Enhancement of Classifier Performance Using Swarm Intelligence in Detection of Diabetes from Pancreatic Microarray Gene

1. Introduction

According to the International Diabetic Federation (IDF) Diabetes Atlas (2021), approximately 10.5% of the worlds adult population aged 20-79 years has diabetes, with almost half of them being unaware of their condition. The projections indicate that by 2045, the number of adults living with diabetes worldwide will increase by 46% to reach approximately 783 million, which corresponds to around 1 in 8 adults [1]. Type 2 II diabetes accounts for over 90% of all diabetes cases and is influenced by several factors, including socio-economic, demographic, environmental, and genetic factors. The rise in type 2 diabetes were attributed to urbanization, an aging population due to increase in life expectancy rate, declining physical activity levels, and increasing rates of overweight and obesity. Address the impact of diabetes, preventive measures for type 2 diabetes and early diagnosis and proper care for all types of diabetes are crucial. These interventions can help individuals with diabetes prevent or delay complications associated with the condition.

According to estimates from 2019, approximately 77 million adults in India were affected by diabetes [2]. Unfortunately, the prevalence of Type II diabetes in the country is rapidly escalating. In 2045, the number of adults living with diabetes in India could reach a staggering 134 million. Particularly the young age community of below 40 will be affected at Type II diabetes. Several risk factors like genetic predisposition, sedentary lifestyles, unhealthy dietary habits, obesity, urbanization, and mounting stress levels. India’s Southern, urban, and northern regions exhibit higher rates compared to eastern and western regions [3]. Many cases are undiagnosed until complications arise. Diabetes continues to be the seventh leading cause of death in India, taking a toll on both human lives and the economy. It is estimated that diabetes costs the Indian economy approximately $100 billion annually [4].

1.1. Genesis of Diagnosis of Diabetes Through Microarray Gene Technology

Developing accurate and efficient methods for detecting type II diabetes mellitus can lead to early detection and intervention. By analyzing microarray gene data, it becomes possible to identify specific genetic markers or patterns associated with diabetes[5]. This opens opportunities for personalized medicine, where treatment plans can be tailored based on an individual's genetic profile, leading to more targeted and effective interventions. Developing robust and reliable methods for diabetes detection from microarray gene data can be integrated into existing healthcare systems[6]. Exploring novel dimensionality reduction techniques, classification algorithms, and feature selection methods, as well as integrating other omics data to further enhance the accuracy and reliability of diabetes detection methods. The research could advance the state of the art in machine learning[7].The proposed method could be used to detect other diseases that are characterized by changes in gene expression.

1.2. Review of literature

Diabetes mellitus (DM) is a chronic disease that affects millions of people worldwide. Early detection and diagnosis of DM in patients is essential for effective treatment and management. However, traditional methods for detecting DM, such as blood glucose testing, are often inaccurate and time-consuming[8]. In recent years, there has been growing interest in the use of microarray gene data to detect DM. Microarray gene data can provide a comprehensive overview of gene expression patterns in the pancreas, which can be used to identify patients who are at risk for DM [9].Jakka et al [10] conducted a study for an experimental analysis using various machine learning classifiers, including K Nearest Neighbor (KNN), Decision Tree (DT), Naive Bayes (NB), Support Vector Machine (SVM), Logistic Regression (LR), and Random Forest (RF). The classifiers were trained and evaluated on the Pima Indians Diabetes dataset, which consists of nine attributes and is available on the UCI Repository. Among the classifiers tested, Logistic Regression (LR) exhibited the best performance, achieving an accuracy of 77.6%. It outperformed the other algorithms in terms of accuracy, f1-score, ROC-AUC score, and misclassification rate. Radja et al [11] gave a study aimed at evaluating the performance of various supervised classification algorithms for medical data analysis, specifically in disease diagnosis. The algorithms tested included Naive Bayes, Support Vector Machine (SVM), decision table, and J48. The evaluation utilized measurement variables such as Correctly Classified, Incorrect Classified, Precision, and Recall. The predictive database of diabetes was used as the testing dataset. The SVM algorithm demonstrated the highest accuracy of 77.3% among the tested algorithms, making it an effective tool for disease diagnosis. Dinh et al [12] analyzed to aim for assess the capabilities of machine learning models in identifying and predicting diabetes and cardiovascular diseases using survey data, including laboratory results. The National Health and Nutrition Examination Survey (NHANES) dataset was utilized, and various supervised machine learning models such as LR, SVM, RF and GB were evaluated. An ensemble model combining the strengths of different models was developed, and key variables contributing to disease detection were identified using information gain of tree-based models. The ensemble model achieved an AU-ROC score of 83.1% for cardiovascular disease detection and 86.2% for diabetes classification. When incorporating laboratory data, the accuracy increased to 83.9% for cardiovascular disease and 95.7% for diabetes. For pre-diabetic patients, the ensemble model achieved an AU-ROC score of 73.7% without laboratory data, and XGBoost performed the best with a score of 84.4% when using laboratory data. Key predictors for diabetes included waist size, age, self-reported weight, leg length, and sodium intake.

Yang et al [13], conducted a study aimed to develop prediction models for diabetes screening using an ensemble learning approach. The dataset was obtained from the National Health and Nutrition Examination Survey (NHANES) from 2011-2016. Three simple machine learning methods (LDA, SVM and RF), the performance of the models was evaluated through 5-fold cross-validation and external validation using the Delong test. The study included 8057 observations and 12 attributes. The ensemble model based on linear discriminant analysis demonstrated the best performance, with an AUC of 0.849, an accuracy of 0.730, a sensitivity of 0.819, and a specificity of 0.709 in the validation set. Muhammed et al [14] gave a study utilized a diagnostic dataset of type 2 diabetes mellitus (DM) collected from Murtala Mohammed Specialist Hospital in Kano, Nigeria. Predictive supervised machine learning models were developed using LR, SVM, KNN, RF, NB and GB algorithms. Among the developed models, the RF predictive learning-based model achieved the highest accuracy of 88.76%. Kim et al [15] This study aimed to assess the impact of nutritional intake on overweight/obesity, dyslipidemia, hypertension, and type 2 diabetes mellitus (T2DM) using deep learning techniques. The researchers developed a deep neural network (DNN) model and compared its performance with logistic regression and decision tree models. Data from the Korea National Health and Nutrition Examination Survey (KNHANES) were analyzed. The DNN model, consisting of three hidden layers with varying numbers of nodes, demonstrated superior prediction accuracy (ranging from 0.58654 to 0.80896) compared to the LoR and decision tree models. In conclusion, the study highlighted the advantage of using a DNN model over conventional machine learning models in predicting the impact of nutritional intake on overweight/obesity, dyslipidemia, hypertension, and T2DM.

Ramdaniah et al [16] conducted a study utilizing Microarray gene data from the GSE18732 dataset to distinguish between different classes of diabetes. The study consisted of 46 samples from diabetic classes and 72 samples from non-diabetic classes. Machine learning techniques, specifically Navie Bayes and SVM with Sigmoid kernel, were employed for classification, achieving accuracy rates of 88.89% and 83.33%, respectively. While numerous researchers have utilized the PIMA Indian diabetic dataset to classify and analyze diabetic and non-diabetic classes, only a limited number of studies have explored the microarray gene-based dataset for the identification of diabetic classes. Consequently, various performance metrics like Accuracy, Sensitivity, Specificity, and MCC were examined in the context of this microarray gene-based dataset.

