# Design of a Treatment Method for Patients with Anxiety Disorders Based on Ball Games and Digital Technology Assistance

Authors: Shuzhi Chang
Journal: Security and Communication Networks
 (2022)

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## Abstract

Patients with anxiety disorders often have a long and often recurring course of the disease, which negatively affects all aspects of the patient’s work life while also causing a significant economic burden. Psychotherapy and medication are common treatments for anxiety disorders, but they are ineffective, especially in cases of chronic anxiety, having a high relapse rate and often causing adverse side effects. Ball games are important sports that have been widely used in training and sports activities. Physical activity has been discovered to be good not only for physical health but also for the treatment of anxiety disorders, according to recent medical studies. Therefore, there is an urgent need to investigate the rehabilitation effects of ball games on anxiety disorder patients and to develop novel training methods. Meanwhile, in recent years, the use of computers for digital technology-assisted mental illness treatment has received widespread attention. In this paper, a new treatment strategy for anxiety patients is proposed by combining ball games with support vector machine algorithm as digital assisted technology. This research examines the shortcomings in the classic support vector machine technique first and then proposes an improved FSVM algorithm for data processing and analysis. The results of the experiments reveal that the proposed technique has a significant impact on the treatment of anxiety disorders and creates the foundation for the study of anxiety patients’ exercise therapy.


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## Body

## 1. Introduction

Anxiety disorder is a neurological disorder mainly characterized by anxiety, nervousness, worry, and other emotional experiences and is one of the more common types of mild mental illnesses, including generalized anxiety disorder, panic attacks, and phobias. Acute anxiety disorder or panic attack is mainly manifested by near-death feeling and symptoms of vegetative dysfunction, that is, a sudden and very out-of-control emotional experience in daily life, or even a near-death feeling may be experienced, accompanied by chest tightness, palpitations, difficulty in breathing, sweating, and shivering. In contemporary society, a truly healthy person must adapt to a rapidly developing society. In addition to being enterprising, pursuing, and indomitable, one must also have the mental capacity to withstand stress.The incidence rate of anxiety disorders has increased year by year due to the fierce competition in society, the complexity of interpersonal relationships, the heavier economic burden, and the acceleration of learning, working, and living rhythm [1]. Anxiety disorder is a kind of psychological disease, which is characterized by sudden and repeated inexplicable panic and depression [2]. The survey of China’s Taiwan Province showed that the prevalence of generalized anxiety disorder (GAD) in urban areas was 3.7%, while that in urban and rural areas was 10.5% and 7.8%. The 1982 survey showed that the prevalence of anxiety disorder was about 1.48%, and women were more than men, about 2 : 1. Other studies have shown that the incidence rate of generalized anxiety disorder in China is about 2–4.7%, and the lifetime prevalence rate of panic disorder is about 1.5–3.5%. GAD mostly starts at the age of 20–40, and panic disorder (PD) mostly starts in late adolescence and early adulthood. Therefore, the research and treatment of anxiety disorder are receiving more and more attention from all walks of life, especially psychologists [3].The pathogenesis of anxiety disorder is generally divided into the following aspects.(1)
Genetic Factors. The incidence of anxiety disorder is closely related to genetic and environmental factors. The survey found that among the close relatives of patients with anxiety disorder, the probability of the disease is about 15%, which is three times that genetics of ordinary residents; these studies suggest that may be one of the causes of anxiety [4].(2)
Environment. Behaviorists believe that the fear conditioned reflex of some stimuli in the environment is an important reason for anxiety disorder [5]. At present, it is generally accepted that anxiety disorder is caused by the joint action of heredity and environment.(3)
Character. The character of anxiety patients is being timid, suspicious, and hesitant and having poor social adaptability [6]. For example, you cannot adapt to a new environment, encounter setbacks, or excessive pressure. However, the current question lies in the causal relationship between personality and anxiety disorder, which leads to the formation of anxiety disorder personality. At present, there is no unified view.Modern sports psychology research has proved that anxiety and tension will gradually reduce the intensity with the strengthening of physical exercise, and the intense emotion will gradually weaken with the maintenance of physical fitness [7]. Cognitive behavior theory holds that physical exercise can induce positive thinking and emotion, which can resist negative psychological states such as depression, anxiety, and confusion. Negative psychological states such as anxiety and confusion can resist [8]. In the process of sports, people actively participate in competition and accept challenges through cognitive activities such as observation, memory, imagination, and thinking, so as to experience the satisfaction brought by success and enhance their self-confidence [9]. Physical exercise can better help patients with anxiety disorder to get out of the psychological shadow, increase their self-confidence and self-relaxation, free themselves from tension, and release their exaggeration of the possibility of failure from unnecessary worry and fear [10].Recent medical research has found that physical activities such as ball games are not only beneficial for physical health but also beneficial for the treatment of anxiety disorders. Therefore, there is a dire need to explore the rehabilitation effects of ball games on anxiety disorder patients and attempt to create new training methods. In this paper, a new treatment mechanism is proposed for anxiety patients using support vector machine algorithm with ball sports. At first stage, this research work analyzes the shortcomings of the traditional support vector machine algorithm. In next stage, an improved fuzzy support vector machine (FSVM) algorithm is designed to process and analyze the data.


