# Clustering by Hybrid K-Means-Based Rider Sunflower Optimization Algorithm for Medical Data

Authors: A. Jaya Mabel Rani; A. Pravin
Journal: Advances in Fuzzy Systems
 (2022)

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## Abstract

Currently, medical data clustering is a very active and effective part of the research area to take proper decisions at the medical field from medical data sets. But medical data clustering is a very challenging issue due to limitless receiving data, vast size, and high frequencies. To achieve this and improve the performance with fast and effective clustering, this paper proposes a hybrid optimization technique, namely, the K-means-based rider sunflower optimization (RSFO) algorithm for medical data. In this research, initially, the data preprocessing phase has been carried out to clean the current input medical data, and then in the second phase, important features are chosen with the help of the Tversky index with holoentropy. Finally, medical data clustering has been carried out by using hybrid K-means-based rider sunflower optimization (RSFO) algorithm. RSFO is designed to produce optimum clustering centroid, which is the combination of two optimization techniques, such as rider optimization algorithm (ROA) and sunflower optimization (SFO). This hybrid algorithm can get the advantages of both K-means and RSFO technique and avoid premature convergence of K-means algorithm and high computation cost of optimization technique. K-Means clustering algorithm is used to cluster the medical data by using an optimum centroid. The efficiency of the proposed K-means-based rider sunflower optimization algorithm is examined with a heart disease data set and analyzed based on three different performance metrics.


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## Body

## 1. Introduction

Today, there are many clustering models under the data mining, which is the sub-branch of artificial intelligence [1]. The main objective of the recent researchers is to project and provide the model in a very fast and effective manner for any type of data. This paper is also designed based on fast and effective clustering than existing models. For effective and efficient clustering of medical data, this paper proposed hybrid data clustering, which can avoid the premature convergence of K-means algorithm and can reduce the computation cost of optimization technique. Today, medical data are in the form of high dimensional with heterogeneous data, remote sensing data, geographical data, and a huge volume of real-time applications with hidden data [2]. For this type of medical data, there needs proper data analysis to take proper analysis decision by the medical personnel. At the time-optimal feature, the selection is also an important task for a proper decision-making system in the sense of good quality prediction. Medical data also have missing data, data redundancy, incomplete data, and data inconsistency, So there is in need of proper data preprocessing technique for the current input data. To manage all these difficult processing, we need proper intelligent techniques under machine learning and data mining, which is simply called medical data mining. The main objective is to cluster the data from a large amount of databases. There are different categories of clustering models such as partitioning clustering [3], density-based clustering [4], optimization-based clustering, and fuzzy-based (soft and clustering) and hybrid-based clustering algorithms [5, 6]. This proposed paper also used a hybrid optimization-based clustering algorithm to produce optimum clustering centroid with a faster clustering solution, which integrates the advantages of traditional clustering with optimization-based clustering centroid. Each hybrid optimization method has its style and procedures for clustering the data. To inherit the advantages of both traditional and optimization-based clustering, this paper proposed the K-means-based rider sunflower optimization (RSFO) [7] algorithm. RSFO is the combination of both rider optimization (ROA) [8] and Sunflower optimization (SFO) [9], which is simply called rider sunflower optimization-based clustering. Here, K-means is the most popular and partition-based traditional clustering algorithm. But, it has some disadvantages like being very sensitive for initializing and premature convergence [10, 11]. The proposed integrated RSFO reduced the complexity of analyzing data, so obviously it takes less time and memory. At the same time, optimization-based clustering techniques take more computation cost due to a greater number of computing steps [12, 13]. This proposed model handles three steps, such as data preprocessing, feature selection by Tversky index with holoentropy [14, 15], and the final step of medical data clustering K-means rider sunflower optimization algorithm.


### 1.1. The Major Contribution of the Research Paper

This paper proposed global optimization technique, to find cluster centroid by using RSFO, and the number of clusters is defined by the user. This research work is structured in the following manner: Section1 explains the basic introduction part, Section 2 gives challenges of medical data clustering, Section 3 explains the proposed method of medical data clustering, Section 4 explains experimental results and discussion with performance metrics, and Section 5 provides the simulation results based on the proposed K-means-based rider sunflower optimization algorithm. Comparative analysis is done in Section 6. Finally, Section 7 concludes the research work.


