# PSO-Based Evolutionary Approach to Optimize Head and Neck Biomedical Image to Detect Mesothelioma Cancer

Authors: Sheeba Praveen; Neha Tyagi; Bhagwant Singh; Girija Rani Karetla; Meenakshi Anurag Thalor; Kapil Joshi; Melkamu Tsegaye
Journal: BioMed Research International
 (2022)

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## Abstract

Mesothelioma is a form of cancer that is aggressive and fatal. It is a thin layer of tissue that covers the majority of the patient’s internal organs. The treatments are available; however, a cure is not attainable for the majority of patients. So, a lot of research is being done on detection of mesothelioma cancer using various different approaches; but this paper focuses on optimization techniques for optimizing the biomedical images to detect the cancer. With the restricted number of samples in the medical field, a Relief-PSO head and mesothelioma neck cancer pathological image feature selection approach is proposed. The approach reduces multilevel dimensionality. To begin, the relief technique picks different feature weights depending on the relationship between features and categories. Second, the hybrid binary particle swarm optimization (HBPSO) is suggested to automatically determine the optimum feature subset for candidate feature subsets. The technique outperforms seven other feature selection algorithms in terms of morphological feature screening, dimensionality reduction, and classification performance.


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## Body

## 1. Introduction

Cancer, as one of the common diseases in the world, has a very high fatality rate, among which head and neck cancer (HNC) ranks first among systemic tumors due to its many primary sites and pathological types. At the same time, because the head and neck include most of the important organs and tissues of the human body, the anatomical relationship is complex, and the treatment of this type of cancer is particularly difficult. Therefore, accurate survival prediction of patients is the key to current cancer problems [1].At present, most common survival predictions start from genomics data [2]. However, in addition to this, other cancer data such as pathological images and clinical information are also closely related to the survival prediction of head and neck cancer [3]. A large number of studies have shown that pathological images contain rich information related to cancer survival prediction, which can directly reflect the type of cancer and distinguish benign and malignant tumors and histopathological grades of tumors. This information is related to the prognosis of head and neck cancer, especially survival. It is directly related to the state of cancer [4] and plays a very important role in the prediction of cancer survival [5, 6]. At present, some cancer survival prediction works based on pathological images have been successfully proposed. Yang et al. extracted 166 pathological image morphological features and used them for classification and survival prediction of non-small cell lung cancer [5]. After that, Dong et al. further used the literature [7] tool to extract 9879-dimensional features containing more comprehensive image information from 2186 lung cancer pathological images [6]. However, the image features extracted by the existing tools have the distinctive characteristics of high data dimension and small number of samples relative to the features. These data often contain irrelevant or redundant features [8], which affect the effect of existing machine learning algorithms on small sample high-dimensional data. Reducing the data dimension through feature selection is an effective way to solve this problem.Histology is the study of how cells and tissues of living things look under a microscope. A thin slice (section) of tissue is looked at under a light (optical) or electron microscope to do a histological analysis. In the current research, looking at histology images is seen as the benchmark for clinically diagnosing cancer and figuring out how to treat it and what its prognosis will be [9]. Histopathology is the study of biopsies under a microscope to find and classify diseases. In histology image analysis for cancer detection, histopathologists visually inspect the regularities of cell shapes and tissue distributions, identify whether tissue regions are malignant, and assess the severity of malignancy. This type of histopathological examination has been widely utilized for cancer detection and grading applications, such as prostate, breast, cervical, and lung cancer grading, neuroblastoma categorization, and follicular lymphoma grading [10].As a common dimensionality reduction method, feature selection can be divided into two categories [11]: correlation-based filtered feature selection and search-based heuristic feature selection. Correlation-based filtered feature selection evaluates the effect of feature subsets on classification targets through statistical properties of samples, thereby selecting optimal feature subsets. It does not incorporate any classifiers into the evaluation criteria and has strong independence from subsequent classification algorithms, which can avoid the higher operating costs of classification algorithms caused by high-dimensional data. But at the same time, this statistical method cannot preserve the influence of the correlation between features on the classification results. Common feature selection algorithms under this type include Relief [8], MRMR (minimum-redundancy maximum-relevancy) [11], Mitra feature selection based on feature similarity [12], CFS (completely fair schedule) [13], and FCBF (fast correlation-based filter) [14] and so on.The other is the feature selection based on search. In this kind of algorithm, a heuristic search method is often used to find the optimal feature subset [15]. The feature subset selected in this way guarantees the common influence of the features on the classification target. However, search-based feature selection is affected by the search space and performs poorly on high-dimensional problems. In recent years, due to the excellent global search ability and versatility of evolutionary algorithms, many researchers have focused on searching feature spaces by improving various evolutionary algorithms. Dökeroğlu et al. [15] applied the backbone particle swarm algorithm combined with the nearest neighbor algorithm to feature selection. Dökeroğlu et al. [15] used decision trees for feature selection and used genetic algorithms to find a set of feature subsets that minimized the classification error rate of decision trees. Liu et al. [16] introduced three new initialization mechanisms, individual and global optimal update mechanisms in particle swarm optimization, which improved both the number of features and the classification performance. A heuristic algorithm is one that prioritizes speed over accuracy, precision, or completeness in order to achieve better results faster than more traditional methods. The algorithms apart from heuristic search methods that can be involved for optimization of HNC are swarm intelligence algorithms [17], Tabu search [18], simulated annealing [19], genetic algorithms [20, 21], artificial neural networks [22], support vector machines [23], etc.The objective of the paper is to target the problem of high-dimensional small samples that are generated after feature extraction of head and neck cancer pathological images. The paper is aimed at proposing a multilevel feature selection algorithm based on ReliefF-HBPSO.(1)
To create a multilevel framework, the ReliefF-HBPSO method combines the filtering feature selection algorithm with the heuristic search algorithm. Due to the challenges of low screening accuracy and efficiency in the heuristic search algorithm in a high-dimensional environment, a filtering feature selection technique is presented to limit the search space, enhance the search accuracy, and reduce the algorithm’s running time. The proposed model preprocesses the dataset in the initial stage and then the resulting dataset is fed as an input to ReliefF algorithm. After that HBPSO parameters are initialized and arranged in descending order as the fitness function. The first half OS sorted particles are retained to update the individual extreme position and global extreme position of the current iteration, and the remaining particles are mutated on the basis of the elite particles to generate new descendant particle swarms to participate in the global update optimal. This process is repeated until the iteration termination condition is satisfied, and the optimal feature subset is generated(2)
Hybrid binary evolutionary particle swarm optimization (HBPSO) combines evolving neural strategies (ENS) with classic binary particle swarm optimization (BPSO) to enhance imaging characteristics in head and neck cancer. Binary PSO is a subset of PSO that applies to binary domains; however, it relies on continuous PSO’s concepts of velocity and momentum. The standard PSO has some issues, resulting in slow convergence rates on various optimization tasks and hence resulting in BPSO. In BPSO, the search space is represented as a hypercube. Within this hypercube, it is possible to observe a particle moving to more nearby or more distant corners of the hypercube depending on the number of bits that are inverted. The BPSO algorithm enhances/optimizes the image characteristics. The algorithm uses ENS to make particle mutations form a new particle population, enriching the variety of the population and allowing the program to escape the local optimal solution and boost search efficiency(3)
HBPSO evaluates the efficiency of the ReliefF-HBPSO method on the head and neck cancer pathological image feature data by using the classification accuracy of the decision tree (DT) classifier as the algorithm’s objective function (i.e., the evaluation criteria). ReliefF-HBPSO is a quick technique that discovers a subset of problematic image features with excellent classification performance and a limited number of featuresThe organization of this paper is as follows: Section2 is the premap of mammography images which is the preprocessing process; Section 3 introduces the framework of this method; Section 4 is divided into three parts: the first part introduces the nonsubsampling contour transformation method (NSCT) principle and its applications, Z-Moments are presented in part II, and the third part discusses the classification algorithm of SVM; Section 5 introduces the experimental dataset and presents the experimental results and analysis; and Section 6 presents the conclusion and scope for future work.