2. Methodology

The methodology of the research is depicted in the Figure 1. It shows that four dimensionality reduction techniques such as Bessel Function (BF), Discrete Cosine Transform (DCT), Least Square Linear Regression (LSLR) are used. To analyse the data further, classification of data without feature selection and with feature selection methods are used. In this, with feature selection methods two optimization algorithm are used like Elephant Herding Optimization (EHO) and Dragon Fly Optimization Algorithm (DFO), Moreover, it has given to ten classifiers as NLR, LR, GMM, EM, BLDC, LoR, SDC, SVM -L, SVM-Poly and SVM-RBF to classify the classes as normal and diabetic.

In Section 1, an introduction to the research is discussed. Section 2 presents the literature review. Section 3 the materials and methods are reviewed. Section 4 explains the process of feature extraction through dimensionality reduction techniques. In Section 5, feature selection methods are discussed, in Section 6 focuses classifiers are used. The results are presented in Section 7. Finding and conclusion are in the Section 8.

2.1. Role of Diabetic in Micro Array Gene:

Microarray gene data plays a critical role in this research. The data can be used to identify patterns of gene expression that are associated with diabetes. It is used to train and evaluate machine learning models and to identify the most relevant features for classification. The machine learning models are used to predict whether a patient has diabetes or not. The models are trained on a dataset of microarray gene data [17] that is labeled with the patient's diabetes status.

3. Materials and Methods

Microarray gene data are readily available at many search engines. To our research, we obtained expression data from human pancreatic islets from the Nordic islet transplantation programme. (https://www.ncbi.nlm.nih.gov/bioproject/PRJNA178122). The data set included 28,735 genes from 57 non-diabetic and 20 diabetic cadaver donors. The data was preprocessed to select only the 22,960 genes with the highest peak intensity per patient. The logarithmic transformation was applied with a base 10 to standardize the individual samples, with a mean of 0 and a variance of 1. The data was then used to train and evaluate a machine learning model for the detection of diabetes. The model was able to achieve an accuracy of 90%, which is a significant improvement over the baseline accuracy of 50%. The results of this research suggest that microarray gene data can be used to develop effective methods for the detection of diabetes. The data is readily available and can be easily processed to identify the most relevant features for classification.

3.1. Data set

Focuses on utilizing microarray gene data to detect diabetes and explore the features associated with its secondary criteria using probability functions based on P-values. Additionally, we aimed to address the issue of false positive errors in the selection of significant genes. The data we used for our analysis is available through multiple portals and comprises a total of 28,735 human genes. We specifically considered 50 non-diabetic and 20 diabetic samples, selecting those with the greatest minimal intensity across 70 samples. To handle the high dimensionality of the dataset, we employed four dimensionality reduction techniques, namely BF, DCT, LSLR, and AAA. This allowed us to reduce the dimensions of the data while maintaining its informative content. The resulting dimensions were [2870*20] for the diabetic group and [2870*50] for the non-diabetic group. To further refine the dataset and improve classification accuracy, we applied feature selection techniques.

Specifically, we employed two techniques as EHO search and DOA. These techniques helped identify the most relevant features in the dataset, leading to a further reduction in dimensions to [287*20] for the diabetic group and [287*50] for the non-diabetic group. To evaluate the performance and accuracy of the classification, we employed ten classifiers as already discussed.

Table 1. Description of Pancreas Micro Array Gene Data set for Diabetic and Non-Diabetic Classes.

Data Set	No of Genes	Class 1 Diabetes	Class 2 Non-Diabetic	Total
Pancreas	28735	20	50	70

Table 1. Description of Pancreas Micro Array Gene Data set for Diabetic and Non-Diabetic Classes.

Data Set	No of Genes	Class 1 Diabetes	Class 2 Non-Diabetic	Total
Pancreas	28735	20	50	70

4. Need for Dimensionality Reduction Techniques

Dimensionality reduction plays a crucial role in our research due to the high-dimensional nature of the microarray gene data. As the number of features (genes) increases, the complexity and computational cost of analyzing the data also increase significantly. Dimensionality reduction techniques allow us to reduce the number of features, making the subsequent analysis more efficient and manageable. Then, dimensionality reduction helps in mitigating the curse of dimensionality [18]. In high-dimensional spaces, data points tend to become sparse, leading to difficulties in accurately representing the underlying structure of the data.

4.1. Dimensionality Reduction

To reduce the dimensionality of the dataset BF, DCT, LSLR and AAA were used in this article.

• Bessel Function as Dimensionality Reduction

In this section, an overview of the Bessel function and its relevant relationships and properties associated with these functions are represented [19]. Furthermore, we investigate several valuable connections and characteristics related to these functions as $J_n\left(x\right)$, possesses the following mathematical definition:

$$J_n\left(x\right)=\sum _{r=0}^{\infty }\frac{{\left(-1\right)}^r}{r!\mathsf{\Gamma }\left(n+r+1\right)}{\left(\frac{x}{2}\right)}^{2r+n}$$

(1)

Where Γ(λ) is the gamma function

$$\mathsf{\Gamma }\left(\lambda \right)={\int }_0^{\infty }{e}^{-t}{t}^{\lambda -1}dt$$

(2)

The series ( $J_n\left(x\right)$) converges for all values of $x$ ranging from negative infinity to positive infinity. In fact, the Bessel function serves as a solution to a specific Sturm-Liouville equation [20]. This equation plays a significant role in the analysis of the Bessel function.

For $x\in \left(-\mathrm{\infty },\mathrm{\infty }\right),(n\in \mathbb{R})$

It is evident that the Bessel functions Jn(x) are linearly independent when n is an integer. Additionally, there exist several recursive relations for Bessel functions that can be utilized in their analysis [20]. These relations provide valuable insights into the properties and behaviour of Bessel functions in various mathematical contexts.

$$\frac{d}{dx}\left(x^n{J}_n\left(x\right)\right)=x^n{J}_{n-1}\left(x\right)$$

(4)

$$J_n^{\prime }\left(x\right)=J_{n-1}\left(x\right)-\frac{n}{x}{J}_n\left(x\right)$$

(5)

$$J_n^{\prime }\left(x\right)=\frac{n}{x}{J}_n\left(x\right)-J_{n+1}\left(x\right)$$

(6)

Lemma: A significant recursion relation that proves useful in the analysis of the Bessel function of the first kind is:

$$J_n^{\prime }\left(x\right)=\frac{1}{2}{J}_{n-1}\left(x\right)-\frac{1}{2}{J}_{n+1}\left(x\right)$$

(7)

The derivative operational matrix of Bessel functions can be derived using the following procedure: Consider the vector Jn = [J0(x), J1(x), J2(x), ..., Jn(x)]T, where J0, J1, J2, ..., Jn denote the Bessel functions of evaluated at x. To obtain the derivative operational matrix, we start with the derivative of J0(x) and denote it as J'0(x), where J'0(x) represents the derivative of J0(x) with respect to x. By constructing a matrix D, known as the derivative operational matrix, we can express Jn = DJ0, where D is a matrix that performs the differentiation operation on J0(x) to obtain Jn(x). This recursion relation allows for the efficient calculation and evaluation of Bessel functions, providing a valuable tool in various mathematical and scientific applications.

$$D=\left[\begin{array}{cc}\begin{array}{ccc}0& -1& 0\\ 1/2& 0& -1/2\\ 0& 1/2& 0\end{array}& \begin{array}{ccc}0& 0& \begin{array}{ccc}\cdots & \cdots & 0\end{array}\\ 0& 0& \begin{array}{ccc}\cdots & \cdots & 0\end{array}\\ -1/2& 0& \begin{array}{ccc}\cdots & \cdots & 0\end{array}\end{array}\\ \begin{array}{ccc}0& 0& 1/2\\ ⋮& \ddots & ⋮\\ a_0& a_1& a_2\end{array}& \begin{array}{ccc}\begin{array}{ccc}0& -1/2& \cdots \end{array}& \cdots & 0\\ \begin{array}{ccc}⋮& \ddots & ⋮\end{array}& \cdots & 0\\ \begin{array}{ccc}{a}_3& \cdots & \cdots \end{array}& 0& a_n\end{array}\end{array}\right]$$

(8)

2.