### 1.2. Literature Review

In this literature review, five various existing methods are reviewed with its advantages and disadvantages. In 2018, Yelipe et al. [16] proposed an imputation-based class-based clustering (IM-CBC) with the help of class-based clustering classifier (CBCC) in the form of hybrid clustering to find the similarity between the two different medical records. This paper used fuzzy-similarity functions and Euclidean distance of K-means algorithm to find the similarity of the clusters. Then, we used support vector machine (SVM) and k-nearest neighbour (k-NN) for performing the classification. Finally proposed algorithm produced the result with high accuracy and performance. However, this method did not consider fuzzy measures for better classifying and predicting of medical data. Then, in that same 2018, Das et al. [4] proposed a modified Bee colony optimization (MBCO) approach for clustering the data with probability-based selection method. This optimization-based clustering shows faster convergence than other methods. This modified Bee colony optimization hybrid is with K-means algorithm to improve the performance and to achieve a global optimal solution and classification accuracy with the help of chaotic theory. But, this optimization method is not used with multiobjective optimization functions for initializing the clustering centroid to process high-frequency data streams. Then, in 2019, Al-Shammari et al. [17] proposed density-based clustering in the sense of dynamic framework for classifying the medical data with the help of piece-wise aggregate approximation and the density-based spatial clustering algorithm to enhance the better performance and maintenance of the dynamic cluster. But, this proposed algorithm is not considered about high frequency of incoming data streams for updating and maintaining the data clusters. In 2019, Chauhan et al. [18] proposed two-step clustering technology for patient’s disorder analysis using different data variables for optimal clusters with different shapes and sizes. The main objective of this paper is diagnosis of liver disease at the earlier stage from the hidden knowledge with huge database. In 2020, Baliarsingh et al. [19] proposed a medical data classification by memetic algorithm-based SVM (M-SVM), which is the combination of social engineering optimizer and emperor penguin optimization. This algorithm can classify the medical data in very accurate manner. But, this method is not applied for large-scale data sets.


## 1.1. The Major Contribution of the Research Paper

This paper proposed global optimization technique, to find cluster centroid by using RSFO, and the number of clusters is defined by the user. This research work is structured in the following manner: Section1 explains the basic introduction part, Section 2 gives challenges of medical data clustering, Section 3 explains the proposed method of medical data clustering, Section 4 explains experimental results and discussion with performance metrics, and Section 5 provides the simulation results based on the proposed K-means-based rider sunflower optimization algorithm. Comparative analysis is done in Section 6. Finally, Section 7 concludes the research work.


## 1.2. Literature Review

In this literature review, five various existing methods are reviewed with its advantages and disadvantages. In 2018, Yelipe et al. [16] proposed an imputation-based class-based clustering (IM-CBC) with the help of class-based clustering classifier (CBCC) in the form of hybrid clustering to find the similarity between the two different medical records. This paper used fuzzy-similarity functions and Euclidean distance of K-means algorithm to find the similarity of the clusters. Then, we used support vector machine (SVM) and k-nearest neighbour (k-NN) for performing the classification. Finally proposed algorithm produced the result with high accuracy and performance. However, this method did not consider fuzzy measures for better classifying and predicting of medical data. Then, in that same 2018, Das et al. [4] proposed a modified Bee colony optimization (MBCO) approach for clustering the data with probability-based selection method. This optimization-based clustering shows faster convergence than other methods. This modified Bee colony optimization hybrid is with K-means algorithm to improve the performance and to achieve a global optimal solution and classification accuracy with the help of chaotic theory. But, this optimization method is not used with multiobjective optimization functions for initializing the clustering centroid to process high-frequency data streams. Then, in 2019, Al-Shammari et al. [17] proposed density-based clustering in the sense of dynamic framework for classifying the medical data with the help of piece-wise aggregate approximation and the density-based spatial clustering algorithm to enhance the better performance and maintenance of the dynamic cluster. But, this proposed algorithm is not considered about high frequency of incoming data streams for updating and maintaining the data clusters. In 2019, Chauhan et al. [18] proposed two-step clustering technology for patient’s disorder analysis using different data variables for optimal clusters with different shapes and sizes. The main objective of this paper is diagnosis of liver disease at the earlier stage from the hidden knowledge with huge database. In 2020, Baliarsingh et al. [19] proposed a medical data classification by memetic algorithm-based SVM (M-SVM), which is the combination of social engineering optimizer and emperor penguin optimization. This algorithm can classify the medical data in very accurate manner. But, this method is not applied for large-scale data sets.


## 2. Challenges

The following challenges are faced by existing methods: the first one is finding proper cluster centroid and producing clustering results based on optimum cluster centroids which are not guaranteed. Second, data preprocessing, such as missing data, data redundancy, and data inconsistency, is the next main challenge in data clustering. Then, in medical data clustering, it is complex research, in real-time applications due to massive volume, unlimited incoming data, a huge amount of heterogeneous data, and high frequency of data [20]. To avoid this problem, here we proposed the most relevant features of the medical data clustering, so it can reduce the complexity of data analysis with less time and memory.