## 2. ReliefF-HBPSO Multilevel Pathological Image Feature Selection

This paper proposes a multilevel pathological image feature selection algorithm—ReliefF-HBPSO, which combines ReliefF and HBPSO. As shown in Figure1, for the head and neck cancer data feature set, first use the average value of the corresponding features to complete the entire sample set, and input the dataset after data preprocessing into ReliefF-HBPSO; secondly, extract the data through ReliefF. Low-dimensional features are used as the input of HBPSO, and the optimal feature subsets are obtained by continuous iteration; finally, the feature-selected dataset is divided into a test set and a training set, where the training set is used to train the relevant parameters of the decision tree classifier. The test set is then fed into a decision tree classification model with fixed parameters to obtain the classification results of head and neck cancer data.Figure 1
Multilevel pathological image feature selection algorithm flow.


### 2.1. ReliefF Algorithm

The ReliefF algorithm is a feature selection method based on random selection of feature weight search [8]. It gives different weights to features according to the correlation between a single feature and the data category and regards features that are higher than a specified threshold or meet certain judgment conditions as features. In the candidate subset, the remaining features are removed. The weights of the features are updated according to
(1)wk=wk−∑j=1Pdiffk,R,HMP+∑C≠classRiPC/1−PclassRi×∑j=1Pdiffk,R,MCMP.Among them,Ri is a sample randomly selected from the training sample set U each time, H and MC are the p nearest neighbors found in the same sample set of Ri and the sample set of different classes (set as class C), respectively. In the samples, the selection of the number of neighbor samples p is determined by the actual situation of the dataset, p>0 and less than the minimum value in the class samples; in this paper, p∈0,14, and PC is the number of class C samples in the total number of samples. The probability of M is the sampling times.The patient’s case image features have both continuous and discrete values. When the attribute of thekth feature is a continuous value, the absolute difference between the sample Ra and the sample Rb on the kth feature is calculated according to
(2)diffk,Ra,Rb=valuek,Ra−valuek,Rbmaxk−mink.When the attribute of thekth feature is a discrete value, it is calculated according to
(3)diffk,Ra,Rb=1,valuek,Ra≠valuek,Rb.0,valuek,Ra=valuek,Rb.If the distance betweenXi and Hj on a feature is less than the distance between Xi and MjC, diffk,Ri,Hj<diffk,Ri,MjC, indicating that the feature pair distinguishes between the same and different class samples are beneficial, and the weight of this feature should be increased; otherwise, the weight of this feature should be decreased. Iterate m times to get the best weight of each feature.The largerwk is, the stronger the classification ability of the feature is, and the feature weight is screened. If wk>∂, ∂ is the feature threshold, and the kth feature is reserved as a candidate feature; otherwise, the feature is deleted. Repeat this process until all i features are traversed.


### 2.2. Binary Particle Swarm Optimization (BPSO)

An optimization method known as particle swarm optimization (PSO) uses a large number of candidate solutions (referred to as particles) that move about the search area in a swarm-like fashion to try to identify the optimum global solution [4]. At any given time, each particle has a location x and a velocity v. Particle velocity is changed using a velocity update algorithm that also takes account the best position the particle so far and the best location found by the entire swarm. When optimizing objective functions, this nature-inspired technique performs exceptionally well in a continuous search space. For feature selection, however, the binary version of this technique is needed. To summarize, the basic idea is that a complete solution for feature selection in a PSO technique can be readily described as a binary position vector, where the 1’s represent feature selection and the 0’s represent feature removal [24]. To find the average classification error given any binary vector reflecting the selection of a subset of features, we can use a good classifier like random forest. In this case, the objective function that needs to be minimized is this.Zhang et al. [25, 26] introduced a discrete particle swarm optimization technique (BPSO) based on binary coding to satisfy the needs of discrete issues. The program maps the solution space of the issue to the flight space of birds, abstracting each bird as a particle to represent possible solutions, by replicating the foraging behavior of biological populations (birds).For the high-dimensional feature selection problem, BPSO has two main deficiencies: First, the particles generated by each iteration in BPSO cannot be eliminated even if they are determined to be nonoptimal particles and still participate in the iterative process of the algorithm, which greatly increases the behavior. Second, the more optimal particles in BPSO discard all valuable information at the end of each iteration and are randomly initialized again at the beginning of the next iteration, such behavior patterns and algorithms throughout the evolution. In the process, the goal of tracking the local optimum and the global optimum is always contradictory, which can easily make BPSO fall into a local minimum.Therefore, this paper adopts the evolutionary neural strategy (ENS) to generate a new particle population through particle mutation to enrich the diversity of the population, while discarding the failed particles and reducing the time complexity of the algorithm.


