this matter, as follows:

(1) Set P1 and P2 as two parents, where the first parent (P1) denotes the WAlpha, and the second parent (P2) denotes the Wbeta.

(2) Determine Xmax and Xmin, Where Xmax denotes the maximum value between P1 and P2, while Xmin denotes the minimum value between them.

(3) Generate two random solutions as offsprings (C1, C2), in range [R1, R2] where

R1=Xmax+Ia        (5)

R2=Xmin-Ia          (6)

where,

I=R1-R2     (7)

and a randume value∈[0, 1].

(4) Evaluate the new generated offsprings (C1, C2)

(5) Compare the fitness of C1 and C2 with the parents P1, and P2.

(6) Keep the original W Alpha and W Beta and replace the best offspring with the poorest parent, if any, as the new alpha and beta.

2.4 Classifier using Support Vector Machine (SVM)

The SVM is utilized to classify a feature after they have been selected, which allows for a method for extracting characteristics that is both effective and efficient as well as a set of criteria for classifier [25]. A unique hyper-plane depicts the discriminative classification technique SVM [26]. Indicate Figure 3. Due to its excellent precision and ability to interpret data in multiple dimensions [27], many different applications, including bioinformatics, signal processing, and computer vision, make extensive use of the SVM classifier [28].

The SVM excels at addressing the two-class issue. The linear discriminant function's generic formula is represented by as w.x + b = 0. To distinguish the samples between the two groups without using noise, an optimal hyper-plane is used, which is mathematically described in the Eq. (8).

$p i[w \cdot x+b]-1 \geq 0,=1,2, N$        (8)

Then, reduce $\|w\|$ 2 in the Eq. (5). As a result, a Lagrange function's saddle point with Lagrange multipliers $\alpha$ solves an optimization problem.

We denote the ideal discriminant function, as in the Eq. (9).

 $(x)={sign}\{(w * x)+b *\}={sign}\{\sum \alpha i N * i=1 . p (x i *-x)+b *\}$         (9)

Data can be categorized even when they cannot be divided linearly thanks to the Support Vector Machine (SVM), which maps data to a high-dimensional feature space. The data is changed such that the separator can be drawn as a hyperplane when a separator between the various categories is selected. The extreme vectors or points that help create the hyperplane are chosen by the SVM. The approach is referred to as the support vector machine because these extreme situations are known as support vectors. In Figure 3, a decision boundary hyperplane is used to group two distinct categories together.

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Figure 3. Support Vector Machine (SVM) [29]

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Figure 4. Flowchart GWO for tuning SVM (GSVM)

2.5 Grey Wolf Optimizer with Crossover for Support Vector Machine (GSVM)

The main issue with almost all of machine learning models is the over-fitting problem, especially when dealing with high-dimensional datasets. In general, there are two main solutions for such issues, either by reducing the total of genes and keep the most important and relevant subset of features, or, by enhancing the training algorithm, which means tuning the hyper-parameters values if any. The success of any model depends mainly on proper parameterization, and in case of SVM, proper kernel choice [27].

The original version of the GWO has been implemented successfully in developing and solving different optimization problems. However, there is a need to enhance the exploitation ability of the algorithm. Choosing the top three answers is what essentially determines how the GWO is exploited, which are called “W_Alpha”, “W_Beta”, and “W_Delta”.

However, SVM suffers from a simple problem, choosing the kernel require tuning a set of two parameters in order to decrease the chances of over or under-fitting. In order to solve such a problem, an efficient tuning algorithm needs to be developed. An enhancement on GWO's search functionality has been created. A crossover operator decreases the chances of the algorithm of falling in the local optima, because it discovers more regions far from the current best solution once there no new improvements [29].

The CGWO is used for tuning the hyper-plane parameters of support vector machine, to enhance the performance of SVM, this lessens the possibility of over-fitting when a right values to the parameters are found. The main parameters need to be tunned are two only, $\gamma$ and c, therefore the solution representation is simple [30]. The steps of the proposed algorithm are exactly same as Algorithm (CGWO); however, it is utilized for a specific problem, represented with two dimensions only. The final model is called GSVM, which is illustrated in the following flowchart Figure 4.

2.6 Evaluation measures

Common performance indicators, such as classification accuracy and loss, were employed. True Positive (TP), True Negative (TN), False Positive (FP), and False Negative (FN) are four parameters that are used to evaluate the overall prediction ability of a model Eq. (10). This works by looking at the sample numbers and correctly classifying them based on a ratio for the total number of samples tested [31].

Accuracy = TP+TN/TP+FN+FP+TN         (10)

Precision: Is determined by subtracting the false positives from the total of the true positives in the following Eq. (11) [31].

Precision = TP/(TP+FP)       (11)

Recall: The total number of true positives multiplied by the sum of the false negatives and true positives in the following Eq. (12).

Recall = TP/(TP+FN)       (12)

F measure: Recall and precision are used in a formula to determine accuracy, as demonstrated. in the following Eq. (13):

F - measure = 2× (Precision × Recall)/(Precision + Recall)         (13)