## 2. Related Work

In order to improve the rehabilitation process of anxiety patients, a large number of researchers recently proposed a detection system for cognitive rehabilitation of anxiety patients. Firstly, the system generates a large amount of data and then analyzes these data by using data mining technology, which can obtain new knowledge to evaluate and improve the effectiveness of the rehabilitation process [11]. In addition, using information analysis and data mining technology, prediction models and decision support systems for treating patients can be created.Different statistical methods and predictive data mining methods have been widely used to predict the clinical outcome of rehabilitation of patients with anxiety disorder. For example, Luengo et al. [12] proposed the Clark prediction method. Li et al. [13] proposed a Fourier discretization prediction method and applied it to a Bayesian network classifier. Botev et al. [14] also proposed classification rule methods for mining label information in the framework of classification rules. The CAIM prediction method proposed by Amorim et al. [15] yields prediction results by maximizing the interdependence of taxonomic properties. Recently, Gupta et al. [16] proposed a kernel density estimation method KDE based on discretization method, which is a mainstream unsupervised prediction method. By introducing the concept of kernel density estimation, the data are discretized without supervision, and better prediction results are obtained. However, most of these studies focus on ensuring survival, predicting disability or patient recovery, and looking for factors that can better predict patient recovery.Traditional data mining algorithms are affected by the sample distribution and dimensionality when classifying a high-dimensional unbalanced dataset, resulting in low classification performance. Support vector machine algorithm is an important tool that can effectively solve the problems of regression, probability density estimation, and classification [17]. Based on statistical learning theory, it has good generalization ability and intuitive geometric interpretation. It has achieved good results in some practical applications such as image recognition and time series motion prediction. Least squares support vector machine is an extension of the standard support vector machine [18, 19]. When using the structural risk principle, it has the advantage of fast convergence by selecting different loss functions for the optimization objectives. However, when the amount of data is large, the calculation resources required in the solution process are large.Lagrange support vector machine was proposed by Mangasarion [20] in 2001. It mainly analyzes the dual problem, first obtains the solution of the dual problem, and then obtains the solution of the original problem from the solution of the dual problem. In the application of linear classification, the classification of large sample sets has faster convergence speed and is relatively simple compared with other algorithms, but when extended to nonlinear problems, it can only deal with medium-sized sample sets.The main idea of granularity support vector machine is to construct granularity space through the granularity division method to obtain a series of information particles and then aggregate the information on each information particle to obtain support vector machine [21]. On this basis, Ding et al. [22] proposed GSVM based on association rules, mapped the original space samples to the feature space through radial basis kernel function and expanded them into McLaughlin series, analyzed the association rules that play an important role in the expansion, divided the granularity, and learned the association rule classifier. Zhang and Wang [23] proposed GSVM based on clustering. The main idea is to use the clustering method to divide the original data into several particles and select the particles with more information to participate in the classification of SVM. Twin support vector machine, also known as double interface support vector machine, has faster training speed, making it better able to deal with large-scale data [24]. However, it does not have the characteristics of standard SVM, so the twin model needs to be further improved. The ordered support vector machine establishes a damage function suitable for specific applications for retrieval problems [25]. Like the standard SVM, the two types of samples can use the same cost function or establish different cost functions, which greatly improves the sorting accuracy of some applications.Fuzzy support vector machine is a method combining fuzzy mathematics and support vector machine to overcome the influence of noise points or outliers on SVM [26, 27]. It mainly assigns small weights to the noise data in the training sample set according to the fuzzy idea, so as to reduce the influence on the construction of the optimal hyperplane.Similarly, machine learning [28], rough set theory [29], case-based reasoning [30], and rule-based reasoning [31] have extensively been used for healthcare and well-being applications, such as recommender system for physical activity recommendations, types of diabetes prediction, well-being recommendation generation, and flexible healthcare framework designing, respectively.


## 3. Data Mining Model

This section describes the details of the proposed data mining model used for the design of treatment method for patients with anxiety disorders.


### 3.1. General Steps of Data Mining

In recent years, data mining has attracted great attention in the information industry. The main reason is that there are a large number of data that can be widely used, and there is an urgent need to convert these data into useful information and knowledge. Data mining is a hot issue in the field of artificial intelligence and database [32]. The so-called data mining refers to a nontrivial process of revealing implicit, previously unknown, and potentially valuable information from a large amount of data in the database. Data mining is a technology to find its rules from a large number of data by analyzing each kind of data.Considering the data, data mining usually needs the following steps.Step 1.
Information collection: according to the determined data analysis object, abstract the characteristic information required in data analysis and then select the appropriate information collection method to store the collected information in the database. For massive data, it is very important to select an appropriate data warehouse for data storage and management.Step 2.
Data integration: organically centralize data from different sources, formats, and characteristics logically or physically, so as to provide comprehensive data sharing for enterprises.Step 3.
Data specification: if most data mining algorithms are implemented, it will take a long time even on a small amount of data, and the amount of data is often very large when doing business operation data mining. Data specification technology can be used to obtain the specification representation of dataset. It is much smaller, but it is still close to maintaining the integrity of the original data, and the data mining results after the specification are the same or almost the same as those before the specification.Step 4.
Data cleaning: some data in the database are incomplete (some attributes of interest lack attribute values), noisy (including wrong attribute values), and inconsistent (the same information is expressed in different ways), so it is necessary to clean up the data and store the complete, correct, and consistent data information in the data warehouse. Otherwise, the mining results will be unsatisfactory.Step 5.
Data transformation: transform data into a form suitable for data mining by means of smooth aggregation, data generalization, and normalization. For some real data, it is also an important step to convert data through concept stratification and data discretization.Step 6.
Data mining process: according to the data information in the data warehouse, select the appropriate analysis tools and apply the methods of statistical method, case-based reasoning, decision tree, rule reasoning, fuzzy set, neural network, and genetic algorithm to process the information and obtain useful analysis information.Step 7.
Pattern evaluation: industry experts verify the correctness of data mining results.Step 8.
Knowledge representation: the analysis information obtained from data mining is presented to users in a visual way and stored in the knowledge base as new knowledge for use by other applications.