Discrete cosine Transform (DCT) as Dimensionality Reduction

The Discrete Cosine Transform (DCT) is a dimensionality reduction technique that approximates the Kernighan-Lin method. It aims to reduce the dimensions of the input data by eliminating the most significant features, thereby simplifying further analysis. By applying the DCT method [21], the input vector and its components are orthogonalized, resulting in a reduction in complexity. This method extracts features by selecting coefficients, which is a crucial step with a significant impact on computation efficiency [22,23]. The DCT can be represented as follows:

$$k\left(x\right)=\propto \left(x\right).{\sum }_{u=0}^{s-1}\mathrm{a}\left(\mathrm{u}\right)\cos \frac{\pi (2u+1)x}{2s}$$

(9)

3.

Least Square Linear Regression (LSLR) as Dimensionality Reduction

Another effective technique for reducing dimensionality is the LSLR. Hotelling [24] initially introduced this concept, utilizing principal component analysis (PCA) as a regression analysis tool. LSLR applies PCA to transform high-dimensional data into a lower-dimensional space, upon which a linear regression model is applied. The transformation is learned by minimizing the sum of squared errors between the predicted lower-dimensional representation and the actual high-dimensional data.

LSLR, as discussed in Hastie et al. [25], performs dimensionality reduction by identifying the best-fit line that represents the relationship between the independent variables (features) and the dependent variable (target). The objective of LSLR is to minimize the sum of squared differences between the actual and predicted values of the target variable. Considering a set of N observations in the form (x1, y1), (x2, y2), ..., (xN, yN), where xi represents the $i^{th}$ observation of the independent variables and yi corresponds to the observation of the target variable, the LSR solution can be represented as a linear equation:

$$z={\alpha }_0+{\alpha }_1{x}_1+{\alpha }_2{x}_2+..+{\alpha }_p{x}_p$$

(10)

In the context of LSR, the linear model is characterized by the parameters ∝_1,∝_2,∝_3,…,∝_p, where p represents the number of independent variables. This minimization process is expressed through the following equation

$$SSE={\sum }_{j=1}^m{(z_i-\left({\alpha }_0+{\alpha }_1{x}_1+{\alpha }_2{x}_2+..+{\alpha }_p{x}_p\right))}^2$$

(11)

After applying dimensionality reduction techniques to Microarray genes data, the resulting outputs are further analyzed using various statistical parameters such as mean, variance, skewness, kurtosis, Pearson correlation coefficient (PCC), f-test, T-test, p-value, and canonical correlation analysis (CCA). These statistical measures are used to assess whether the outcomes accurately represent the intrinsic properties of the underlying microarray genes in the reduced subspace.

4.

Artificial Algae Algorithm (AAA) as Dimensionality Reduction

The Artificial Algae Algorithm (AAA) [26] is a nature-inspired optimization algorithm that mimics the behavior and characteristics of real algae to solve complex problems. Each solution in the problem space is represented by an artificial alga, which captures the essence of algae's traits. Like real algae, artificial algae exhibit helical swimming patterns and can move towards a light source for photosynthesis. The AAA consists of three fundamental components: the Evolutionary Process, Adaptation, and Helical Movement. The behavior of algal colony to act as a cohesive unit, moving and responding to environmental conditions. By incorporating the principles of artificial algae into the algorithm, the AAA offers a novel approach to solving optimization problems.

$$Population=\left[\begin{array}{cc}\begin{array}{cc}{X}_{11}& X_{12}\\ X_{21}& X_{22}\end{array}& \begin{array}{cc}\cdots & X_{1D}\\ \cdots & X_{2D}\end{array}\\ \begin{array}{cc}⋮& ⋮\\ X_{n1}& X_{n2}\end{array}& \begin{array}{cc}\ddots & ⋮\\ \cdots & X_{nD}\end{array}\end{array}\right]$$

(12)

Where $X_{nD}$ is algal cell in D^th dimension of n^th algal colony.

During the evolutionary process[27] of the Artificial Algae Algorithm (AAA), the growth and reproduction of algal colonies are influenced by the availability of nutrients and light. When an algal colony is exposed to sufficient light and nutrient conditions, it undergoes growth and replicates itself through a process like real mitotic division. In this process, two new algal cells are generated at time t. Conversely, if an algal colony does not receive enough light, it can survive for a certain period but eventually perishes. It is important to note that ${\mu }_{max}$is assumed to be 1, as the maximum biomass conversion should be equivalent to the substrate consumption in unit time, following the conservation of mass principle. The size of the $i^{th}$ algal colony at time t + 1 is determined by the Monod equation, as expressed in the subsequent equation.

$$H_i^t={\mu }_i^t{H}_i^t$$

(13)

Where i = 1,2,3….N

$H_i^t$ represents $i^{th}$ algal colony in time t,

N represents no of algal colonies

In the Artificial Algae Algorithm (AAA), nutrient-rich algal colonies with optimal solutions thrive, while successful traits are transferred from larger colonies to smaller ones through cell replication during the evolutionary process.

Maximum^t= max $H_i^t$ , whereas i = 1,2,3…N

Minimum^t = min $H_i^t$ , Whereas i = 1,2,3… N

Minimum^t = Maximum^t , whereas m = 1,2,3…D

In the AAA, algal colonies are ranked by size at time t. In each dimension, the smallest algal colony's cell dies while the largest colony's cell replicates itself.

Adaptation occurs in the AAA when algal colonies that cannot grow sufficiently in their environment attempt to resemble the largest colony. This process leads to a change in the starvation level within the algorithm. Each artificial alga starts with a starvation value of zero, which increases over time when the algal cell receives insufficient light. The artificial alga with the highest starvation value becomes the focus of adaptation.

$${Star}^t=max{B}_i^t\mathrm{Where}\mathrm{i}=1,2,3\dots \mathrm{N}$$

(14)

$${Star}^{t+1}={Star}^t+\left({max}^t-{Star}^t\right)*rand$$

(15)

Helical Movement: Algal cells and colonies exhibit specific swimming behaviour, striving to stay near the water surface where sufficient light for their survival is available. They move in a helical manner, propelled by their flagella, which face limitations from gravity and viscous drag. In the AAA, gravity's influence is represented by a value of 0, while viscous drag is simulated as shear force, proportional to the size of the algal cell. The cell is modelled as a spherical shape, with its size determined by its volume, and the friction surface is equivalent to the surface area of a hemisphere,

$$\tau \left(x_i\right)=2\pi r^2$$

(15)

$$\tau \left(x_i\right)=2\pi {\left(\sqrt[3]{\frac{3H_i}{4\pi }}\right)}^2$$

(17)

where $\tau \left(x_i\right)$ is the friction surface.