## 3. Proposed K-Means Clustering-Based RSFO for Medical Data Clustering

This section boons the proposed clustering algorithm K-means clustering based on RSFO, for medical data clustering. Rider sunflower optimization (RSFO) technique is designed by combining ROA and SFO. This technique hybridizes the advantages of both optimization such as ROA and SFO to define optimum centroid with faster convergence. Figure1 illustrates the view of the proposed hybrid optimization-based clustering.Figure 1
Pictorial representation of the proposed hybrid optimization-based clustering.


### 3.1. Data Preprocessing

The good quality of input data can produce good quality of output. The medical input data may have missing data or inconsistent data or noisy data. This type of uncleaned input data may affect the quality of output. To produce good quality of input data, data must be cleaned by preprocessing techniques. Data preprocessing must be done with every input data to clean noisy data, missing data, and inconsistent data. So, data preprocessing is very important part for processing the input medical data to smoothen from the huge amount of data and eliminate inconsistent and noisy data to produce better clustering results.


### 3.2. Feature Selection

The significance feature selection or feature extraction is the next important step to identify high relevant features to produce a better clustering solution. Here, all irrelevant features can be avoided or eliminated by using feature selection method. At the same time, complexity of the data is also reduced by reducing the number of features. There are different feature selection methods available to identify and remove irrelevant features, which depends on the data types used such as Laplacian score feature selection, and reference [21]explains about spectral feature selection for supervised and unsupervised learning [22], unsupervised feature selection with multisubspace randomization [23], etc. In this paper, feature selection is done by using the Tversky index with holoentropy.


#### 3.2.1. Tversky Index Using Holoentropy

The Tversky index compares two data sets and finds similarities between the two data sets and is also used to extract the most relevant terms from the database, by using a feature evaluation function. At the same time, it can reduce the computational complexity to improve accuracy [24]. Tversky index uses Dice’s coefficient and Tanimoto coefficient, which has a value between 0 and 1. The holoentropy is applied in Tversky index parameters α and β to find the relationship between features and attributes [25]. Holoentropy is calculated by using the product of entropy and weight function, which is given in the following:(1)HEγ=ω×Entγ.Here,HE(γ) refers to holoentropy, weight function is ω, and Ent(γ) is called as entropy measure. Here, the entropy Ent(γ) is calculated by(2)Entγ=−∑i=1uγpilogpi.Here,u(γ) is the number of unique values in data and γ is used to apply on the Tversky parameters on α and β.The procedural steps for RSFO are given as follows:Step 1: initialize the initial parameters and randomly select the initial cluster centroidsC = {Cen1, Cen2, . . ., Cenj}Step 2: evaluate the fitness function by equation(3)Ffits=ofZ,where “Z” is the number of clusters and Of is the objective function, which is calculated by the (4)0f=∑j=1z∑i=1pDisxij,GjUij.Here, “P “denotes the total number of data points and |Uij| is the total amount of data elements belonging to the cluster. Here, two data points distance measure is calculated by the (5)DisXi,Gj=∑i=1DXij−Gj2.Cluster centroid will be recalculated by the(6)Gj=1Nj∑∀Xj∈CjXi.Find performance fitness value based on Euclidean distance measure between cluster centroid and data points of each intercluster and intracluster [26]. Then, cluster centroid will be found by rider sunflower optimization (RSFO).(7)Ffits=∑j=1Z∑i=1PDisXij,Gj/UijK.Update the optimal clustering centroid based on rider sunflower optimization (RSFO), which is given in following section.