### 3.2. Basic Principle of SVM Algorithm

Support vector machine is a classification algorithm based on statistical learning theory, which has good classification ability and generalization ability. There are two main situations of SVM.


#### 3.2.1. Linearly Separable Experiment

Let the training setT=x1⋅y1,…,xl⋅yl∈x×yl, where xi∈x∈Rn,yi∈y∈−1,1i=1,2,…,l. If w∈Rn,b∈R and positive numbers exist (ξ), for all subscripts i that make yi=1, there is w⋅xi+b≥ξ. For all subscripts i that make yi=−1 have w⋅xi+b≤ξ, the training set T is said to be linearly separable, and its corresponding classification problem is also linearly separable.The circle and cross represent two types of samples to be classified. H is the required optimal classification hyperplane. H1 and H2 are straight lines parallel to the optimal classification plane and pass through the nearest sample points in these two types of samples. As can be seen, there are many straight lines parallel to H1 and H2, but only the optimal classification hyperplane can ensure the maximum nearest distance between the two types of samples. SVM is a supervised machine learning algorithm requiring the training of the SVM to obtain the optimal classification hyperplane and then the classification according to the training results. The plane with classification ability is described as follows:(1)w⋅x+b=0,s.t.w⋅xi+b≥0yi=1,w⋅xi+b<0yi=−1.It can be seen that the classification interval is2/w, and to maximize the classification interval, w needs to be as small as possible, so that the optimal classification superplane can be obtained by solving the following formula:(2)min12w2,s.t.yiw⋅xi+b≥1,i=1,2,…,l.Then, it is transformed into dual form:(3)min12∑i=1l∑j=1lyiyjaiajxi⋅xj−∑j=1laj,s.t.∑i=1lyiai=0,ai≥0,i=1,2,…,l.Solve equation (3) to obtain the value of Lagrange coefficient a∗; then, w∗=∑i=1lyiai∗xi, select a positive fraction quantity of a∗, and calculate b∗=yj−∑i=1lyiai∗xi⋅xj. At this time, the classification function is(4)fx=sgnw∗⋅x+b∗.


#### 3.2.2. Linearly Inseparable Experiment

Linear separability is to find the optimal classification hyperplane that can correctly divide the training samples in the space where the samples exist. However, the training sample set composed of samples obtained in the real world often cannot find such a classification hyperplane that makes the interval between all training samples about the classification hyperplane positive. However, if we still want to find a hyperplane, we must soften the conditions appropriately to allow the existence of samples that do not meet the constraint conditionyiw⋅xi+b≥1. Therefore, the solution of the optimal classification hyperplane is expressed as(5)min12w2+c∑i=1lξi,s.t.yiw⋅xi+b≥1−ξi,ξi≥0,i=1,2,…,l.Then, turn it into a dual form as(6)12∑i=1l∑j=1lyiyjaiajxi⋅xj−∑j=1laj,s.t.∑i=1lyiai=0,0≤ai≤c,i=1,2,…,l.At this time, the classification function is(7)fx=sgnw∗⋅x+b∗.For the first kind of points, the relaxation variable is adjusted by adjusting the penalty parameter. For the second kind of points, because these points often cannot provide any help to improve the performance of the classifier and will greatly increase the computational burden of the classifier, resulting in over-learning phenomenon, they should be eliminated.