The helical movement of algal cells involves three randomly determined dimensions. One of these dimensions corresponds to linear movement, as described by Equation (18), while the other two dimensions contribute to angular movement, as expressed by Equations (19) and (20). Equation (18) is utilized for one-dimensional problems, enabling the algal cell or colony to move in a single direction. In two-dimensional problems, algal movement follows a sinusoidal pattern, and therefore, Equations (18) and (20) are employed. For three or more dimensions, algal movement takes on a helical trajectory, and Equations (18)-(20) are utilized. The step size of the movement is determined by the friction surface and the distance to the source of light.

$$X_{im}^{t+1}=X_{im}^t+\left(X_{jm}^t-X_{im}^t\right)\left(\mathsf{\Delta }-{\tau }^t\left(X_i\right)\right)P$$

(18)

$$X_{ik}^{t+1}=X_{ik}^t+\left(X_{jk}^t-X_{ik}^t\right)\left(\mathsf{\Delta }-{\tau }^t\left(X_i\right)\right)\cos \alpha$$

(19)

$$X_{il}^{t+1}=X_{il}^t+\left(X_{jl}^t-X_{il}^t\right)\left(\mathsf{\Delta }-{\tau }^t\left(X_i\right)\right)\sin \beta$$

(20)

Where, $X_{im}^{t+1},X_{ik}^{t+1},X_{il}^{t+1}$represents x, y and z coordinates of $i^{th}$ algal cell at time t;

The variables α and β are in the range [0, 2π], while p is within the interval [-1, 1]. Δ represents the shear force, and ${\tau }^t\left(X_i\right)$ denotes the friction surface area of the i-th algal cell.

Figure 2. Flow diagram for Artificial Algae Algorithm.

Figure 2. Flow diagram for Artificial Algae Algorithm.

4.2. Statistical Analysis

The dimensionally reduced Micro array genes through four DR methods are analysed by the statistical parameters like mean, variance, skewness, kurtosis, Pearson correlation coefficient (PCC), and CCA to identify whether the outcomes are representing the underlying micro array genes properties in the reduced subspace. As mentioned in the Table 2 that in the AAA based DR methods depicts higher values of mean, and variance among the classes. All the other three DR Methods namely, Bessel Function, DCT, and LSLR display low and overlapping values of mean and variance among the classes. The negative skewness depicted only by the LSLR DR method which indicates the presence of skewed components embedded in the classes. DCT and LSLR DR methods indicate negative kurtosis. This in turn leads to the observance that the DR methods are not modifying the underlying Micro array genes characteristics. PCC values indicate the high correlation within the class of attained outputs. In the case of Bessel function DR Method all the four statistical parameters are positive and minimum values. This indicates that the statistical parameters are associated with non-Gaussian and non-linear one. The same is further examined by the histogram, Normal probability plots and Scatter plots of DR techniques outputs. Canonical correlation Analysis (CCA) visualizes the correlation of DR methods outcomes among the Diabetic and non-Diabetic cases. The low CCA value in the Table 2 indicates that the DR outcomes are less correlated among the two classes.

Figure 3 shows the Histogram of Bessel Function DR Techniques in Diabetic Gene Class. It is identified that in the Figure 3 the histogram depicts a skewed group of values, gap, and presence of non-linearity in this method. The patient from 1 to 10 are represented as x(:,1) to x(:,10).

Figure 4 exhibits the Histogram of Bessel function DR Techniques in non-Diabetic Gene Class with the marker of x(:,1) represents as patient 1 and x(:,10) represents as patient 10. It is observed from the Figure 4 that the histogram depicts a skewed group of values, gap and presence of non-linearity in this method.

In this Figure 5, Data 1 to 5 represents references, data 6 to 10 notices upper bound and data 11 to 15 cluster variable points. It indicates the Normal Probability plot for DCT DR Techniques Features for Diabetic Gene Class. As exhibits from the figure 5 that the normal probability plot displays the total cluster of DCT DR outputs and the presence of non-linearly correlated variables among the classes.

Figure 6 shows the normal Probability plot for DCT DR Techniques Features for non-Diabetic Gene Class as data is presented from 1 to 5 as references, and upper bound value are represented from 6 to 10, and cluster variable points from 11 to 15. As exhibits from the figure 6 that the normal probability plot displays the total cluster of DCT DR outputs and the presence of non-linearly correlated variables among the classes. This is due to low values of mean and variance and the presence of negative kurtosis variables in the DR method outcomes.

Data 1 to 5 are mentioned in the Figure 7 as references, data 6 to 10 are mentioned as upper bound values and data 11 to 15 are mentioned as variable points. It is normal Probability plot for LSLR DR Techniques Features for Diabetic Gene Class. As mentioned by the figure 6 that the normal probability plots display the group clusters for LSLR DR outputs. This indicates the presence of non-Gaussian and non-linearly variables within the classes. This is due to low variance and negative Kurtosis variables of the DR method outcomes.

Figure 8 demonstrates the normal Probability plot for LSLR DR Techniques Features for non-Diabetic Gene Class. As shown in the figure 8 that the normal probability plots display the discrete group of clusters for LSLR DR outputs. Data representation from 1 to 5 as references, from 6 to 10 as upper bound and from 11 to 15 as variable points. This indicates the presence of non-Gaussian and nonlinear variables within the classes. This is due to low variance and flat Kurtosis variables of the DR method outcomes.

Figure 9 shows the Scatter plot for AAA Algorithm DR Techniques Features for Diabetic and non-Diabetic Gene Class. As revealed by the figure 9 that the scatter plots from AAA algorithm displays the total clustering and overlapping of the variables of both classes across the entire subspace. The scatter plot also indicates the presence of non-Gaussian, non-linear and higher values of all statistical parameters. Furthermore, the AAA algorithm will have heavy computational cost on the classifier design. To reduce the burden of the classifiers, a feature selection process which comprises the elephant Herd Optimization (EHO) and Dragon fly algorithms are initiated

5. Feature Selection Methods

Two metaheuristic algorithms are used in this article are the EHO algorithm and DOA. By emulating the behaviour observed in elephants and dragonflies, respectively, these algorithms offer effective approaches to address the challenges in optimization.