#### 3.2.2. Proposed RSFO Algorithm

For better clustering results, we are in need to produce optimum clustering centroids. So, to find a better clustering centroid, we used the RSFO algorithm, which is the combination of sunflower optimization (SFO) and rider optimization algorithm (ROA). This proposed model gets the rewards of both ROA and SFO to produce better clustering solutions with faster convergence. ROA [27] works by the behavior of different types of riders to the terminus. Here are four different types of riders such as bypass rider, attacker, follower, and overtaker, respectively. The sunflower optimization (SFO) works by the rotation of the sun. Sunflower always mimics the rotation, which is nature-inspired optimization [28]. This model can determine the good locations for better performance. At the same time, it uses high computation complexity due to high computation steps. To obtain a global optimal solution with better computation steps and fast performance, we used the hybrid ROA method with the SFO.The procedural steps for hybrid K-means-based rider sunflower optimization is given as follows:Step 1.
Initialize the initial parametersStep 2.
Evaluate fitness function by Lagrangian optimization principle, which is given in the equations:(8)M=∑p=1K∑q=1gwqpdp−lp2+ρlnwqp+ρlndq−lp2=∑q=1gηq−1∑p=1kwqp.
Here,dq refers to data object, user defined constant is denoted by ρ, lp refers to the center of the cluster, lp is the fuzzy membership function, K indicates the total cluster centers, and g is the total data. Then, the above equation will derivate as follows:(9)∂M∂wqp=dq−lp2+ρwqp−ηq=0,wqp=ρηq−dq−lp2.
Since∑p=1KWqp=1, which is given as(10)∑p=1K1ηq−dq−lp2=1ρ,we should ensure wqp≥0 ≥0.Step 3.
Update the Position for the rider groups
For position updation, we used bypass rider to maximize the achievement rate. Bypass riders always track and follow a common usual path without other riders’ information. The equation for position updation based on bypass rider is shown as(11)Bt+1r,p=ϑBtt,p∗mp+Btμ,p∗1−mp.
Here, the parametersϑ, t, m, and μ indicate the random numbers from 0 to 1. Then, k indicates the number of iterations, which is defined by user. Assuming μ = r, the equation is rewritten as(12)Bt+1r,p=ϑBtt,p∗mp+Btr,p∗1−mp.
The sunflower optimization (SFO) updates the position or solution space by the rotation of sun. Sunflower always mimics the rotation of sun. Thus, the position updation of SFO is given by(13)Br,p=Btr,p+yr×gr.
Here,Bt(r, p) denotes the current position at the time t, Bt+1(r, p) is the updated position at the time t+1, Bt+1r,p denotes the step of sunflower, and gr refers to the direction of the sunflower.(14)Btr,p=Bt+1r,pyr×gr.
For position updation, substitute the (15), which is the position updation of sunflower optimization in (13), that is the position updation of rider optimization.(15)Bt+1r,p=ϑBtt,p∗mp+Bt+1r,pyr×gr∗1−mp,(16)Bt+1r,p=ϑBtt,p∗mp+Bt+1r,p1−mp−yr×gr∗1−mp.
Then, rearranging (15) and (16), we get(17)Bt+1r,p=ϑBtt,p∗mp+Bt+1r,p−Bt+1r,pmpyrgr+yrgrmp,Bt+1r,pBt+1r,pϑ+ϑBr+1r,pmp=ϑBtt,p∗mpyrtr+yrtrmp,Bt+1r,p1−ϑ+ϑmp=ϑBtt,p∗mpyrtr+yrtrmp.
Then, the final equation will be written as(18)Bt+1r,p=11−ϑ1−mpϑBtt,p∗mpyrtr1−mp.Step 4.
Defining the best solution
Here, the maximal fitness value is considered as a best solution and update rider optimization parameters for the best solution.Step 5.
Termination condition
The above steps 2 to 4 are repeated until the defined number of iterations are reached.


## 3.1. Data Preprocessing

The good quality of input data can produce good quality of output. The medical input data may have missing data or inconsistent data or noisy data. This type of uncleaned input data may affect the quality of output. To produce good quality of input data, data must be cleaned by preprocessing techniques. Data preprocessing must be done with every input data to clean noisy data, missing data, and inconsistent data. So, data preprocessing is very important part for processing the input medical data to smoothen from the huge amount of data and eliminate inconsistent and noisy data to produce better clustering results.


## 3.2. Feature Selection

The significance feature selection or feature extraction is the next important step to identify high relevant features to produce a better clustering solution. Here, all irrelevant features can be avoided or eliminated by using feature selection method. At the same time, complexity of the data is also reduced by reducing the number of features. There are different feature selection methods available to identify and remove irrelevant features, which depends on the data types used such as Laplacian score feature selection, and reference [21]explains about spectral feature selection for supervised and unsupervised learning [22], unsupervised feature selection with multisubspace randomization [23], etc. In this paper, feature selection is done by using the Tversky index with holoentropy.


### 3.2.1. Tversky Index Using Holoentropy

The Tversky index compares two data sets and finds similarities between the two data sets and is also used to extract the most relevant terms from the database, by using a feature evaluation function. At the same time, it can reduce the computational complexity to improve accuracy [24]. Tversky index uses Dice’s coefficient and Tanimoto coefficient, which has a value between 0 and 1. The holoentropy is applied in Tversky index parameters α and β to find the relationship between features and attributes [25]. Holoentropy is calculated by using the product of entropy and weight function, which is given in the following:(1)HEγ=ω×Entγ.Here,HE(γ) refers to holoentropy, weight function is ω, and Ent(γ) is called as entropy measure. Here, the entropy Ent(γ) is calculated by(2)Entγ=−∑i=1uγpilogpi.Here,u(γ) is the number of unique values in data and γ is used to apply on the Tversky parameters on α and β.The procedural steps for RSFO are given as follows:Step 1: initialize the initial parameters and randomly select the initial cluster centroidsC = {Cen1, Cen2, . . ., Cenj}Step 2: evaluate the fitness function by equation(3)Ffits=ofZ,where “Z” is the number of clusters and Of is the objective function, which is calculated by the (4)0f=∑j=1z∑i=1pDisxij,GjUij.Here, “P “denotes the total number of data points and |Uij| is the total amount of data elements belonging to the cluster. Here, two data points distance measure is calculated by the (5)DisXi,Gj=∑i=1DXij−Gj2.Cluster centroid will be recalculated by the(6)Gj=1Nj∑∀Xj∈CjXi.Find performance fitness value based on Euclidean distance measure between cluster centroid and data points of each intercluster and intracluster [26]. Then, cluster centroid will be found by rider sunflower optimization (RSFO).(7)Ffits=∑j=1Z∑i=1PDisXij,Gj/UijK.Update the optimal clustering centroid based on rider sunflower optimization (RSFO), which is given in following section.