### 3.3. Improved Data Mining FSVM Algorithm

Fuzzy support vector machine (FSVM) has strong generalization ability and good nonlinear data processing ability, so it showed good performance in many applications, but it also has the disadvantages of existing data mining classification algorithms, such as the noise point or wild value points caused by poor noise resistance, and when the number of samples is large, the training speed and classification speed are slow.Without losing generality, this method uses two kinds of classification problems, that is, the training samples are positive and negative. Because the training speed of support vector machine is related to the size of training sample set and the samples distributed at the class boundary, that is, support vector, play a decisive role in decision making, this technique reduces the number of training samples and improves the training speed by preselecting effective candidate support vectors. The main reason for preselecting effective candidate support vectors is that the support vectors are usually located at the class boundary. Compared with other samples of this class, they are far from the center of this class and close to the center of dissimilarity. Therefore, select the samples whose mutual center distance (the distance between samples and dissimilarity centers) is less than the center distance between the two types of samples as effective candidate support vectors.In order to effectively distinguish the noise points from the normal samples, the membership function is weighted by the nearest neighbor sample density. As shown in Figure1, the normal sample X1 has a large number of samples in the adjacent range e, that is, the adjacent sample density is large, while the noise point x2 has a small number of samples in its adjacent range, that is, the adjacent sample density is small. Therefore, the membership function can be weighted by the adjacent sample density to reduce the influence of noise points without weakening the function of normal samples.Figure 1
Noise points were compared with the nearest neighbor samples of normal samples.Currently, the training speed and the slower classification speed are the major factors limiting the application of SVM. Based on this, the particle swarm optimization algorithm is used to reduce the support vector and improve the classification speed without affecting the classification accuracy. Taking the fuzzy membership vector of the support vector set obtained after training FSVM as the particles in the particle swarm and the average classification error of the test set as the fitness function, the optimal support vector quantum set is selected to reduce the support vector, so as to improve the classification speed.PSO algorithm searches the solution by constantly adjusting the position of particles. Assuming that the populationX=x1,x2,…,xn is composed of n particles in the d-dimensional search space, the current position of the i-th particle is Xi=xi1,xi2,…,xin, the current flight speed of the particle is Vi=vi1,vi2,…,vin, the best position passed by i-th particle is Pi=pi1,pi2,…,pin, and the best position passed by all particles is Pg=pg1,pg2,…,pgn, then the current position of the i-th particle at t+1 is(8)vidt+1=vidt+c1r1pidt+xidt+c2r2pgdt−xidt,xidt+1=xidt+vidt+1.In the particle group optimization algorithm, each particle represents a solution, the particle group optimization algorithm is applied to the reduced support vector of the fuzzy support vector machine, and the number of support vectors obtained by the trained FSVM is the dimension of the particles. Define the fitness function as(9)fitness=1M∑i=1Mfi−yi2.It can be seen from the above formula that the smaller the particle fitness value, the better the effect.. Therefore, an improved algorithm for fuzzy support vector machine classification for data mining is performed as follows.Input: the training sample set. Output: the FSVM decision function.(1)
The positive and negative class centers are calculated, and the two classes’ center distance is obtained.(2)
The distance between the two classes of samples to their class centers was calculated separately, and samples with this distance less than the two classes were selected as candidate support vectors to form the candidate support vector set.(3)
Sample membership was calculated to obtain the ambiguous set of candidate support vectors.(4)
The FSVM was trained for the obscured candidate support vector set, yielding the support vector set.(5)
Initialize the particle groupX, where the calculated weight vector of the resulting l support vectors is one particle in the initialized particle group.(6)
Keep the position of all the particles in the particle group.(7)
Determine the retained particle position in turn and keep the position unchanged if it is above the threshold valuep; otherwise, the value of the position is changed to 0 to select a subset of support vectors.(8)
The FSVM is trained on a subset of support vectors selected for each particle to obtain the judgment function.(9)
Examine the test set according to the decision function and adjust the individual optimal position and global optimal position of particles according to the obtained particle fitness function value.(10)
The FSVM is trained with the output results, and the decision function after the reduction support vector is obtained and classified with the decision function.


### 3.4. Data Mining for Anxiety Rehabilitation Evaluation

According to the law of data mining, this paper takes the anxiety of patients with anxiety disorder and ball games as the input, trains the improved FSVM algorithm proposed in this paper, and obtains the classification results. The overall framework of the model is shown in Figure2.Figure 2
Overall framework of the model.


## 3.1. General Steps of Data Mining

In recent years, data mining has attracted great attention in the information industry. The main reason is that there are a large number of data that can be widely used, and there is an urgent need to convert these data into useful information and knowledge. Data mining is a hot issue in the field of artificial intelligence and database [32]. The so-called data mining refers to a nontrivial process of revealing implicit, previously unknown, and potentially valuable information from a large amount of data in the database. Data mining is a technology to find its rules from a large number of data by analyzing each kind of data.Considering the data, data mining usually needs the following steps.Step 1.
Information collection: according to the determined data analysis object, abstract the characteristic information required in data analysis and then select the appropriate information collection method to store the collected information in the database. For massive data, it is very important to select an appropriate data warehouse for data storage and management.Step 2.
Data integration: organically centralize data from different sources, formats, and characteristics logically or physically, so as to provide comprehensive data sharing for enterprises.Step 3.
Data specification: if most data mining algorithms are implemented, it will take a long time even on a small amount of data, and the amount of data is often very large when doing business operation data mining. Data specification technology can be used to obtain the specification representation of dataset. It is much smaller, but it is still close to maintaining the integrity of the original data, and the data mining results after the specification are the same or almost the same as those before the specification.Step 4.
Data cleaning: some data in the database are incomplete (some attributes of interest lack attribute values), noisy (including wrong attribute values), and inconsistent (the same information is expressed in different ways), so it is necessary to clean up the data and store the complete, correct, and consistent data information in the data warehouse. Otherwise, the mining results will be unsatisfactory.Step 5.
Data transformation: transform data into a form suitable for data mining by means of smooth aggregation, data generalization, and normalization. For some real data, it is also an important step to convert data through concept stratification and data discretization.Step 6.
Data mining process: according to the data information in the data warehouse, select the appropriate analysis tools and apply the methods of statistical method, case-based reasoning, decision tree, rule reasoning, fuzzy set, neural network, and genetic algorithm to process the information and obtain useful analysis information.Step 7.
Pattern evaluation: industry experts verify the correctness of data mining results.Step 8.
Knowledge representation: the analysis information obtained from data mining is presented to users in a visual way and stored in the knowledge base as new knowledge for use by other applications.


## 3.2. Basic Principle of SVM Algorithm

Support vector machine is a classification algorithm based on statistical learning theory, which has good classification ability and generalization ability. There are two main situations of SVM.