## 2.1. ReliefF Algorithm

The ReliefF algorithm is a feature selection method based on random selection of feature weight search [8]. It gives different weights to features according to the correlation between a single feature and the data category and regards features that are higher than a specified threshold or meet certain judgment conditions as features. In the candidate subset, the remaining features are removed. The weights of the features are updated according to
(1)wk=wk−∑j=1Pdiffk,R,HMP+∑C≠classRiPC/1−PclassRi×∑j=1Pdiffk,R,MCMP.Among them,Ri is a sample randomly selected from the training sample set U each time, H and MC are the p nearest neighbors found in the same sample set of Ri and the sample set of different classes (set as class C), respectively. In the samples, the selection of the number of neighbor samples p is determined by the actual situation of the dataset, p>0 and less than the minimum value in the class samples; in this paper, p∈0,14, and PC is the number of class C samples in the total number of samples. The probability of M is the sampling times.The patient’s case image features have both continuous and discrete values. When the attribute of thekth feature is a continuous value, the absolute difference between the sample Ra and the sample Rb on the kth feature is calculated according to
(2)diffk,Ra,Rb=valuek,Ra−valuek,Rbmaxk−mink.When the attribute of thekth feature is a discrete value, it is calculated according to
(3)diffk,Ra,Rb=1,valuek,Ra≠valuek,Rb.0,valuek,Ra=valuek,Rb.If the distance betweenXi and Hj on a feature is less than the distance between Xi and MjC, diffk,Ri,Hj<diffk,Ri,MjC, indicating that the feature pair distinguishes between the same and different class samples are beneficial, and the weight of this feature should be increased; otherwise, the weight of this feature should be decreased. Iterate m times to get the best weight of each feature.The largerwk is, the stronger the classification ability of the feature is, and the feature weight is screened. If wk>∂, ∂ is the feature threshold, and the kth feature is reserved as a candidate feature; otherwise, the feature is deleted. Repeat this process until all i features are traversed.


## 2.2. Binary Particle Swarm Optimization (BPSO)

An optimization method known as particle swarm optimization (PSO) uses a large number of candidate solutions (referred to as particles) that move about the search area in a swarm-like fashion to try to identify the optimum global solution [4]. At any given time, each particle has a location x and a velocity v. Particle velocity is changed using a velocity update algorithm that also takes account the best position the particle so far and the best location found by the entire swarm. When optimizing objective functions, this nature-inspired technique performs exceptionally well in a continuous search space. For feature selection, however, the binary version of this technique is needed. To summarize, the basic idea is that a complete solution for feature selection in a PSO technique can be readily described as a binary position vector, where the 1’s represent feature selection and the 0’s represent feature removal [24]. To find the average classification error given any binary vector reflecting the selection of a subset of features, we can use a good classifier like random forest. In this case, the objective function that needs to be minimized is this.Zhang et al. [25, 26] introduced a discrete particle swarm optimization technique (BPSO) based on binary coding to satisfy the needs of discrete issues. The program maps the solution space of the issue to the flight space of birds, abstracting each bird as a particle to represent possible solutions, by replicating the foraging behavior of biological populations (birds).For the high-dimensional feature selection problem, BPSO has two main deficiencies: First, the particles generated by each iteration in BPSO cannot be eliminated even if they are determined to be nonoptimal particles and still participate in the iterative process of the algorithm, which greatly increases the behavior. Second, the more optimal particles in BPSO discard all valuable information at the end of each iteration and are randomly initialized again at the beginning of the next iteration, such behavior patterns and algorithms throughout the evolution. In the process, the goal of tracking the local optimum and the global optimum is always contradictory, which can easily make BPSO fall into a local minimum.Therefore, this paper adopts the evolutionary neural strategy (ENS) to generate a new particle population through particle mutation to enrich the diversity of the population, while discarding the failed particles and reducing the time complexity of the algorithm.


## 3. Hybrid Binary Evolutionary Particle Swarm Optimization (HBPSO)

### 3.1. Evolutionary Neural Strategies (ENS)

Evolutionary neural strategies (ENS) is an appropriate strategy learned in mathematical games by Chandrashekar and Sahin [27]. The strategy consists of m neural networks pii=1,2,⋯,m, each network has an adaptive parameter vector σij, each component of σij corresponds to a weight or bias set values, which govern the step size of searching for new mutated parameters of the neural network. Weights or bias values are generated by sampling from a uniform distribution over −2,2.For each parentpi, the offspring p′ii=1,2,⋯,m can be created by
(4)σi′j=σijexpτNj0,1,j=1,2,⋯..,Nw,(5)wi′j=wjj+σi′Nj0,1,j=1,2,⋯..,Nw,whereNj0,1 is the standard normal distribution resampled for each j, Nw represents the maximum number of weights and biases, and τ=1/2Nw.