### 3.2.2. Proposed RSFO Algorithm

For better clustering results, we are in need to produce optimum clustering centroids. So, to find a better clustering centroid, we used the RSFO algorithm, which is the combination of sunflower optimization (SFO) and rider optimization algorithm (ROA). This proposed model gets the rewards of both ROA and SFO to produce better clustering solutions with faster convergence. ROA [27] works by the behavior of different types of riders to the terminus. Here are four different types of riders such as bypass rider, attacker, follower, and overtaker, respectively. The sunflower optimization (SFO) works by the rotation of the sun. Sunflower always mimics the rotation, which is nature-inspired optimization [28]. This model can determine the good locations for better performance. At the same time, it uses high computation complexity due to high computation steps. To obtain a global optimal solution with better computation steps and fast performance, we used the hybrid ROA method with the SFO.The procedural steps for hybrid K-means-based rider sunflower optimization is given as follows:Step 1.
Initialize the initial parametersStep 2.
Evaluate fitness function by Lagrangian optimization principle, which is given in the equations:(8)M=∑p=1K∑q=1gwqpdp−lp2+ρlnwqp+ρlndq−lp2=∑q=1gηq−1∑p=1kwqp.
Here,dq refers to data object, user defined constant is denoted by ρ, lp refers to the center of the cluster, lp is the fuzzy membership function, K indicates the total cluster centers, and g is the total data. Then, the above equation will derivate as follows:(9)∂M∂wqp=dq−lp2+ρwqp−ηq=0,wqp=ρηq−dq−lp2.
Since∑p=1KWqp=1, which is given as(10)∑p=1K1ηq−dq−lp2=1ρ,we should ensure wqp≥0 ≥0.Step 3.
Update the Position for the rider groups
For position updation, we used bypass rider to maximize the achievement rate. Bypass riders always track and follow a common usual path without other riders’ information. The equation for position updation based on bypass rider is shown as(11)Bt+1r,p=ϑBtt,p∗mp+Btμ,p∗1−mp.
Here, the parametersϑ, t, m, and μ indicate the random numbers from 0 to 1. Then, k indicates the number of iterations, which is defined by user. Assuming μ = r, the equation is rewritten as(12)Bt+1r,p=ϑBtt,p∗mp+Btr,p∗1−mp.
The sunflower optimization (SFO) updates the position or solution space by the rotation of sun. Sunflower always mimics the rotation of sun. Thus, the position updation of SFO is given by(13)Br,p=Btr,p+yr×gr.
Here,Bt(r, p) denotes the current position at the time t, Bt+1(r, p) is the updated position at the time t+1, Bt+1r,p denotes the step of sunflower, and gr refers to the direction of the sunflower.(14)Btr,p=Bt+1r,pyr×gr.
For position updation, substitute the (15), which is the position updation of sunflower optimization in (13), that is the position updation of rider optimization.(15)Bt+1r,p=ϑBtt,p∗mp+Bt+1r,pyr×gr∗1−mp,(16)Bt+1r,p=ϑBtt,p∗mp+Bt+1r,p1−mp−yr×gr∗1−mp.
Then, rearranging (15) and (16), we get(17)Bt+1r,p=ϑBtt,p∗mp+Bt+1r,p−Bt+1r,pmpyrgr+yrgrmp,Bt+1r,pBt+1r,pϑ+ϑBr+1r,pmp=ϑBtt,p∗mpyrtr+yrtrmp,Bt+1r,p1−ϑ+ϑmp=ϑBtt,p∗mpyrtr+yrtrmp.
Then, the final equation will be written as(18)Bt+1r,p=11−ϑ1−mpϑBtt,p∗mpyrtr1−mp.Step 4.
Defining the best solution
Here, the maximal fitness value is considered as a best solution and update rider optimization parameters for the best solution.Step 5.
Termination condition
The above steps 2 to 4 are repeated until the defined number of iterations are reached.