### 3.2.1. Linearly Separable Experiment

Let the training setT=x1⋅y1,…,xl⋅yl∈x×yl, where xi∈x∈Rn,yi∈y∈−1,1i=1,2,…,l. If w∈Rn,b∈R and positive numbers exist (ξ), for all subscripts i that make yi=1, there is w⋅xi+b≥ξ. For all subscripts i that make yi=−1 have w⋅xi+b≤ξ, the training set T is said to be linearly separable, and its corresponding classification problem is also linearly separable.The circle and cross represent two types of samples to be classified. H is the required optimal classification hyperplane. H1 and H2 are straight lines parallel to the optimal classification plane and pass through the nearest sample points in these two types of samples. As can be seen, there are many straight lines parallel to H1 and H2, but only the optimal classification hyperplane can ensure the maximum nearest distance between the two types of samples. SVM is a supervised machine learning algorithm requiring the training of the SVM to obtain the optimal classification hyperplane and then the classification according to the training results. The plane with classification ability is described as follows:(1)w⋅x+b=0,s.t.w⋅xi+b≥0yi=1,w⋅xi+b<0yi=−1.It can be seen that the classification interval is2/w, and to maximize the classification interval, w needs to be as small as possible, so that the optimal classification superplane can be obtained by solving the following formula:(2)min12w2,s.t.yiw⋅xi+b≥1,i=1,2,…,l.Then, it is transformed into dual form:(3)min12∑i=1l∑j=1lyiyjaiajxi⋅xj−∑j=1laj,s.t.∑i=1lyiai=0,ai≥0,i=1,2,…,l.Solve equation (3) to obtain the value of Lagrange coefficient a∗; then, w∗=∑i=1lyiai∗xi, select a positive fraction quantity of a∗, and calculate b∗=yj−∑i=1lyiai∗xi⋅xj. At this time, the classification function is(4)fx=sgnw∗⋅x+b∗.


### 3.2.2. Linearly Inseparable Experiment

Linear separability is to find the optimal classification hyperplane that can correctly divide the training samples in the space where the samples exist. However, the training sample set composed of samples obtained in the real world often cannot find such a classification hyperplane that makes the interval between all training samples about the classification hyperplane positive. However, if we still want to find a hyperplane, we must soften the conditions appropriately to allow the existence of samples that do not meet the constraint conditionyiw⋅xi+b≥1. Therefore, the solution of the optimal classification hyperplane is expressed as(5)min12w2+c∑i=1lξi,s.t.yiw⋅xi+b≥1−ξi,ξi≥0,i=1,2,…,l.Then, turn it into a dual form as(6)12∑i=1l∑j=1lyiyjaiajxi⋅xj−∑j=1laj,s.t.∑i=1lyiai=0,0≤ai≤c,i=1,2,…,l.At this time, the classification function is(7)fx=sgnw∗⋅x+b∗.For the first kind of points, the relaxation variable is adjusted by adjusting the penalty parameter. For the second kind of points, because these points often cannot provide any help to improve the performance of the classifier and will greatly increase the computational burden of the classifier, resulting in over-learning phenomenon, they should be eliminated.


## 3.2.1. Linearly Separable Experiment

Let the training setT=x1⋅y1,…,xl⋅yl∈x×yl, where xi∈x∈Rn,yi∈y∈−1,1i=1,2,…,l. If w∈Rn,b∈R and positive numbers exist (ξ), for all subscripts i that make yi=1, there is w⋅xi+b≥ξ. For all subscripts i that make yi=−1 have w⋅xi+b≤ξ, the training set T is said to be linearly separable, and its corresponding classification problem is also linearly separable.The circle and cross represent two types of samples to be classified. H is the required optimal classification hyperplane. H1 and H2 are straight lines parallel to the optimal classification plane and pass through the nearest sample points in these two types of samples. As can be seen, there are many straight lines parallel to H1 and H2, but only the optimal classification hyperplane can ensure the maximum nearest distance between the two types of samples. SVM is a supervised machine learning algorithm requiring the training of the SVM to obtain the optimal classification hyperplane and then the classification according to the training results. The plane with classification ability is described as follows:(1)w⋅x+b=0,s.t.w⋅xi+b≥0yi=1,w⋅xi+b<0yi=−1.It can be seen that the classification interval is2/w, and to maximize the classification interval, w needs to be as small as possible, so that the optimal classification superplane can be obtained by solving the following formula:(2)min12w2,s.t.yiw⋅xi+b≥1,i=1,2,…,l.Then, it is transformed into dual form:(3)min12∑i=1l∑j=1lyiyjaiajxi⋅xj−∑j=1laj,s.t.∑i=1lyiai=0,ai≥0,i=1,2,…,l.Solve equation (3) to obtain the value of Lagrange coefficient a∗; then, w∗=∑i=1lyiai∗xi, select a positive fraction quantity of a∗, and calculate b∗=yj−∑i=1lyiai∗xi⋅xj. At this time, the classification function is(4)fx=sgnw∗⋅x+b∗.