• Elephant Herding Optimization (EHO) algorithm

Elephant Herding Optimization (EHO) is a meta-heuristic algorithm introduced by Wang et al. [28], inspired by the behaviour of elephants in the African savanna. It has demonstrated effectiveness in solving optimization problems and has been successfully applied in various domains, including feature selection. In feature selection, the objective is to identify a subset of informative features from a larger set that are relevant to the target variable. EHO employs a herd of elephants to search for the optimal solution, with each elephant representing a potential solution. By combining global and local search strategies, the algorithm guides the elephants towards the best solution. EHO offers immense potential as a feature selection technique due to its ability to strike a balance between global and local searches, making it suitable for high-dimensional data. The initialization of the elephant herd involves assigning random positions to the elephants in the feature space, providing a comprehensive representation of the elephants' positions and the overall movement of the herd.

$$y_i^{new}=y_i^{old}+\propto \left(Y_{best}-Y_i^{old}\right)*r$$

(21)

The EHO algorithm [29] involves updating the positions of elephants within the herd. This update process considers both the old position (y𝑖𝑜𝑙𝑑) and the new position (y𝑖𝑛𝑒𝑤) of each elephant. A control parameter (𝛼), which falls within the range of [0,1], is used in conjunction with a randomly generated number (r ∈ [0,1]) to determine the new position. Additionally, each elephant in the herd maintains a memory of its best position in the feature space. The best position is updated using the following equation, ensuring that the elephant's memory is updated accordingly.

$$Y_{best}=\beta *Y_{centre}$$

(22)

$$Y_{centre}=\frac{1}{m}*{\sum }_{i=1}^m{y}_i$$

(23)

The algorithm includes the concept of the best position (Y𝑏𝑒𝑠𝑡) for each elephant within the herd. This best position is determined by considering the control parameter (𝛽), which falls within the range of [0,1]. The control parameter plays a role in updating and adjusting the best position of the elephant, ensuring that it reflects the optimal solution obtained during the optimization process.

By considering both the best and worst solutions, the EHO algorithm ensures a more comprehensive exploration of the solution space, leading to improved optimization performance.

$$Y_{worst}=Y_{min}+\left(Y_{max}-Y_{min}+1\right)*rand$$

(24)

Figure 10. Flow Chart of Elephant Herding Optimization Algorithm.

Figure 10. Flow Chart of Elephant Herding Optimization Algorithm.

• Dragonfly Optimization Algorithm (DOA)

The Dragonfly Algorithm (DA) is an optimization technique based on swarm intelligence, taking inspiration from the collective behaviors of dragonflies. Introduced by Mirjalili in 2016 [30], this algorithm mimics the dynamic and static swarming behaviors observed in nature. During the dynamic or exploitation phase, dragonflies form large swarms and travel in a specific direction to confuse potential threats. In the static or exploration phase, they form smaller groups, moving within a limited area to hunt and attract prey [31]. The DA is guided by five fundamental principles: separation, alignment, cohesiveness, attraction, and diversion. These principles dictate the behavior of individual dragonflies and their interactions within the swarm. In the equations that follow, K and Ki denote the current position and the ith position of a dragonfly, respectively, while N represents the total number of neighboring flies.

• Separation: This implies that the static phase of the algorithm focuses on preventing dragonflies from colliding with each other in their vicinity. This calculation aims to ensure the avoidance of collisions among flies.

$${Se}_j=-{\sum }_{i=1}^{n}k-k_j$$

(25)

Where ${Se}_j$represents the motion of the ith individual aimed at maintaining separation from other dragonflies.

2.

Alignment: This denotes the synchronization of velocities among dragonflies belonging to the same group. It is represented as.

$${Ag}_j=\frac{{\sum }_{i=1}^n{Ve}_i}{n}$$

(26)

This is represented by${Ag}_j$, which represents the velocity of the i^th individual.

3.

Cohesiveness: This represents the inclination of individual flies to converge towards the centre of swarms. The calculation for this is given by.

$${Co}_j=\frac{{\sum }_{i=1}^n{k}_i}{N}-k$$

(26)

4.

Attraction: The attraction towards the food source is quantified as

$$H_j=K^{+}-K$$

(27)

The attraction towards the food source is represented by $H_j$, while $K^{+}$ represents the position of the food source.

5.

Diversion: The diversion from the enemy is determined by the outward distance, which is calculated as.

$$D_j=K^{-}+K$$

(28)

The calculation of the outward distance determines the diversion from the enemy, and it is expressed as.

The step vector (∆K) and the current position vector (K) are used to update the locations of artificial dragonflies within the search space. The movement direction of the dragonfly is determined by the step vector (∆K), which is calculated as follows:

$${∆K}_j^{t+1}=\left(s{Se}_j+a{Ag}_j+c{Co}_j+h{H}_j+d{D}_j\right)+\omega {∆K}_j^t$$

(30)

The separation weight (s), alignment weight (a), cohesion weight (c), attraction weight (h), and enemy weight (d) influence the behaviour of the dragonfly algorithm. The inertia weight is represented by "ω," and "t" represents the iteration number. By adjusting these weights, the exploration and exploitation phases of the algorithm can be achieved. The position of the i^th dragonfly at t + 1 iterations is determined by the following equation:

$$K_j^{t+1}=K_j^t+{∆K}_j^{t+1}$$

(9)

Figure 11. Flowchart of Dragonfly Optimization Algorithm.

Figure 11. Flowchart of Dragonfly Optimization Algorithm.

The success of the feature selection methods outputs is analysed through the significance of the p-value from t-Test. Table 3 illustrates the p-value significance for the EHO and Dragon fly algorithm feature selection methods for the four DR techniques. As shown in the Table 3 that the EHO and Dragon fly algorithm Feature selection methods are not showing any significant p-values among the classes for all four DR methods. This p-value will be a precursor to quantify the presence of outliers, non-linear and non-Gaussian variables among the classes after feature selection methods.

6.1. Training and Testing of Classifiers

Due to the limited availability of training data, we employed k-fold cross-validation, a widely used technique for evaluating machine-learning models. The methodology described by Fushiki et al. [42] was followed to conduct the k-fold cross-validation process. Initially, the dataset was divided into k equally sized subsets or "folds". For each fold, denoted as i, the model was trained on the remaining data excluding the i^th fold, and then tested on the i^th fold. This process was repeated for all k folds, ensuring that each fold was used once for testing. Consequently, k performance estimates (one for each fold) were obtained. To obtain an overall estimate of the model's performance, the average of these k performance estimates was calculated. After training and validating the model using k-fold cross-validation, it was retrained on the complete dataset to make predictions on new, unseen data. The significant advantage of utilizing k-fold cross-validation is its ability to provide a more reliable estimate of the model's performance compared to a simple train-test split, as it maximizes the utilization of available data. In our study, we adopted a k-value of 10-fold cross-validation. Furthermore, the research incorporated 2870 dimensionally reduced features per patient, focusing on a cohort of 20 patients with diabetes and 50 non-diabetic patients. The utilization of cross-validation eliminates any reliance on a specific pattern for the test set, enhancing the robustness of our findings. The training process is regulated by monitoring the Mean Square Error (MSE) proposed by Wang et al. [43], which is defined as follows:

$$MSE=\frac{1}{N}{\sum }_{j=1}^N{\left(O_j-T_j\right)}^2$$

(65)

Where Oj is the observed value at time j, T_j is the target value at model j;

j=1and 2, and N is the total number of observations per epoch in our case it is 2870. As the training progressed the MSE value reached 1.0 E-12 within 2000 iterations.

Table 4. Confusion matrix for Diabetic Detection.

Truth of Clinical Situation		Predicted Values
		Diabetic	Normal
Actual Values	Diabetic	TP	FN
	Normal	FP	TN

Table 4. Confusion matrix for Diabetic Detection.

Truth of Clinical Situation		Predicted Values
		Diabetic	Normal
Actual Values	Diabetic	TP	FN
	Normal	FP	TN

In the case of lung cancer detection, the following terms can be defined as:

True Positive (TP): A patient is correctly identified as diabetic class.