## 3.2.1. Tversky Index Using Holoentropy

The Tversky index compares two data sets and finds similarities between the two data sets and is also used to extract the most relevant terms from the database, by using a feature evaluation function. At the same time, it can reduce the computational complexity to improve accuracy [24]. Tversky index uses Dice’s coefficient and Tanimoto coefficient, which has a value between 0 and 1. The holoentropy is applied in Tversky index parameters α and β to find the relationship between features and attributes [25]. Holoentropy is calculated by using the product of entropy and weight function, which is given in the following:(1)HEγ=ω×Entγ.Here,HE(γ) refers to holoentropy, weight function is ω, and Ent(γ) is called as entropy measure. Here, the entropy Ent(γ) is calculated by(2)Entγ=−∑i=1uγpilogpi.Here,u(γ) is the number of unique values in data and γ is used to apply on the Tversky parameters on α and β.The procedural steps for RSFO are given as follows:Step 1: initialize the initial parameters and randomly select the initial cluster centroidsC = {Cen1, Cen2, . . ., Cenj}Step 2: evaluate the fitness function by equation(3)Ffits=ofZ,where “Z” is the number of clusters and Of is the objective function, which is calculated by the (4)0f=∑j=1z∑i=1pDisxij,GjUij.Here, “P “denotes the total number of data points and |Uij| is the total amount of data elements belonging to the cluster. Here, two data points distance measure is calculated by the (5)DisXi,Gj=∑i=1DXij−Gj2.Cluster centroid will be recalculated by the(6)Gj=1Nj∑∀Xj∈CjXi.Find performance fitness value based on Euclidean distance measure between cluster centroid and data points of each intercluster and intracluster [26]. Then, cluster centroid will be found by rider sunflower optimization (RSFO).(7)Ffits=∑j=1Z∑i=1PDisXij,Gj/UijK.Update the optimal clustering centroid based on rider sunflower optimization (RSFO), which is given in following section.


## 3.2.2. Proposed RSFO Algorithm

For better clustering results, we are in need to produce optimum clustering centroids. So, to find a better clustering centroid, we used the RSFO algorithm, which is the combination of sunflower optimization (SFO) and rider optimization algorithm (ROA). This proposed model gets the rewards of both ROA and SFO to produce better clustering solutions with faster convergence. ROA [27] works by the behavior of different types of riders to the terminus. Here are four different types of riders such as bypass rider, attacker, follower, and overtaker, respectively. The sunflower optimization (SFO) works by the rotation of the sun. Sunflower always mimics the rotation, which is nature-inspired optimization [28]. This model can determine the good locations for better performance. At the same time, it uses high computation complexity due to high computation steps. To obtain a global optimal solution with better computation steps and fast performance, we used the hybrid ROA method with the SFO.The procedural steps for hybrid K-means-based rider sunflower optimization is given as follows:Step 1.
Initialize the initial parametersStep 2.
Evaluate fitness function by Lagrangian optimization principle, which is given in the equations:(8)M=∑p=1K∑q=1gwqpdp−lp2+ρlnwqp+ρlndq−lp2=∑q=1gηq−1∑p=1kwqp.
Here,dq refers to data object, user defined constant is denoted by ρ, lp refers to the center of the cluster, lp is the fuzzy membership function, K indicates the total cluster centers, and g is the total data. Then, the above equation will derivate as follows:(9)∂M∂wqp=dq−lp2+ρwqp−ηq=0,wqp=ρηq−dq−lp2.
Since∑p=1KWqp=1, which is given as(10)∑p=1K1ηq−dq−lp2=1ρ,we should ensure wqp≥0 ≥0.Step 3.
Update the Position for the rider groups
For position updation, we used bypass rider to maximize the achievement rate. Bypass riders always track and follow a common usual path without other riders’ information. The equation for position updation based on bypass rider is shown as(11)Bt+1r,p=ϑBtt,p∗mp+Btμ,p∗1−mp.
Here, the parametersϑ, t, m, and μ indicate the random numbers from 0 to 1. Then, k indicates the number of iterations, which is defined by user. Assuming μ = r, the equation is rewritten as(12)Bt+1r,p=ϑBtt,p∗mp+Btr,p∗1−mp.
The sunflower optimization (SFO) updates the position or solution space by the rotation of sun. Sunflower always mimics the rotation of sun. Thus, the position updation of SFO is given by(13)Br,p=Btr,p+yr×gr.
Here,Bt(r, p) denotes the current position at the time t, Bt+1(r, p) is the updated position at the time t+1, Bt+1r,p denotes the step of sunflower, and gr refers to the direction of the sunflower.(14)Btr,p=Bt+1r,pyr×gr.
For position updation, substitute the (15), which is the position updation of sunflower optimization in (13), that is the position updation of rider optimization.(15)Bt+1r,p=ϑBtt,p∗mp+Bt+1r,pyr×gr∗1−mp,(16)Bt+1r,p=ϑBtt,p∗mp+Bt+1r,p1−mp−yr×gr∗1−mp.
Then, rearranging (15) and (16), we get(17)Bt+1r,p=ϑBtt,p∗mp+Bt+1r,p−Bt+1r,pmpyrgr+yrgrmp,Bt+1r,pBt+1r,pϑ+ϑBr+1r,pmp=ϑBtt,p∗mpyrtr+yrtrmp,Bt+1r,p1−ϑ+ϑmp=ϑBtt,p∗mpyrtr+yrtrmp.
Then, the final equation will be written as(18)Bt+1r,p=11−ϑ1−mpϑBtt,p∗mpyrtr1−mp.Step 4.
Defining the best solution
Here, the maximal fitness value is considered as a best solution and update rider optimization parameters for the best solution.Step 5.
Termination condition
The above steps 2 to 4 are repeated until the defined number of iterations are reached.