### 3.2. Improved Algorithm of BPSO HBPSO

The position and velocity of each particlei in the K-dimensional space in the population of m particles can be represented as a vector.The position vectorXi=Xi1,Xi2,⋯,Xik represents the candidate feature subset, and Xik represents the kth feature of the ith particle;The velocity vectorVi=Vi1,Vi2,⋯,Vik represents the probability of selecting this subset of features, i.e., the probability that the particle position Xi is assigned to 1.In the HBPSO algorithm, the position vector and velocity vector of the particle are initialized randomly, and the velocity vector of the particle is updated according to formulas (6) and (7), and the position vector is updated according to
(6)Vikn+1=w×Vikn+c1rand×pbestikn−Xikn+c2rand×pbestikn−Xikn,(7)sigVikn+1=11+exp−Vikn+1,k=1,2,⋯⋯.,K,(8)Xikn+1=1,rand≤sigVikn+1,0,otherwise,(9)fpi=TP+TNF.Among them, TP (true positives) is the number of samples that are correctly classified as positive examples by the classifier, TN (true negatives) is the number of correctly classified as negative examples, andF is the total number of samples.In this paper, the idea of feature selection is introduced into the optimization search algorithm, and the hybrid binary evolutionary particle swarm algorithm (HBPSO) is used, which combines BPSO and ENS to enrich the diversity of particle population through the mutation between the parent and the child in the iterative process. Collaboration and information sharing among individuals also enables better search for optimal feature sets.As shown in Figure2, at each iteration, the fitness function values are sorted, and the winning particles corresponding to the first half of the better fitness values are retained. The optimized individual (or solution) is directly inherited to the next generation and inherits all its information through BPSO regarded as elite particles. And the remaining failed particles with the lowest fitness function value will be discarded. On the basis of the winning particle, new particles are generated by mutation according to formulas (4) and (5) and combined with the elite particles in the original parent pi to form a new population pi′ for the next iteration.Figure 2
HBPSO particle mutation network.The evolution process of particlei in the HBPSO algorithm is shown in Figure 3.Figure 3
Particle evolution process in HBPSO.The mutation feature in ENS is to help the particle population diversify by making particles “fly into” a new search space to achieve the purpose of enriching the population diversity and solve the local optimal solution problem generated by BPSO in the iterative process. At the same time, the same number of particles from the BPSO parent mutation will be used to fill the gaps of the discarded particles. These new particles inherit cognitive traits from their parents, which will in turn enhance the competitiveness and diversity of the ENS.After thek+1th particle state update is completed, the individual optimal value and the population optimal value of the particle are updated. The update methods of the local optimal pbest and the global optimal gbest are as follows
(10)pbestikn+1=Xikn,fXikn<fpbestikn,pbestikn,fXikn≥fpbestikn,gbestn=pbestg,k,g=argmin1≤n≤Mfpbestn,k.Step-1: randomly initialize the parameter PID of the HBPSO algorithm, including the number of particles m, the number of iterationsn, the neighborhood size −a,a, constant parameters c1,c2, etc.Step-2: randomly select a set of particles and initialize the particle positionsrandomXik,Vik, that is, randomly select feature vectors.Step-3: calculate the fitness function f(pi) of all particles according to formula (9).Step-4: traverse all currently existing fitness functionsfpi and sort them in descending order. Simultaneously compute fpi numbers d.Step-5: iffpi≥fpd/2, keep all the information of the elite particle. Update the current particle optimal pbest and population optimal gbest.Step-6: iffpi<fpd/2, calculate the adaptive parameter σi′ according to the formula (4) for each elite particle in step 5, and then calculate the position information of the new particle according to the formula (5). The fitness function fpi corresponding to the elite particles remains unchanged, and new particles are obtained, the number of which is equal to the number of elite particles.Step-7: update the position and velocity of elite particles according to equations (6) to (8), and combine the parent elite particles and mutant particles as the child particle swarm for the next iteration.Step-8: if the current iteration numberj≥n, end the iteration loop and go to step 9; otherwise, go to step 3.Step-9: output the optimal gbest of the population as the optimal solution of the problem and obtain the optimal feature set.


## 3.1. Evolutionary Neural Strategies (ENS)

Evolutionary neural strategies (ENS) is an appropriate strategy learned in mathematical games by Chandrashekar and Sahin [27]. The strategy consists of m neural networks pii=1,2,⋯,m, each network has an adaptive parameter vector σij, each component of σij corresponds to a weight or bias set values, which govern the step size of searching for new mutated parameters of the neural network. Weights or bias values are generated by sampling from a uniform distribution over −2,2.For each parentpi, the offspring p′ii=1,2,⋯,m can be created by
(4)σi′j=σijexpτNj0,1,j=1,2,⋯..,Nw,(5)wi′j=wjj+σi′Nj0,1,j=1,2,⋯..,Nw,whereNj0,1 is the standard normal distribution resampled for each j, Nw represents the maximum number of weights and biases, and τ=1/2Nw.


## 3.2. Improved Algorithm of BPSO HBPSO

The position and velocity of each particlei in the K-dimensional space in the population of m particles can be represented as a vector.The position vectorXi=Xi1,Xi2,⋯,Xik represents the candidate feature subset, and Xik represents the kth feature of the ith particle;The velocity vectorVi=Vi1,Vi2,⋯,Vik represents the probability of selecting this subset of features, i.e., the probability that the particle position Xi is assigned to 1.In the HBPSO algorithm, the position vector and velocity vector of the particle are initialized randomly, and the velocity vector of the particle is updated according to formulas (6) and (7), and the position vector is updated according to
(6)Vikn+1=w×Vikn+c1rand×pbestikn−Xikn+c2rand×pbestikn−Xikn,(7)sigVikn+1=11+exp−Vikn+1,k=1,2,⋯⋯.,K,(8)Xikn+1=1,rand≤sigVikn+1,0,otherwise,(9)fpi=TP+TNF.Among them, TP (true positives) is the number of samples that are correctly classified as positive examples by the classifier, TN (true negatives) is the number of correctly classified as negative examples, andF is the total number of samples.In this paper, the idea of feature selection is introduced into the optimization search algorithm, and the hybrid binary evolutionary particle swarm algorithm (HBPSO) is used, which combines BPSO and ENS to enrich the diversity of particle population through the mutation between the parent and the child in the iterative process. Collaboration and information sharing among individuals also enables better search for optimal feature sets.As shown in Figure2, at each iteration, the fitness function values are sorted, and the winning particles corresponding to the first half of the better fitness values are retained. The optimized individual (or solution) is directly inherited to the next generation and inherits all its information through BPSO regarded as elite particles. And the remaining failed particles with the lowest fitness function value will be discarded. On the basis of the winning particle, new particles are generated by mutation according to formulas (4) and (5) and combined with the elite particles in the original parent pi to form a new population pi′ for the next iteration.Figure 2
HBPSO particle mutation network.The evolution process of particlei in the HBPSO algorithm is shown in Figure 3.Figure 3
Particle evolution process in HBPSO.The mutation feature in ENS is to help the particle population diversify by making particles “fly into” a new search space to achieve the purpose of enriching the population diversity and solve the local optimal solution problem generated by BPSO in the iterative process. At the same time, the same number of particles from the BPSO parent mutation will be used to fill the gaps of the discarded particles. These new particles inherit cognitive traits from their parents, which will in turn enhance the competitiveness and diversity of the ENS.After thek+1th particle state update is completed, the individual optimal value and the population optimal value of the particle are updated. The update methods of the local optimal pbest and the global optimal gbest are as follows
(10)pbestikn+1=Xikn,fXikn<fpbestikn,pbestikn,fXikn≥fpbestikn,gbestn=pbestg,k,g=argmin1≤n≤Mfpbestn,k.Step-1: randomly initialize the parameter PID of the HBPSO algorithm, including the number of particles m, the number of iterationsn, the neighborhood size −a,a, constant parameters c1,c2, etc.Step-2: randomly select a set of particles and initialize the particle positionsrandomXik,Vik, that is, randomly select feature vectors.Step-3: calculate the fitness function f(pi) of all particles according to formula (9).Step-4: traverse all currently existing fitness functionsfpi and sort them in descending order. Simultaneously compute fpi numbers d.Step-5: iffpi≥fpd/2, keep all the information of the elite particle. Update the current particle optimal pbest and population optimal gbest.Step-6: iffpi<fpd/2, calculate the adaptive parameter σi′ according to the formula (4) for each elite particle in step 5, and then calculate the position information of the new particle according to the formula (5). The fitness function fpi corresponding to the elite particles remains unchanged, and new particles are obtained, the number of which is equal to the number of elite particles.Step-7: update the position and velocity of elite particles according to equations (6) to (8), and combine the parent elite particles and mutant particles as the child particle swarm for the next iteration.Step-8: if the current iteration numberj≥n, end the iteration loop and go to step 9; otherwise, go to step 3.Step-9: output the optimal gbest of the population as the optimal solution of the problem and obtain the optimal feature set.