True Negative (TN): A patient is correctly identified as a non-diabetic class.

False Positive (FP): A patient is incorrectly identified as diabetic class when they are in non-diabetic class.

False Negative (FN): A patient is incorrectly identified as non-diabetic class when they are in diabetic class.

Table 5 reveals the training and testing MSE performance of the classifiers without feature selection Method for four Dimensionality Reduction Techniques. The training MSE are always varied between 10^-04 to 10^-10, while the testing MSE varies from 10^-04 to 10^-08. SVM (RBF) classifier in AAA DR techniques without feature selection method settled at minimum training and Testing MSE of 1.93E-10 and 1.77E-08 respectively. The minimum testing MSE will be a marker of the better classifier performance. As shown in the Table 5 that higher the values of testing MSE leads to the poorer performance of the classifier irrespective of the Dimensionality reduction Techniques.

Table 6 exhibits the training and testing MSE performance of the classifiers with EHO feature selection Method for four Dimensionality Reduction Techniques. The training MSE is varied between 10⁻⁵ to 10⁻¹⁰, while the testing MSE varies from 10⁻⁵ to 10⁻⁸. SVM (RBF) classifier in AAA DR method with PSO feature selection is achieved minimum training and Testing MSE of 1.99× 10⁻¹⁰and 2.5× 10⁻⁸ respectively. Bessel function DR method indicates slightly lower training and testing MSE values for the classifiers when compared to other three DR techniques. All the classifiers slightly improved the performance in the Testing MSE when compared to without Feature selection methods. This will indicate the enhancement of the classifier performance irrespective of Dimensionality Reduction Techniques.

Table 7 represents the training and testing MSE performance of the classifiers with Dragon fly algorithm-based feature selection Method for four Dimensionality Reduction Techniques. The training MSE are always varied between 10^-6 to 10^-9, while the testing MSE varies from 10^-5 to 10^-8. SVM (RBF) classifier with Dragon fly feature selection method settled at minimum training and Testing MSE of 1.66× 10⁻⁹and 3.25× 10⁻⁸ respectively. In this feature selection method, all classifiers are enhanced in their training and testing performance. This will be indicated by the improvement of the accuracy, MCC and Kappa parameters of the classifier performance irrespective of the type of Dimensionality Reduction Techniques.

6.2. Selection of target

The target value for the non-diabetic case ${(T}_{\mathrm{N}\mathrm{D}})$ is taken at the lower side of zero to one (0→1) scale and this mapping is made according to the constraint of

$$\frac{1}{N}{\sum }_{i=1}^N{\mu }_i\le T_{ND}$$

(66)

where${\mu }_{\mathit{i}}$ is the mean value of input feature vectors for the N number of Non-diabetic Features taken for classification. Similarly, the target value for the Diabetic case ($T_{\mathrm{D}\mathrm{i}\mathrm{a}}$) is taken at the upper side of zero to one (0→1) scale and this mapping is made based on

$$\frac{1}{M}{\sum }_{j=1}^N{\mu }_j\le T_{\mathrm{D}\mathrm{i}\mathrm{a}}$$

(67)

where${\mu }_j$ is the average value of input feature vectors for the M number of Diabetic cases taken for classification. Note that the target value $T_{\mathrm{D}\mathrm{i}\mathrm{a}}$ would be greater than the average value of ${\mu }_i$and ${\mu }_j$. The difference between the selected target values must be greater than or equal to 0.5, which is given by:

$$\left|\right|T_{\mathrm{D}\mathrm{i}\mathrm{a}}-T_{\mathrm{N}\mathrm{D}}\left|\right|\ge 0.5$$

(68)

Based on the above constraints, the targets $T_{\mathrm{N}\mathrm{D}}$ and $T_{Dia}$ for Non-Diabetic and Diabetic patient output classes are chosen at 0.1 and 0.85 respectively. After selecting the target values, the Mean Squared Error (MSE) is used for evaluating the performance of machine learning Classifiers.

Table 8. Selection of Optimum Parametric Values for Classifiers.

Classifiers	Description
NLR	Uniform weight w=0.4, bias b=0.001, iteratively modified sum of Least square Error, Criterion: MSE
Linear Regression	Uniform weight w=0.451, bias b=0.003, Criterion: MSE
GMM	Mean, Covariance of the input samples and tuning parameter is EM steps. Criterion: MSE
EM	test point likelihood probability 0.13,cluster Probability of 0.45, with convergence rate of 0.631, Criterion: MSE
BDLC	P(y), Prior probability: 0.5, Class mean: 0.85,0.1; Criterion: MSE
Logistic regression	Threshold H𝞱(x) <0.48 with Criterion: MSE
SDC	γ=0.5 along with mean of each class target values as 0.1, and 0.85
SVM (linear)	C (Regularization Parameter): 0.85, Class Weights: 0.4, Convergence Criteria: MSE
SVM(Polynomial)	C: 0.76, Coefficient of the kernel function (gamma): 10, Class weights: 0.5, Convergence Criteria: MSE
SVM(RBF)	C: 1, Coefficient of the kernel function (gamma): 100, Class weights: 0.86, Convergence Criteria: MSE

Table 8. Selection of Optimum Parametric Values for Classifiers.

Classifiers	Description
NLR	Uniform weight w=0.4, bias b=0.001, iteratively modified sum of Least square Error, Criterion: MSE
Linear Regression	Uniform weight w=0.451, bias b=0.003, Criterion: MSE
GMM	Mean, Covariance of the input samples and tuning parameter is EM steps. Criterion: MSE
EM	test point likelihood probability 0.13,cluster Probability of 0.45, with convergence rate of 0.631, Criterion: MSE
BDLC	P(y), Prior probability: 0.5, Class mean: 0.85,0.1; Criterion: MSE
Logistic regression	Threshold H𝞱(x) <0.48 with Criterion: MSE
SDC	γ=0.5 along with mean of each class target values as 0.1, and 0.85
SVM (linear)	C (Regularization Parameter): 0.85, Class Weights: 0.4, Convergence Criteria: MSE
SVM(Polynomial)	C: 0.76, Coefficient of the kernel function (gamma): 10, Class weights: 0.5, Convergence Criteria: MSE
SVM(RBF)	C: 1, Coefficient of the kernel function (gamma): 100, Class weights: 0.86, Convergence Criteria: MSE

• Results and Discussion

The research uses standard ten-fold testing and training in which 10% of input features are employed for testing, whereas 90% are employed for training. The choice of performance measures is significant in evaluating classifier performance. The confusion matrix is used to evaluate the performance of Classifiers, especially in binary classification (i.e., classification into two classes, such as Diabetic or non-diabetic from the pancreas Micro array Genes). It can be used to calculate performance metrics such as Accuracy, F1 score, MCC, Error Rate, FM Metrics, and Kappa, commonly used to evaluate the model's overall performance. Table 9 depicts the parameters associated with the classifiers for performance Analysis.

Here are the definitions of TP, TN, FP, and FN:

True positive (TP): A prediction that was correct and the actual value was positive.

True negative (TN): A prediction that was correct and the actual value was negative.

False positive (FP): A prediction that was incorrect and the actual value was negative.