## 3.2.2. Linearly Inseparable Experiment

Linear separability is to find the optimal classification hyperplane that can correctly divide the training samples in the space where the samples exist. However, the training sample set composed of samples obtained in the real world often cannot find such a classification hyperplane that makes the interval between all training samples about the classification hyperplane positive. However, if we still want to find a hyperplane, we must soften the conditions appropriately to allow the existence of samples that do not meet the constraint conditionyiw⋅xi+b≥1. Therefore, the solution of the optimal classification hyperplane is expressed as(5)min12w2+c∑i=1lξi,s.t.yiw⋅xi+b≥1−ξi,ξi≥0,i=1,2,…,l.Then, turn it into a dual form as(6)12∑i=1l∑j=1lyiyjaiajxi⋅xj−∑j=1laj,s.t.∑i=1lyiai=0,0≤ai≤c,i=1,2,…,l.At this time, the classification function is(7)fx=sgnw∗⋅x+b∗.For the first kind of points, the relaxation variable is adjusted by adjusting the penalty parameter. For the second kind of points, because these points often cannot provide any help to improve the performance of the classifier and will greatly increase the computational burden of the classifier, resulting in over-learning phenomenon, they should be eliminated.


## 3.3. Improved Data Mining FSVM Algorithm

Fuzzy support vector machine (FSVM) has strong generalization ability and good nonlinear data processing ability, so it showed good performance in many applications, but it also has the disadvantages of existing data mining classification algorithms, such as the noise point or wild value points caused by poor noise resistance, and when the number of samples is large, the training speed and classification speed are slow.Without losing generality, this method uses two kinds of classification problems, that is, the training samples are positive and negative. Because the training speed of support vector machine is related to the size of training sample set and the samples distributed at the class boundary, that is, support vector, play a decisive role in decision making, this technique reduces the number of training samples and improves the training speed by preselecting effective candidate support vectors. The main reason for preselecting effective candidate support vectors is that the support vectors are usually located at the class boundary. Compared with other samples of this class, they are far from the center of this class and close to the center of dissimilarity. Therefore, select the samples whose mutual center distance (the distance between samples and dissimilarity centers) is less than the center distance between the two types of samples as effective candidate support vectors.In order to effectively distinguish the noise points from the normal samples, the membership function is weighted by the nearest neighbor sample density. As shown in Figure1, the normal sample X1 has a large number of samples in the adjacent range e, that is, the adjacent sample density is large, while the noise point x2 has a small number of samples in its adjacent range, that is, the adjacent sample density is small. Therefore, the membership function can be weighted by the adjacent sample density to reduce the influence of noise points without weakening the function of normal samples.Figure 1
Noise points were compared with the nearest neighbor samples of normal samples.Currently, the training speed and the slower classification speed are the major factors limiting the application of SVM. Based on this, the particle swarm optimization algorithm is used to reduce the support vector and improve the classification speed without affecting the classification accuracy. Taking the fuzzy membership vector of the support vector set obtained after training FSVM as the particles in the particle swarm and the average classification error of the test set as the fitness function, the optimal support vector quantum set is selected to reduce the support vector, so as to improve the classification speed.PSO algorithm searches the solution by constantly adjusting the position of particles. Assuming that the populationX=x1,x2,…,xn is composed of n particles in the d-dimensional search space, the current position of the i-th particle is Xi=xi1,xi2,…,xin, the current flight speed of the particle is Vi=vi1,vi2,…,vin, the best position passed by i-th particle is Pi=pi1,pi2,…,pin, and the best position passed by all particles is Pg=pg1,pg2,…,pgn, then the current position of the i-th particle at t+1 is(8)vidt+1=vidt+c1r1pidt+xidt+c2r2pgdt−xidt,xidt+1=xidt+vidt+1.In the particle group optimization algorithm, each particle represents a solution, the particle group optimization algorithm is applied to the reduced support vector of the fuzzy support vector machine, and the number of support vectors obtained by the trained FSVM is the dimension of the particles. Define the fitness function as(9)fitness=1M∑i=1Mfi−yi2.It can be seen from the above formula that the smaller the particle fitness value, the better the effect.. Therefore, an improved algorithm for fuzzy support vector machine classification for data mining is performed as follows.Input: the training sample set. Output: the FSVM decision function.(1)
The positive and negative class centers are calculated, and the two classes’ center distance is obtained.(2)
The distance between the two classes of samples to their class centers was calculated separately, and samples with this distance less than the two classes were selected as candidate support vectors to form the candidate support vector set.(3)
Sample membership was calculated to obtain the ambiguous set of candidate support vectors.(4)
The FSVM was trained for the obscured candidate support vector set, yielding the support vector set.(5)
Initialize the particle groupX, where the calculated weight vector of the resulting l support vectors is one particle in the initialized particle group.(6)
Keep the position of all the particles in the particle group.(7)
Determine the retained particle position in turn and keep the position unchanged if it is above the threshold valuep; otherwise, the value of the position is changed to 0 to select a subset of support vectors.(8)
The FSVM is trained on a subset of support vectors selected for each particle to obtain the judgment function.(9)
Examine the test set according to the decision function and adjust the individual optimal position and global optimal position of particles according to the obtained particle fitness function value.(10)
The FSVM is trained with the output results, and the decision function after the reduction support vector is obtained and classified with the decision function.


## 3.4. Data Mining for Anxiety Rehabilitation Evaluation

According to the law of data mining, this paper takes the anxiety of patients with anxiety disorder and ball games as the input, trains the improved FSVM algorithm proposed in this paper, and obtains the classification results. The overall framework of the model is shown in Figure2.Figure 2
Overall framework of the model.