## 4. ReliefF-HBPSO Multilevel Feature Selection Algorithm

The algorithm flow of the ReliefF-HBPSO multilevel feature selection algorithm is shown in Figure4. First, the dataset is preprocessed, and the processed data is sent to the ReliefF algorithm. Large features serve as candidate feature subsets. Secondly, initialize the HBPSO parameters and sort them in descending order with the classification accuracy of the decision tree classifier as the fitness function. The first half of the sorted particles are retained as elite particles to update the individual extreme position and global extreme position of the current iteration, while the remaining particles are mutated on the basis of the elite particles to generate new descendant particle swarms to participate in the global update optimal. This process is repeated until the iteration termination condition is satisfied, and the optimal feature subset is generated.Figure 4
ReliefF-HBPSO multilevel pathological image feature selection algorithm.Let the number of iterations of ReliefF-HBPSO ben and the number of particles to be m, where the total number of features of the ReliefF algorithm is N, the number of sampling times is M, and the number of selected neighbor samples is p, then the time complexity of executing the ReliefF algorithm is OM×maxN×p,N2 . Assuming that the number of features retained after the ReliefF algorithm is executed is K1, the time complexity of the HBPSO algorithm is On×maxm2,mK1/2. The traditional BPSO algorithm does not need to sort the fitness function and mutate the new particles. If the number of features is K2, the time complexity is On×m×K2. Since K1 in the HBPSO algorithm is selected by the ReliefF algorithm for low-dimensional feature selection, it is much lower than K2 using all features in BPSO, and m is usually smaller than K1 and K2, so the time complexity of HBPSO is smaller than that of BPSO. At this point, the time complexity of ReliefF-HBPSO is
(11)OmaxM×maxN×p,N2,n×maxm2,mK12.In terms of space complexity, the HBPSO of the ReliefF-HBPSO algorithm in this paper adds a constant order of intermediate variables in each iteration than the standard BPSO algorithm, such asσij and σi′ in equations (4) and (5) and the storage of related temporary variables, the space complexity has increased, but because the ReliefF algorithm is used before iteration to greatly reduce the length of the particle vector as input in the HBPSO algorithm, the storage space is reduced, so the space is complex. Compared with the standard BPSO algorithm, the degree is still lower.


## 5. Experimental Results

### 5.1. Experimental Data

The experimental data adopts the real patient dataset provided by the California hospital in the United States, in which sensitive personal information about the patients has been removed, and the dataset is preprocessed before use. The original data is the RT pathological image of the patient, and the image format is the CT image of dicom, as shown in Figure5. Text data in csv format with data shape 60,1385 was extracted from CT images of patients by Ibex software [28]. Among them, 60 refer to a total of 60 patients as samples to participate in the prediction, and 1385 refer to the extracted image features with a total of 1385 dimensions.Figure 5
CT image display in Ibex.Since the dataset is real case data, some information is missing, and the average value of the entire column of features is used for completion. For some feature attributes, in order to avoid some attributes with small values from being hidden and to improve the accuracy, the data is standardized.The distribution of survival (in months) for the 60 patients given by the hospital’s raw data is shown in Figure6. According to the analysis of relevant medical literature and doctors’ experience, the survival time of 60 patients was divided into 3 categories, which were denoted by 0, 1, and 2, respectively. Among them, 0 ~ 18 months is the first category, which is represented by 0, with a total of 24 people; 18~36 months is the second category, which is represented by 1, with a total of 15 people; 36~150 months is the third category, with 2 said, a total of 20 people. The proportion of each type of labels to the total is 41%, 25%, and 34%, respectively.Figure 6
Label distribution of survival time.


### 5.2. Experimental Design

The experimental environment of this paper is Windows 10 64-bit operating system, the processor is Intel i5-8250U, 2.6 GHz, and the installed memory RAM is 4.00 GB. Software environment pycharm compiler, python3.5.In order to verify the effectiveness and superiority of the ReliefF-HBPSO algorithm in the feature selection of head and neck cancer pathological images, this paper compares the nondimensionality reduction and feature dimension reduction methods—PCA [29], ReliefF algorithm [30], and whale optimization algorithm-simulate anneal, respectively, with, WOA-SA [31], binary particle swarm optimization (BPSO) [32, 33], hybrid binary evolutionary particle swarm optimization (HBPSO), and ReliefF-BPSO for comparative experiments.Among them, the maximum number of iterationsn of the five models of WOA-SA, BPSO, HBPSO, ReliefF-BPSO, and ReliefF-HBPSO is 100. Other parameters of the WOA-SA model are set according to the literature [34–36]. BPSO and HBPSO model parameter settings: population size m=50, learning factor c1=c2=0.5, inertia coefficient w=2.5, maximum particle velocity Vmax=4, and minimum velocity Vmin=−4. ReliefF-BPSO and ReliefF-HBPSO parameter settings: sampling times M=5, threshold ∂=30293.46, number of nearest neighbor samples p=10, and other parameters are the same as BPSO and HBPSO models. ReliefF parameters: sampling times M=5, threshold ∂=50588.91, and number of nearest neighbor samples p=10.