False negative (FN): A prediction that was incorrect and the actual value was positive.

The performance of the classifier was evaluated using a few metrics, including accuracy, F1 score, MCC, error rate, FM metric, and kappa. Accuracy is the fraction of predictions that are correct, and it is a measure of the overall performance of the classifier. F1 score is the harmonic mean of precision and recall, and it is a measure of the classifier's ability to both correctly identify positive instances and to correctly identify negative instances. MCC is a measure of the correlation between the observed and predicted classifications, and it is a more sensitive metric than accuracy or F1 score. Error rate is the fraction of predictions that are incorrect, and it is the complement of accuracy. FM metric is a generalization of the F-measure that adds a beta parameter, and it is a measure of the classifier's ability to both correctly identify positive instances and to correctly identify negative instances, with a weighting that can be adjusted to favor one or the other. Kappa is a statistic that measures agreement between observed and predicted classifications, adjusted for chance. The results are tabulated in the following tables.

Table 10 expresses the performance analysis of the ten classifiers based on parameters like Accuracy, F1 Score, MCC, Error Rate, F Measure, and Kappa values for the four Dimensionality Reduction method without two feature selection methods. It is noted from the Table 9 that EM Classifier in the Bessel function DR techniques is settled at middle accuracy of 61.42%, F1 Score of 54.23% with moderate Error rate of 38.57% and F Measure of 57.28%. The EM Classifier is also exhibiting a low value of MCC 0.3092 and Kappa value of 0.2645. The SVM (linear) Classifier in Bessel function DR Method displays low accuracy of 52.85% with high Error Rate of 47.15%, and F1 score of 40% along with F Measure of 41.57%. The MCC and Kappa for SVM (linear) classifier is placed at the lower ebb of 0.06324 and0.05714 respectively. All the classifiers are poorly performed across the performance metrics in the Bessel function DR Techniques. This is due to inherit property of Bessel function and it is displayed in the non-negative values of statistical parameters. The SVM (RBF) Classifier for DCT DR Technique is maintained at accuracy of 88.57%, with low Error Rate of 11.42% F1 Score of 81.81% and F Measure of 82.15%. The MCC and Kappa values of SVM (RBF) classifier is at 0.7423 and 0.7358 respectively. The AAA DR technique in SVM (RBF) classifier attains high accuracy of 90% with low error rate of 10% and F1 Score of 84.44% with F measure of 84.97%. The MCC and kappa values for SVM(RBF) classifier settled at 0.7825 and 0.772 respectively. Irrespective of the Dimensionality Reduction Techniques all the classifiers are maintained at accuracy within the range of 52%-85%. This is due the inherit limitation of the Dimensionality Reduction Techniques. Hence, it is suggested to incorporate the Feature selection methods towards the enhancement of classifier’s performance.

Figure 13 depicts the performance analysis of the ten classifiers based on parameters such as Accuracy, F1 Score, Error Rate, and F measure values for the four Dimensionality Reduction method without feature selection methods. It is depicted from the Table 10 that EM Classifier in the Bessel function DR techniques is settled at middle accuracy of 61.42%, F1 Score of 54.23% with moderate Error rate of 38.57% and F Measure of 57.28%. The SVM (linear) Classifier in Bessel function DR Method displays low accuracy of 52.85% with high Error Rate of 47.15%, and F1 score of 40% along with F Measure of 41.57%. All the classifiers are poorly performed across the performance metrics in the Bessel function DR Techniques. The SVM (RBF) Classifier for DCT DR Technique is maintained at accuracy of 88.57%, with low Error Rate of 11.42% F1 Score of 81.81% and F Measure of 82.15%. The AAA DR technique in SVM (RBF) classifier attains high accuracy of 90% with low error rate of 10% and F1 Score of 84.44% with F measure of 84.97%.

Table 11 reveals the performance analysis of the ten classifiers for the four Dimensionality Reduction method with EHO feature selection method. It is examined from the Table 10 that SVM(RBF) Classifier in the AAA DR techniques is settled at high accuracy of 95.71%, F1 Score of 92.68% with low Error rate of 4.28% and F Measure of 92.71%. The SVM(RBF) Classifier is also displays a high value of MCC 0.897 and Kappa value of 0.8965. The SVM(Linear) Classifier for Bessel function DR Technique once again is placed in the lower ebb of accuracy of 50%, with high Error Rate of 50% F1 Score of 36.36% and F Measure of 37.79%. The null value of MCC and Kappa are attained by SVM (Linear) classifier which is a very peculiar phenomenon of the classifiers performance. All the classifiers exhibit enhanced accuracy in the DCT, LSLR and AAA DR techniques. The effect of EHO feature selection is not revealing any appreciable improvements in the classifiers for Bessel function DR Method.

Figure 14 displays the performance analysis of the ten classifiers s for the four Dimensionality Reduction methods with EHO feature selection methods. It is also observed from the Table 11 that SVM(RBF) Classifier in the AAA DR techniques is settled at high accuracy of 95.71%, F1 Score of 92.68% with low Error rate of 4.29% and F Measure of 92.71%. The SVM (linear) Classifier for Bessel Function DR Technique is settled in the lower end of accuracy of 50%, with high Error Rate of 50% F1 Score of 36.36% and F Measure of 37.79%. All the classifiers are poorly performed in the Bessel function DR techniques.

Table 12 explores the performance analysis of the ten classifiers for the four Dimensionality Reduction method with Dragon Fly feature selection method. It is mentioned from the Table 12 that SVM(RBF) Classifier in the AAA DR techniques is settled at high accuracy of 94.28%, F1 Score of 90.47% with low Error rate of 5.72% and F Measure of 90.57%. The SVM (RBF) Classifier is also exhibits a high value of MCC 0.866 and Kappa value of 0.864. The SVM (polynomial) Classifier for Bessel function DR Technique is assigned at the lower accuracy of 58.57%, with high Error Rate of 41.43% F1 Score of 43.13% and F Measure of 44.17%. The MCC and Kappa values of SVM (polynomial) classifier is at 0.1364and 0.1287 respectively. Except SVM (RBF) classifier all the other nine classifiers in the Bessel function DR method attains accuracy of less than 78%. SVM (RBF) classifier in DCT DR and LSLR DR Method achieved high accuracy of 91% and 90% respectively.

Figure 15 demonstrates the performance analysis of the ten classifiers for the four Dimensionality Reduction methods with Dragon fly feature selection methods. It is also examined from the Table 12 that SVM(RBF) Classifier in the AAA DR techniques is settled at high accuracy of 94.28%, F1 Score of 90.47% with low Error rate of 5.72% and F Measure of 90.57%. The SVM (polynomial) Classifier for Bessel function DR Technique is placed at the lower accuracy of 58.57%, with high Error Rate of 41.43% F1 Score of 43.13% and F Measure of 44.17%. Across four DR methods SVM (RBF) classifier achieved individual accuracy of more than 81%. The classifiers performance in Bessel function DR method with Dragon fly Feature selection is settled at poor category only.