## 4. Experiments and Results

### 4.1. Raw Data Analysis

The specific analysis is as follows: among the effective subjects, 384 cases performed ball games, accounting for 39.51% of the total investigated subjects; 588 cases played other sports, accounting for 60.49% of the total respondents. Among the 384 people who played ball games, 183 had no anxiety disorder, accounting for 47.66%, 131 had mild anxiety disorder, accounting for 34.1%, 37 had moderate anxiety disorder, accounting for 9.645, and 33 had severe anxiety disorder, accounting for 8.59%. Among the 588 people who performed other kinds of sports, 265 cases had no anxiety disorder, accounting for 45.07%, 197 cases had mild anxiety disorder, accounting for 33.05%, 70 cases had moderate anxiety disorder, accounting for 11.0996%, and 89 cases had severe anxiety disorder, accounting for 9.52%.It can be seen from Figure3 that during the development of subhealth from none to severe, the proportion difference between other sports and ball sports continues to narrow and finally exceeds that of ball sports. It suggests that the anxiety disorder of other sports is more serious than that of ball games. Then, we explore the impact of different ball games on patients with anxiety disorder. In this study, the subjects are divided into four parts: playing basketball, playing football, playing tennis, and playing volleyball. Among them, 173 cases played basketball, accounting for 17.80% of all respondents; the number of cases playing football was 642, accounting for 66.05% of all the respondents; 122 cases played tennis, accounting for 12.55% of the total respondents; the number of volleyball playing cases was 35, accounting for 3.6096 of all respondents. The results are shown in Figure 4.Figure 3
Composition of exercise categories in anxiety patients.Figure 4
Composition of different ball games in people with anxiety disorder.It can be seen from Figure4 that among patients without anxiety disorder, the population of ball games is basically the same, and the population of basketball is slightly higher (53.28%). The overall performance is as follows: with the increase of the severity of anxiety disorder, the people playing football and tennis are more prone to subhealth.Then, the composition of different exercise durations in anxiety patients was studied, as shown in Figure5. In this study, the daily exercise duration of the respondents was divided into five levels: among them, the number of people who played under 1 hour was 51, accounting for 5.25% of the total respondents; the number of cases who played for 1∼2 hours was 27, accounting for 2.78% of all respondents; the number of cases who played for 2∼3 hours was 171, accounting for 17.59% of all respondents; the number of cases who played for 3∼4 hours was 375, accounting for 38.58% of all respondents; the number of people who played for over 4 hours was 348, accounting for 35.80% of all respondents. It can be seen from the table and figure that among the people without anxiety disorder, the higher the education level, the smaller the proportion; among the people with mild anxiety disorder, the people under 1 hour were the least (9.8%), and the rest were basically the same. In the population with moderate anxiety disorder, the proportion of 1∼2 hours is similar; the proportion of anxiety disorder increased rapidly with the decrease of exercise time in the population with severe anxiety disorder. It suggests that the lower the duration of exercise, the more serious the state of anxiety.Figure 5
Comparison of ball game duration composition among anxiety patients.


### 4.2. Comparison of Experimental Results

To validate the performance of the algorithm, simulation experiments were performed on an improved data mining FSVM classification algorithm proposed in this section and compared with SVM and FSVM. Without generality, this technique verifies the algorithm with two classes of two-dimensional datasets: the training sample set includes the two randomly generated two-class 2D samples; the test sample also includes random two-class 2D samples. The kernel function parameters and penalty parameters in the algorithm are obtained by 5-fold cross validation, and the grid search method is used. The training speed and classification accuracy of the three algorithms are shown in Table1.Table 1
The training speed and classification accuracy of the three algorithms.
Training setTest setClassification time (s)Accuracy (%)SVMFSVMOur modelSVMFSVMOur model2002003.43.372.7391.5692.1492.1450030043.443.3135.6737.6894.5594.53800400150.51149.3591.2496.2596.2596.29It can be seen from Table1 that with the increasing number of training samples, the proposed algorithm improves the training speed and classification speed compared with the other two algorithms, ensuring its classification accuracy. When training support vector machine and fuzzy support vector machine, the whole kernel function matrix needs to be calculated and stored many times. Therefore, when the number of training samples is large, their training speed is slow. It can be seen from Table 1 that with the increase of the number of training samples, the training time of the algorithm in this paper is significantly less than that of SVM and FSVM. This is because this algorithm preprocesses the training samples before training FSVM, reduces the number of training samples, and improves the training speed. In addition, this algorithm uses particle swarm optimization algorithm to optimize the membership of samples for the support vector set obtained after training FSVM. The support vector which makes the average classification error smaller is selected to train the fuzzy support vector machine with the quantum set, and the reduction of the support vector is realized, so as to ensure the classification accuracy and improve the classification speed.