### 5.3. Result Analysis

For the head and neck cancer pathological image feature dataset extracted by Ibex software, the experiment uses the original data (that is, the dimensionality reduction data), PCA, ReliefF, WOA-SA, BPSO, HBPSO, ReliefF-BPSO, and ReliefF-HBPSO, a total of 8 models. The optimal feature sets under the real dataset are obtained, respectively, and the decision tree classification model is used as the classifier. The dimensionality-reduction technique, known as principal component analysis (PCA) [37], reduces the size of huge datasets by condensing the number of variables in the original dataset into a manageable number [38]. Dimensionality reduction algorithms compromises some accuracy in exchange for more simplicity, and this is the tradeoff that must be made when trying to reduce the size of a dataset. Since small datasets are easy to evaluate and visualize, they allow machine learning algorithms to handle data more quickly without having to deal with additional variables [39]. In this paper, the proposed algorithm is evaluated against this technique to prove its efficiency.The test uses 5-fold cross-validation to calculate the accuracy, precision, recall,F1-score, and running time (unit: s) and compare the multiple items of the 8 models. The classification performance index and its feature subset size illustrate the ability of the algorithm in feature selection and classification prediction. It can be seen from Table 1 that the size of feature subsets selected by the PCA, ReliefF, WOA-SA, BPSO, HBPSO, ReliefF-BPSO, and ReliefF-HBPSO algorithms are reduced by 92%, 94%, 59%, 47%, 53%, 93% and 98%, respectively, compared with those before dimension reduction. And when the dimensionality reduction ratio is the lowest 98%, the ReliefF-HBPSO algorithm achieves the best classification effect of 87%.Table 1
Number of features under different algorithms.
AlgorithmData dimensionAccuracyDimensionality reductionRunning time (s)Not dimensionally reduced13850.5508.61PCA1000.640.927.03ReliefF1100.780.941.89WOA-SA5950.710.5951.04BPSO7250.640.4731.45HBPSO6700.750.5321.93Relief-BPSO400.860.9317.08Relief-HBPSO240.870.9811.06When the dimensionality reduction rate of PCA and ReliefF algorithms are 92% and 94%, respectively, the classification accuracy rates on the dataset are 64% and 78%, respectively, and they are both better than the data before dimensionality reduction. Therefore, on the dataset of this paper, the classification performance obtained by using the feature selection algorithm is better.Under the same iteration conditions, the classification accuracy of HBPSO is 75%, which is 11 percentage points higher than that of BPSO, and the dimensionality reduction rate of features is also increased by 3 percentage points, and the number of features is reduced to 670 compared with 725 of BPSO. ReliefF-BPSO achieved 86% accuracy when the dimensionality reduction rate was 93%, and ReliefF-HBPSO achieved 87% accuracy when the dimensionality reduction rate was 98%, and the number of features was reduced by 51.8% compared to the 41% of Relief F-BPSO. Therefore, HBPSO performs better than traditional BPSO on this dataset and achieves better classification performance with a higher dimensionality reduction rate. Whether it is BPSO, Relief F-BPSO, or HBPSO, compared with ReliefF-HBPSO, the algorithm that uses the ReliefF algorithm to select low-dimensional features first can achieve better dimensionality reduction and improve classification accuracy. Figure7 shows the comparative analysis over accuracy under different models for dimension reduction.Figure 7
Comparative analysis over accuracy under different models for dimension reduction.The WOA-SA algorithm is a heuristic algorithm proposed by Mafarja for feature selection in 2017, and it has a good performance in the UCI classic dataset. Under the same iterative conditions, it can be seen from Table1 that WOA-SA has a dimensionality reduction rate and an accuracy rate of 59% and 71%, respectively. Although the performance is better than the traditional BPSO algorithm, it is still inferior to the ReliefF-HBPSO algorithm proposed in this paper.When the dimensionality reduction rates of BPSO, HBPSO, ReliefF-BPSO, and ReliefF-HBPSO are 47%, 53%, 93%, and 98%, respectively, the classification accuracies are 64%, 75%, 86%, and 87%. As the dimensionality reduction rate increases, the classification accuracy also increases. But, in WOA-SA, when the dimensionality reduction rate is 59%, the classification accuracy is only 71%. Therefore, the dimensionality reduction rate is proportional to the classification accuracy rate, which is only established within a certain interval. With the increase of the dimensionality reduction rate, the classification accuracy rate reaches the highest at a certain time, and then, there is a possibility of decreasing. Figure8 shows the comparative analysis over dimension reduction under different models for dimension reduction.Figure 8
Comparative analysis over dimension reduction under different models for dimension reduction.From the perspective of running time, under the same number of iterations, the running times of BPSO, HBPSO, ReliefF-BPSO, and ReliefF-HBPSO are 31.79 s, 22.99 s, 16.63 s, and 10.84 s, respectively. The running times of ReliefF-BPSO and ReliefF-HBPSO are compared with BPSO and HBPSO, and it improves 15.16 s and 12.15 s, respectively, without reducing the classification performance. Compared with BPSO and Relief F BPSO, the running time of HBPSO and ReliefF-HBPSO is also improved. It can be seen that using the ReliefF algorithm to select low-dimensional features first can greatly reduce the computing time and maintain a good classification accuracy.In summary, the ReliefF-HBPSO algorithm has excellent feature selection ability on the dataset of this paper, and can obtain a smaller proportion of feature subsets; and based on the original thousand-dimensional features, the algorithm only uses about 2% of the features. The best classification performance is achieved with the shortest running time. Therefore, the ReliefF-HBPSO algorithm can not only obtain a smaller scale of feature subsets, but also ensure the highest classification performance in a relatively short period of time. Figure9 shows the comparison of classification performance of different feature selection and dimensionality reduction algorithms.Figure 9
Comparison of classification performance of different feature selection and dimensionality reduction algorithms.The classification performance of the eight algorithms under the multi-label classifier of decision tree is shown in Table2. The parameters that are taken into consideration for evaluating the efficacy of the proposed methodology is accuracy, precision, recall, and F1-score. However, comparing with nondimensionality reduction, PCA, WOA-SA, BPSO, HBPSO, and ReliefF-BPSO algorithms, the ReliefF-HBPSO algorithm has greatly improved by achieving accuracy 87%, precision values obtained are 0.73 and 0.85, recall values are 0.86 and 0.82, and F1-score is 0.76 and 0.85, respectively. However, while comparing with the ReliefF-BPSO algorithm, ReliefF-HBPSO improves the classification accuracy, classification precision, and F1 parameters and maintains a similar recall rate.Table 2
Comparison of classification performance of different feature selection and dimensionality reduction algorithms.
AlgorithmAccuracyPrecisionRecallMacro-F1-scoreNot dimensionally reduced0.550.280.520.34PCA0.640.640.680.68ReliefF0.780.870.740.76WOA-SA0.710.710.750.75BPSO0.640.700.680.69HBPSO0.750.820.730.78Relief-BPSO0.860.730.860.76Relief-HBPSO0.870.850.820.85In summary, the ReliefF-HBPSO algorithm can effectively remove feature redundancy, obtain a smaller feature subset, and outperform similar algorithms in overall performance, and the output feature subset is more streamlined and effective. Therefore, this paper proposes the ReliefF-HBPSO multilevel feature selection algorithm, and it is feasible to apply it to the selection of head and neck cancer pathological image features. Pathological image features after feature selection can be used to design individualized radiation therapy to potentially improve clinical outcomes.