Figure 16 displays the Performance of MCC and Kappa Parameters across the classifiers for four DR Techniques without and with Two Feature Selection Methods. The MCC and Kappa are the benchmark parameter which indicates the outcomes of the classifiers for different inputs. As in this research there are three categories of inputs like dimensionally reduced without Feature selection, with EHO and Dragon fly Feature selection methods. The classifiers performance is observed through the attained MCC and Kappa values for these inputs. The average MCC and Kappa values from the classifiers are at 0.2984 and 0.2849 respectively. A methodology is devised to identify the performance of the classifiers with reference to figure 14. The MCC values are divided into three ranges like 0.0 - 0.25, 0.251-0.54 and 0.55-0.9. The performance of the classifiers is poor in the range 1 and there is a steep increase in the MCC Vs Kappa slope in the region 2 of the MCC values. The region 3 of MCC is settled at higher performance of the classifiers without any glitches.

Figure 17 shows Histogram performance of Error Rate and MCC (%) Parameters across the classifiers for four DR Techniques without and with Two Feature Selection Methods. From the figure 17 it is also identified that maximum error rate is settled at 50% and Maximum MCC at 90%. The Histogram of Error rate is skewed at the right side of the graph which indicates that for any DR method and irrespective of Feature selection method the classifier’s error rate does not go beyond 50%. The histogram of MCC across the classifier depicts the sparser in the edges and covers more points in the middle area.

6.3. Computational Complexity

The analysis of the classifiers in this study considers their computational complexity, which is determined based on the size of the input (denoted as O(n)). A lower computational complexity, indicated by O(1), is desirable as it indicates that the complexity remains constant regardless of the input size. However, as the number of inputs increases, the computational complexity will also increase. It is noteworthy that in this research, the computational complexity is independent of the input size, which is a favourable characteristic for any algorithm. If the computational complexity increases logarithmically with the increase in 'n', it is represented as O(logn). Additionally, all the classifiers used in this study are hybrid models that incorporate dimensionality reduction techniques and feature selection methods in their classification process.

Table 13 presents the Computational Complexity of the Classifiers for the four Dimensionality Reduction Techniques without incorporating Feature selection methods. A noteworthy observation from the table is that the computational complexity of all the classifiers is relatively similar. However, their performance in terms of accuracy is relatively low. Among the classifiers, the Bessel Function Classifier demonstrates a moderate computational complexity of O(n3 logn), while the Discrete Cosine transform, Least Square Linear Regression, and Artificial Algae Algorithm exhibit higher computational complexity with improved accuracy, represented by O(2n4log2n), O(2n5log4n), and O(2n5log8n) respectively, when compared to the other classifiers. Additionally, when considering the values of MCC and Kappa, the DST, LSLR, and AAA classifiers exhibit similar performance.

Table 14 inferred the Computational Complexity of the Classifiers for the four Dimensionality Reduction Techniques when utilizing the EHO Feature selection method. The table reveals that the computational complexity of all the classifiers is relatively similar, while their performance demonstrates significant accuracy. Similar to the case without feature selection, the Expectation Maximum classifier exhibits higher computational complexity of O(n5 logn) along with remarkable accuracy. Regarding the DCT, LSLR, and AAA classifiers, they achieve similar computational complexity to the SVM(RBF) classifier with O(2n6 log2n), O(2n7 log4n), and O(2n7 log8n) respectively. Notably, the SVM(RBF) classifier in combination with the EHO feature selection technique for DCT, LSLR, and AAA achieves the highest accuracy among all classifiers, with accuracies of 90%, 88.57%, and 95.71% respectively. Furthermore, the corresponding kappa values for these classifiers are 0.7655, 0.65, and 0.8965, indicating their strong performance.

Table 15 provides insights into the Computational Complexity of the Classifiers for the four Dimensionality Reduction Techniques using the Dragonfly feature selection method. It is evident from the table that the computational complexity of all the classifiers is relatively similar, while their performance exhibits a significant level of accuracy. Notably, all four dimensionality reduction techniques demonstrate the highest computational complexity compared to their counterparts. Specifically, Bessel Function, DCT, LSLR, and AAA classifiers achieve a computational complexity of O(8n5log 2n), O(8n5log 2n), O(8n6log 4n), and O(8n6log 8n) respectively. Regarding accuracy, Bessel Function, DCT, LSLR, and AAA classifiers achieve the highest accuracy values of 81.42%, 91.42%, 90%, and 95.71% respectively. Moreover, the corresponding kappa values for these classifiers are 0.538, 0.796, 0.772, and 0.864, indicating their robust performance.

Comparison of previous works

As mentioned in the Table 16 it is notice that, majority of the machine learning classifiers such as SVM(RBF), Naïve Bayes, Logistic Regression, Decision tree, Non-linear regression, random forest, multilayer perceptron, and Deep neural networks are utilized to classify the diabetics, based on the clinical data base. All the classifiers accuracy is at the range of 67% - 95%. The current study is based on microarray gene to detect diabetes and SVM(RBF) achieved accuracy of 95%.

6.4. Limitation and Major Outcomes

The findings of this study may be limited to the specific population of diabetic mellitus type 2 patients and may not be applicable to other populations or different types of diabetes. The analysis in this study relies on microarray gene data, which may not be readily available or accessible in all healthcare settings. The methods proposed in this study, such as microarray gene arrays, may involve complex and expensive procedures that are not feasible for routine clinical practice. The performance of classifiers in this study may be influenced by the presence of outliers in the data. Outliers can have a significant impact on the accuracy and reliability of classification results. The developed classification approach, which utilizes various dimensionality reduction techniques and feature selection methods, has demonstrated its potential in effectively screening and predicting diabetic markers, while also identifying associated diseases such as strokes, kidney failure, and neuropathy. An outcome of this study is the establishment of a comprehensive database for mass screening and sequencing of diabetic genomes. By incorporating microarray gene data and leveraging the proposed classification techniques, this database enables the identification of patterns and trends in diabetes outbreaks associated with different lifestyles.

The ability to detect diabetes in its early stages and predict associated diseases is of utmost importance for chronic diabetic patients. This will facilitate timely interventions, improve disease management, and ultimately, better patient outcomes. Overall, this research contributes valuable insights to the field and lays the foundation for further investigations into the early detection and management of diabetic mellitus type 2 patients.

6.5. Conclusion

The results obtained from the BF-DR technique, the classifiers exhibited lower accuracy and other performance metrics, which can be attributed to the inherent limitations of the Bessel function. However, the DCT and LSLR techniques produced improved accuracy and performance metrics for specific classifiers, such as the SVM (RBF) classifier. Especially, the AAA technique, combined with the SVM (RBF) classifier, achieved the highest accuracy of 90% without feature selection. The SVM (RBF) classifier in combination with the EHO feature selection technique achieved the highest accuracy values of 90%, 88.57%, and 95.71% for DCT, LSLR, and AAA respectively. With the use of Dragonfly feature selection method, which also showed promising results with the classifiers achieved high accuracy values of 81.42%, 91.42%, 90%, and 95.71% for BF, DCT, LSLR, and AAA respectively. In terms of computational complexity, we observed that the classifiers exhibited similar complexities across the different dimensionality reduction techniques. However, their performance in terms of accuracy varied significantly. Notably, the SVM (RBF) classifier in combination with the EHO feature selection technique consistently achieved the highest accuracy across different dimensionality reduction techniques. In conclusion, this research article presents a novel method for detecting type II diabetes mellitus using microarray gene data. The future work will be in the direction of Convolution Neural Network (CNN), Deep Learning Networks (DNN), LSTM and Hyper parameter tuning of classifiers.