## 4. Experimental Results and Discussion

The experimental results provide for the proposed K-means-based rider sunflower optimization which is implemented using the programming language of Python 3.8.6 version in the Windows 10 operating system, Intel i5 core processor. Heart disease-based medical data set is used for conducting the experimentation from online source [29] to predict the heart disease risk factors with 300 instances and 7 main attributes such as age, random blood sugar, gender, body mass index, cholesterol, random blood sugar, smoking, systolic BP [30–33]with 500 iterations. These data were collected from Mr. Jims Johnson, Staff Nurse, whose goal is to provide the proper decision and suggestion to that particular heart patient. This decision can provide various suggestions to the patient such as healthy food diet, type of exercise, walking distance, medicine to take, walking distance, and regular medical checkup. For experimental results, only less quantity of data were taken. In real time, this algorithm can handle large quantity of data sets.


### 4.1. Performance Metric

The performance metrics for K-means-based rider sunflower optimization is to find data quality, similarity, and correct decision ratio from true positives, true negatives, false positives, and false negatives [34–37].


#### 4.1.1. Accuracy

(19)Accuracy=AccTp+AccTnAccTp+AccTn+AccFp+AccFn,where the parameters AccTp, AccTn, AccFp, and AccFn are indicating the total quantity of true positives, true negatives, false positives, and false negatives.


#### 4.1.2. Jaccard Coefficient

(20)JackX,Y=X∩YX∪Y,which is also called Jaccard similarity coefficient, which finds the similarity of two data sets that fall from the range 0% to 100%. When the percentage value increases, the similarity of two data sets also increases. Here, X and Y are two different data sets.


#### 4.1.3. Random Coefficient

(21)Randc=RcTp+RcTnRctp+RcFp+RcFn+RcTn,where the parameters RcTp, RcTn, RcFp, and RcFn are indicating the total quantity of true positives, true negatives, false positives, and false negatives.


## 4.1. Performance Metric

The performance metrics for K-means-based rider sunflower optimization is to find data quality, similarity, and correct decision ratio from true positives, true negatives, false positives, and false negatives [34–37].


### 4.1.1. Accuracy

(19)Accuracy=AccTp+AccTnAccTp+AccTn+AccFp+AccFn,where the parameters AccTp, AccTn, AccFp, and AccFn are indicating the total quantity of true positives, true negatives, false positives, and false negatives.


### 4.1.2. Jaccard Coefficient

(20)JackX,Y=X∩YX∪Y,which is also called Jaccard similarity coefficient, which finds the similarity of two data sets that fall from the range 0% to 100%. When the percentage value increases, the similarity of two data sets also increases. Here, X and Y are two different data sets.


### 4.1.3. Random Coefficient

(21)Randc=RcTp+RcTnRctp+RcFp+RcFn+RcTn,where the parameters RcTp, RcTn, RcFp, and RcFn are indicating the total quantity of true positives, true negatives, false positives, and false negatives.


## 4.1.1. Accuracy

(19)Accuracy=AccTp+AccTnAccTp+AccTn+AccFp+AccFn,where the parameters AccTp, AccTn, AccFp, and AccFn are indicating the total quantity of true positives, true negatives, false positives, and false negatives.


## 4.1.2. Jaccard Coefficient

(20)JackX,Y=X∩YX∪Y,which is also called Jaccard similarity coefficient, which finds the similarity of two data sets that fall from the range 0% to 100%. When the percentage value increases, the similarity of two data sets also increases. Here, X and Y are two different data sets.


## 4.1.3. Random Coefficient

(21)Randc=RcTp+RcTnRctp+RcFp+RcFn+RcTn,where the parameters RcTp, RcTn, RcFp, and RcFn are indicating the total quantity of true positives, true negatives, false positives, and false negatives.