## 5.1. Experimental Data

The experimental data adopts the real patient dataset provided by the California hospital in the United States, in which sensitive personal information about the patients has been removed, and the dataset is preprocessed before use. The original data is the RT pathological image of the patient, and the image format is the CT image of dicom, as shown in Figure5. Text data in csv format with data shape 60,1385 was extracted from CT images of patients by Ibex software [28]. Among them, 60 refer to a total of 60 patients as samples to participate in the prediction, and 1385 refer to the extracted image features with a total of 1385 dimensions.Figure 5
CT image display in Ibex.Since the dataset is real case data, some information is missing, and the average value of the entire column of features is used for completion. For some feature attributes, in order to avoid some attributes with small values from being hidden and to improve the accuracy, the data is standardized.The distribution of survival (in months) for the 60 patients given by the hospital’s raw data is shown in Figure6. According to the analysis of relevant medical literature and doctors’ experience, the survival time of 60 patients was divided into 3 categories, which were denoted by 0, 1, and 2, respectively. Among them, 0 ~ 18 months is the first category, which is represented by 0, with a total of 24 people; 18~36 months is the second category, which is represented by 1, with a total of 15 people; 36~150 months is the third category, with 2 said, a total of 20 people. The proportion of each type of labels to the total is 41%, 25%, and 34%, respectively.Figure 6
Label distribution of survival time.


## 5.2. Experimental Design

The experimental environment of this paper is Windows 10 64-bit operating system, the processor is Intel i5-8250U, 2.6 GHz, and the installed memory RAM is 4.00 GB. Software environment pycharm compiler, python3.5.In order to verify the effectiveness and superiority of the ReliefF-HBPSO algorithm in the feature selection of head and neck cancer pathological images, this paper compares the nondimensionality reduction and feature dimension reduction methods—PCA [29], ReliefF algorithm [30], and whale optimization algorithm-simulate anneal, respectively, with, WOA-SA [31], binary particle swarm optimization (BPSO) [32, 33], hybrid binary evolutionary particle swarm optimization (HBPSO), and ReliefF-BPSO for comparative experiments.Among them, the maximum number of iterationsn of the five models of WOA-SA, BPSO, HBPSO, ReliefF-BPSO, and ReliefF-HBPSO is 100. Other parameters of the WOA-SA model are set according to the literature [34–36]. BPSO and HBPSO model parameter settings: population size m=50, learning factor c1=c2=0.5, inertia coefficient w=2.5, maximum particle velocity Vmax=4, and minimum velocity Vmin=−4. ReliefF-BPSO and ReliefF-HBPSO parameter settings: sampling times M=5, threshold ∂=30293.46, number of nearest neighbor samples p=10, and other parameters are the same as BPSO and HBPSO models. ReliefF parameters: sampling times M=5, threshold ∂=50588.91, and number of nearest neighbor samples p=10.