## 4.1. Raw Data Analysis

The specific analysis is as follows: among the effective subjects, 384 cases performed ball games, accounting for 39.51% of the total investigated subjects; 588 cases played other sports, accounting for 60.49% of the total respondents. Among the 384 people who played ball games, 183 had no anxiety disorder, accounting for 47.66%, 131 had mild anxiety disorder, accounting for 34.1%, 37 had moderate anxiety disorder, accounting for 9.645, and 33 had severe anxiety disorder, accounting for 8.59%. Among the 588 people who performed other kinds of sports, 265 cases had no anxiety disorder, accounting for 45.07%, 197 cases had mild anxiety disorder, accounting for 33.05%, 70 cases had moderate anxiety disorder, accounting for 11.0996%, and 89 cases had severe anxiety disorder, accounting for 9.52%.It can be seen from Figure3 that during the development of subhealth from none to severe, the proportion difference between other sports and ball sports continues to narrow and finally exceeds that of ball sports. It suggests that the anxiety disorder of other sports is more serious than that of ball games. Then, we explore the impact of different ball games on patients with anxiety disorder. In this study, the subjects are divided into four parts: playing basketball, playing football, playing tennis, and playing volleyball. Among them, 173 cases played basketball, accounting for 17.80% of all respondents; the number of cases playing football was 642, accounting for 66.05% of all the respondents; 122 cases played tennis, accounting for 12.55% of the total respondents; the number of volleyball playing cases was 35, accounting for 3.6096 of all respondents. The results are shown in Figure 4.Figure 3
Composition of exercise categories in anxiety patients.Figure 4
Composition of different ball games in people with anxiety disorder.It can be seen from Figure4 that among patients without anxiety disorder, the population of ball games is basically the same, and the population of basketball is slightly higher (53.28%). The overall performance is as follows: with the increase of the severity of anxiety disorder, the people playing football and tennis are more prone to subhealth.Then, the composition of different exercise durations in anxiety patients was studied, as shown in Figure5. In this study, the daily exercise duration of the respondents was divided into five levels: among them, the number of people who played under 1 hour was 51, accounting for 5.25% of the total respondents; the number of cases who played for 1∼2 hours was 27, accounting for 2.78% of all respondents; the number of cases who played for 2∼3 hours was 171, accounting for 17.59% of all respondents; the number of cases who played for 3∼4 hours was 375, accounting for 38.58% of all respondents; the number of people who played for over 4 hours was 348, accounting for 35.80% of all respondents. It can be seen from the table and figure that among the people without anxiety disorder, the higher the education level, the smaller the proportion; among the people with mild anxiety disorder, the people under 1 hour were the least (9.8%), and the rest were basically the same. In the population with moderate anxiety disorder, the proportion of 1∼2 hours is similar; the proportion of anxiety disorder increased rapidly with the decrease of exercise time in the population with severe anxiety disorder. It suggests that the lower the duration of exercise, the more serious the state of anxiety.Figure 5
Comparison of ball game duration composition among anxiety patients.


## 4.2. Comparison of Experimental Results

To validate the performance of the algorithm, simulation experiments were performed on an improved data mining FSVM classification algorithm proposed in this section and compared with SVM and FSVM. Without generality, this technique verifies the algorithm with two classes of two-dimensional datasets: the training sample set includes the two randomly generated two-class 2D samples; the test sample also includes random two-class 2D samples. The kernel function parameters and penalty parameters in the algorithm are obtained by 5-fold cross validation, and the grid search method is used. The training speed and classification accuracy of the three algorithms are shown in Table1.Table 1
The training speed and classification accuracy of the three algorithms.
Training setTest setClassification time (s)Accuracy (%)SVMFSVMOur modelSVMFSVMOur model2002003.43.372.7391.5692.1492.1450030043.443.3135.6737.6894.5594.53800400150.51149.3591.2496.2596.2596.29It can be seen from Table1 that with the increasing number of training samples, the proposed algorithm improves the training speed and classification speed compared with the other two algorithms, ensuring its classification accuracy. When training support vector machine and fuzzy support vector machine, the whole kernel function matrix needs to be calculated and stored many times. Therefore, when the number of training samples is large, their training speed is slow. It can be seen from Table 1 that with the increase of the number of training samples, the training time of the algorithm in this paper is significantly less than that of SVM and FSVM. This is because this algorithm preprocesses the training samples before training FSVM, reduces the number of training samples, and improves the training speed. In addition, this algorithm uses particle swarm optimization algorithm to optimize the membership of samples for the support vector set obtained after training FSVM. The support vector which makes the average classification error smaller is selected to train the fuzzy support vector machine with the quantum set, and the reduction of the support vector is realized, so as to ensure the classification accuracy and improve the classification speed.


## 5. Conclusion

At present, with the trend of accelerating the pace of people’s life and increasing work pressure, anxiety disorder has become a common mental disease. Ball games are considered an important part of sports. Therefore, it is urgent to explore the rehabilitation effect of ball games in the treatment of anxiety patients and try to establish new training methods. Based on this, this paper uses support vector machine as data mining algorithm to study the impact of ball games on the rehabilitation of anxiety patients. Firstly, the shortcomings of the traditional support vector machine algorithm are analyzed, and on this basis, an improved data mining fuzzy support vector machine classification algorithm is proposed. The particle swarm optimization algorithm is applied to select the optimal support to reduce the number of support vectors and improve the classification speed. The results of data analysis experiment show that the anxiety symptoms of people who play ball games are lighter than those who do not play ball games or even those who do not play sports at all. The anxiety symptoms of people who play basketball are the lightest and those who play tennis are the heaviest. The longer the time of ball games every day, the lighter the symptoms of anxiety disorder, which is in line with the attempt of medical research. Then, a comparative experiment is carried out to verify the effectiveness of this algorithm. The comparative experimental results show that the improved FSVM significantly improves the classification speed, training speed, and classification accuracy.



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*Source: 6068373-2022-04-13.xml*