## 5. Simulation Results

Figure2 shows 2-dimensional simulation results for the projected K-means-based rider sunflower optimization with different features of medical data in the sense of three different stages of the clusters.Figure 2
(a) Two-dimensional clustering simulation for age vs cholesterol by using hybrid K-means-based RSFO algorithm. (b) The 2-D clustering simulation of age vs body mass index by using K-means-based RSFO algorithm. (c) The 2-D clustering simulation for age vs random blood pressure using hybrid K-means-based RSFO algorithm.
(a)(b)(c)In this figure, 2-D simulation results, i.e., red color indicates the high-risk factor of the heart disease; blue color indicates average risk factor; and green color denotes the less-risk factor of heart disease based on age vs cholesterol (in Figure2(a)), age vs body mass index (in Figure 2(b)), and age vs random blood pressure (in Figure 2(c)). The abovementioned three diagrams differentiated based on the input features.


## 6. Comparative Analysis

The comparative analysis for the proposed K-means-based rider sunflower optimization using the performance metric is given below based on input size.


### 6.1. Comparative Result Analysis by Input Size

Figures3(a)–3(c) show the qualified comparative study analysis by using input size which is varying from 50 to 300. The accuracy, Jaccard coefficient, and random coefficient proposed K-means-based RSFO input size 50 which are 67.037%, 60.748, and 61.907, as well as for the input size 300 are 90.026%, 89.3426%, and 92.767%, respectively.Figure 3
The comparative study analysis by input size using (a) accuracy, (b) Jaccard coefficient, and (c) random coefficient.
(a)(b)(c)


### 6.2. Comparative Analysis by Table

The comparative analysis table is given in Table1 with the performance measures of best accuracy, Jaccard coefficient, and random coefficient for the proposed K-means-based RSFO which are 90.026%, 89.3426%, and 92.767%, respectively. In this table, the proposed hybrid K-means and rider sunflower optimization technique are compared with existing K-means algorithm, K-harmonic means algorithm, and fuzzy C-means algorithm and show how much more accurate efficient solution is produced. Here, the proposed hybrid KM + RSFO technique produced more accurate efficient solution than existing methods.Table 1
Comparative result analysis table.
InputComparative metricsK-meansKHMFCMKM + RSFOInput sizeAccuracy (%)79.98481.02183.284290.026Jaccard coefficient (%)64.10974.25378.73589.3426Random coefficient (%)70.95372.09578.93692.767Bold values show the result of the proposed KM+RSFO algorithm.


## 6.1. Comparative Result Analysis by Input Size

Figures3(a)–3(c) show the qualified comparative study analysis by using input size which is varying from 50 to 300. The accuracy, Jaccard coefficient, and random coefficient proposed K-means-based RSFO input size 50 which are 67.037%, 60.748, and 61.907, as well as for the input size 300 are 90.026%, 89.3426%, and 92.767%, respectively.Figure 3
The comparative study analysis by input size using (a) accuracy, (b) Jaccard coefficient, and (c) random coefficient.
(a)(b)(c)


## 6.2. Comparative Analysis by Table

The comparative analysis table is given in Table1 with the performance measures of best accuracy, Jaccard coefficient, and random coefficient for the proposed K-means-based RSFO which are 90.026%, 89.3426%, and 92.767%, respectively. In this table, the proposed hybrid K-means and rider sunflower optimization technique are compared with existing K-means algorithm, K-harmonic means algorithm, and fuzzy C-means algorithm and show how much more accurate efficient solution is produced. Here, the proposed hybrid KM + RSFO technique produced more accurate efficient solution than existing methods.Table 1
Comparative result analysis table.
InputComparative metricsK-meansKHMFCMKM + RSFOInput sizeAccuracy (%)79.98481.02183.284290.026Jaccard coefficient (%)64.10974.25378.73589.3426Random coefficient (%)70.95372.09578.93692.767Bold values show the result of the proposed KM+RSFO algorithm.


## 7. Conclusion

Thus, the proposed hybrid K-means-based rider sunflower optimization clustering algorithm for medical data analyses the risk factor of heart disease. The optimal centroid-based clustering solution is produced by using hybrid K-means-based rider sunflower optimization for heart disease-based medical data. The achievement of the proposed K-means-based RSFO algorithm is produced with best accuracy of 90.0236%, Jaccard coefficient of 89.3426%, and random coefficient of 92.767%. This hybrid clustering algorithm can get the advantages of both rider optimization and sunflower optimization thehniques. Here, RSFO is used to produce optimum clustering centroid and K-means algorithm is used to produce fast clustering solution. So, this hybrid clustering algorithm can protect from premature convergence. As a future enhancement, this algorithm can be extended with multiobjective functions for more effective and better clustering centroid.



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*Source: 7783196-2022-03-07.xml*