## 5.3. Result Analysis

For the head and neck cancer pathological image feature dataset extracted by Ibex software, the experiment uses the original data (that is, the dimensionality reduction data), PCA, ReliefF, WOA-SA, BPSO, HBPSO, ReliefF-BPSO, and ReliefF-HBPSO, a total of 8 models. The optimal feature sets under the real dataset are obtained, respectively, and the decision tree classification model is used as the classifier. The dimensionality-reduction technique, known as principal component analysis (PCA) [37], reduces the size of huge datasets by condensing the number of variables in the original dataset into a manageable number [38]. Dimensionality reduction algorithms compromises some accuracy in exchange for more simplicity, and this is the tradeoff that must be made when trying to reduce the size of a dataset. Since small datasets are easy to evaluate and visualize, they allow machine learning algorithms to handle data more quickly without having to deal with additional variables [39]. In this paper, the proposed algorithm is evaluated against this technique to prove its efficiency.The test uses 5-fold cross-validation to calculate the accuracy, precision, recall,F1-score, and running time (unit: s) and compare the multiple items of the 8 models. The classification performance index and its feature subset size illustrate the ability of the algorithm in feature selection and classification prediction. It can be seen from Table 1 that the size of feature subsets selected by the PCA, ReliefF, WOA-SA, BPSO, HBPSO, ReliefF-BPSO, and ReliefF-HBPSO algorithms are reduced by 92%, 94%, 59%, 47%, 53%, 93% and 98%, respectively, compared with those before dimension reduction. And when the dimensionality reduction ratio is the lowest 98%, the ReliefF-HBPSO algorithm achieves the best classification effect of 87%.Table 1
Number of features under different algorithms.
AlgorithmData dimensionAccuracyDimensionality reductionRunning time (s)Not dimensionally reduced13850.5508.61PCA1000.640.927.03ReliefF1100.780.941.89WOA-SA5950.710.5951.04BPSO7250.640.4731.45HBPSO6700.750.5321.93Relief-BPSO400.860.9317.08Relief-HBPSO240.870.9811.06When the dimensionality reduction rate of PCA and ReliefF algorithms are 92% and 94%, respectively, the classification accuracy rates on the dataset are 64% and 78%, respectively, and they are both better than the data before dimensionality reduction. Therefore, on the dataset of this paper, the classification performance obtained by using the feature selection algorithm is better.Under the same iteration conditions, the classification accuracy of HBPSO is 75%, which is 11 percentage points higher than that of BPSO, and the dimensionality reduction rate of features is also increased by 3 percentage points, and the number of features is reduced to 670 compared with 725 of BPSO. ReliefF-BPSO achieved 86% accuracy when the dimensionality reduction rate was 93%, and ReliefF-HBPSO achieved 87% accuracy when the dimensionality reduction rate was 98%, and the number of features was reduced by 51.8% compared to the 41% of Relief F-BPSO. Therefore, HBPSO performs better than traditional BPSO on this dataset and achieves better classification performance with a higher dimensionality reduction rate. Whether it is BPSO, Relief F-BPSO, or HBPSO, compared with ReliefF-HBPSO, the algorithm that uses the ReliefF algorithm to select low-dimensional features first can achieve better dimensionality reduction and improve classification accuracy. Figure7 shows the comparative analysis over accuracy under different models for dimension reduction.Figure 7
Comparative analysis over accuracy under different models for dimension reduction.The WOA-SA algorithm is a heuristic algorithm proposed by Mafarja for feature selection in 2017, and it has a good performance in the UCI classic dataset. Under the same iterative conditions, it can be seen from Table1 that WOA-SA has a dimensionality reduction rate and an accuracy rate of 59% and 71%, respectively. Although the performance is better than the traditional BPSO algorithm, it is still inferior to the ReliefF-HBPSO algorithm proposed in this paper.When the dimensionality reduction rates of BPSO, HBPSO, ReliefF-BPSO, and ReliefF-HBPSO are 47%, 53%, 93%, and 98%, respectively, the classification accuracies are 64%, 75%, 86%, and 87%. As the dimensionality reduction rate increases, the classification accuracy also increases. But, in WOA-SA, when the dimensionality reduction rate is 59%, the classification accuracy is only 71%. Therefore, the dimensionality reduction rate is proportional to the classification accuracy rate, which is only established within a certain interval. With the increase of the dimensionality reduction rate, the classification accuracy rate reaches the highest at a certain time, and then, there is a possibility of decreasing. Figure8 shows the comparative analysis over dimension reduction under different models for dimension reduction.Figure 8
Comparative analysis over dimension reduction under different models for dimension reduction.From the perspective of running time, under the same number of iterations, the running times of BPSO, HBPSO, ReliefF-BPSO, and ReliefF-HBPSO are 31.79 s, 22.99 s, 16.63 s, and 10.84 s, respectively. The running times of ReliefF-BPSO and ReliefF-HBPSO are compared with BPSO and HBPSO, and it improves 15.16 s and 12.15 s, respectively, without reducing the classification performance. Compared with BPSO and Relief F BPSO, the running time of HBPSO and ReliefF-HBPSO is also improved. It can be seen that using the ReliefF algorithm to select low-dimensional features first can greatly reduce the computing time and maintain a good classification accuracy.In summary, the ReliefF-HBPSO algorithm has excellent feature selection ability on the dataset of this paper, and can obtain a smaller proportion of feature subsets; and based on the original thousand-dimensional features, the algorithm only uses about 2% of the features. The best classification performance is achieved with the shortest running time. Therefore, the ReliefF-HBPSO algorithm can not only obtain a smaller scale of feature subsets, but also ensure the highest classification performance in a relatively short period of time. Figure9 shows the comparison of classification performance of different feature selection and dimensionality reduction algorithms.Figure 9
Comparison of classification performance of different feature selection and dimensionality reduction algorithms.The classification performance of the eight algorithms under the multi-label classifier of decision tree is shown in Table2. The parameters that are taken into consideration for evaluating the efficacy of the proposed methodology is accuracy, precision, recall, and F1-score. However, comparing with nondimensionality reduction, PCA, WOA-SA, BPSO, HBPSO, and ReliefF-BPSO algorithms, the ReliefF-HBPSO algorithm has greatly improved by achieving accuracy 87%, precision values obtained are 0.73 and 0.85, recall values are 0.86 and 0.82, and F1-score is 0.76 and 0.85, respectively. However, while comparing with the ReliefF-BPSO algorithm, ReliefF-HBPSO improves the classification accuracy, classification precision, and F1 parameters and maintains a similar recall rate.Table 2
Comparison of classification performance of different feature selection and dimensionality reduction algorithms.
AlgorithmAccuracyPrecisionRecallMacro-F1-scoreNot dimensionally reduced0.550.280.520.34PCA0.640.640.680.68ReliefF0.780.870.740.76WOA-SA0.710.710.750.75BPSO0.640.700.680.69HBPSO0.750.820.730.78Relief-BPSO0.860.730.860.76Relief-HBPSO0.870.850.820.85In summary, the ReliefF-HBPSO algorithm can effectively remove feature redundancy, obtain a smaller feature subset, and outperform similar algorithms in overall performance, and the output feature subset is more streamlined and effective. Therefore, this paper proposes the ReliefF-HBPSO multilevel feature selection algorithm, and it is feasible to apply it to the selection of head and neck cancer pathological image features. Pathological image features after feature selection can be used to design individualized radiation therapy to potentially improve clinical outcomes.


## 6. Conclusion

In this paper, the feature selection technique is used to investigate pathological imaging features of patients with head and neck cancer, and a multilevel feature selection method based on ReliefF-HBPSO is developed. The algorithm first uses the ReliefF algorithm to quickly reduce the dimensionality of the morphological features of the pathological image and then initializes the particle swarm with the feature candidate subset with larger feature weight, with the feature subset’s evaluation being the classification accuracy of the decision tree classifier (DT). This function combines discrete binary particle swarm optimization (BPSO) with evolutionary neural strategy (ENS) across numerous iterations to get the optimum feature subset. Experiments show that the ReliefF-HBPSO technique outperforms the six models of PCA, ReliefF, WOA-SA, BPSO, HBPSO, and ReliefF-BPSO in removing redundant features and screening out highly linked pathological image morphological traits. A dimensionality reduction rate of 98 percent is achieved with 98 percent classification accuracy and a fast operating speed. The ReliefF-HBPSO approach provides a multilevel hybrid model that combines filtering and searching techniques to not only reduce data dimension quickly but also to automatically discover the optimal feature subset in a predetermined way. It is proposed in this paper that use of hybrid approach outperforms other techniques to identify cancer by deleting extraneous information from various models. There may be concerns with overfitting the training dataset if a large amount of data is used in this suggested approach. Deep learning and other forms of computational intelligence are both options that can be considered.



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*Source: 3618197-2022-08-05.xml*