# Revealing the Inner-relevance of College Students’ Physical Fitness by Association Analysis and Neural Network

Authors: Yiqun Pang; Yun-Xiang Pang; Qiurui Wang
Journal: Computational Intelligence and Neuroscience
 (2022)

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## Abstract

Background: The physical activity and health status of the students in China are not optimistic, there is a general lack of exercise volume and exercise intensity. Normal college students shoulder the future of China’s education. Promoting their physical health is the basic requirement for cultivating teachers in the new era;
Methods:Testing and recording 1123 male, 3266 female college students’ physical fitness indicators in a normal college, the relationship between these indicators was mined by correlation analysis and Apriori, and the intelligent prediction models was constructed according to the mined knowledge;
Results: There was no correlation between male 1000m running and vital capacity (P > 0.05), but it was correlated with vital capacity weight index (P < 0.05); Most indicators of women showed varying degrees of correlation. There are many association rules between female 50m sprint and standing long jump, sit-ups, and BMI. The introduction of vital capacity weight index slightly improved the accuracy of the 1000m run prediction model; The prediction model of female 50m sprint with standing long jump, sit-ups and BMI as inputs not only keeps the accuracy in a reasonable range, but also reduces the complexity and parameters;
ConclusionsFor male students, the ostensibly paradoxical relationships between vital capacity and a 1000 meter run and between vital capacity and pull up were actually due to body shape; Body shape, lower limb explosive power, and core strength play key roles for female college students’ speed quality; BMI, standing long jump and one minute sit-up can be used to predict the 50m sprint performance of general female college students.


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## Body

## 1. Introduction

With the rapid development of the national economy and the continuous improvement of people’s living standards, people pay more and more attention to their physical health. It is reported that the physical activity and health status of the students in China are not optimistic, there is a general lack of exercise volume and exercise intensity, and presents a change law that physical activity gradually decreases with the growth of grade [1]. Normal college students shoulder the future of China’s education. Promoting their physical health is the basic requirement for cultivating teachers in the new era. Public Physical Education in normal colleges should be paid more attention.With the arrival of the era of big data, a large number of physical monitoring data would be analyzed through artificial intelligence and data mining technology, so that the important information and knowledge is hidden therein can be found, which provides a scientific basis for the public physical education teaching in universities. Neural networks [2], decision trees [3], clustering [4], and other algorithms are often used for data mining in sports. Mello et al. [5] analyzed the relationship between lifestyle habits (physical activity, sedentary, diet, etc.) and obesity in adolescents and performed a cluster analysis. Some studies [6,7] have worked on machine learning to predict the classification of physical fitness levels rather than exploring the intrinsic relationships between fitness metrics. Yin et al. [8] analyzed height, weight, vital capacity, step test, grip strength, and vertical jump through decision trees and found that the most influential indicator for boys was vital capacity, while for girls it was the step test. Qiao, et al. [9] proved the validity and feasibility of applying association rule data mining technology to physical fitness monitoring data. He found that the size of vital capacity had a certain relationship with strength, explosive power, and reaction ability [10]. Since then, some researchers have focused on mining the association rules for college students’ physical health: The study [11] found that male college students had a low cardiopulmonary function and poor strength; Female college students have good flexibility, low cardiopulmonary function and strength, and the phenomenon of “fat people with normal weight” widely exists. The author believes that male college students should take more strength and cardiopulmonary function training; Ma [12] holds that the development of male college students’ physical fitness is unbalanced. The association rules are explained from the perspective of key abilities to clarify the absolute strength of upper limb muscles, lower limb explosiveness and aerobic endurance of boys, and the abdominal muscle strength endurance, lower limb explosiveness and aerobic endurance of girls are the key abilities. Other studies have improved the Apriori algorithm for college students’ physical health data. Based on the analysis of the “support confidence” mining mode of traditional association rules, Zhu [13] improved the association rules by using the idea of “state transformation”, and introduces the lifting interest measure to mine the rules that users are interested in. Based on the Apriori algorithm, Shi et al. [14] analyzes the physical fitness test results and physical education curriculum data of college students, and finds that the physical education curriculum plays a positive role in the growth of College Students’ physique. There is a strong correlation between endurance quality, speed quality and many physical qualities, which can effectively promote the improvement of other qualities. Due to its powerful modeling ability, machine learning algorithms are gradually favored in the research of college students’ physical health. Zhang, et al. [15] established a comprehensive evaluation model by using an artificial neural network to determine the importance of three types of indicators for adults in order: physical quality, body shape, and body function. The study [16] constructed a neural network regression model between the measured values of test indicators and the total score of physical health. Kou et al. [17] used gradient boosting decision tree (GBDT), random forest, and artificial neural network to predict the classification of a physical test grade according to other physical test results.Through data mining and artificial intelligence to analyze and model the physical fitness of college students, teachers can guide them to exercise purposefully under the condition of better understanding the physical health of college students. Moreover, through the analysis of the data, we can deepen the understanding of the test of college students’ physical health standards, and provide a theoretical basis for further promoting and reforming the “national student physical health standard”. We analyzed the physical fitness of normal college students by data mining; Then, according to the analysis results, the physical fitness was predicted by an artificial neural network and random forest; We took the analysis results as prior knowledge for screening the features, which improved the prediction model; By comparing and analyzing the performance of the model, the knowledge mined is inversely verified.


## 2. Materials and Methods

### 2.1. ．Participants

This experiment was conducted at Zibo Normal College in Shandong Province, China. The ethics committee of Zibo Normal College approved this study. 1123 male college students and 3266 female college students were tested (age = 20Y ± 2). All participants were healthy and free from major diseases.


### 2.2. ．Data Collection

Obey the “national student physical health standard (revised in 2014)” [18], the various 80 physical fitness indicators of participants were recorded.


#### 2.2.1. Body Mass Index

Height measurement: the measured person stands barefoot on the base plate of the height meter in a “stand at attention” posture, whose heels, sacral and two shoulders are close to the column of the height meter; Adjust the head so that the upper edge of the tragus is flush with the lowest point of the lower edge of the orbit. Weight measurement: the examinee takes off his shoes, stands on the base of the weight measuring instrument, stands in a correct position and stands upright. Read and record the reading of the pointer on the weight measuring instrument, that is, the subject’s weight, expressed in kg. According to the body mass index (BMI) = weight / height2. The BMI of all the participants was calculated and recorded.


#### 2.2.2. Vital Capacity

The vital capacity was measured with the spirometers (HJ-101 of Ningbo huajuhe Electronic Technology Co., Ltd.). After the measuring instrument issued the measurement instruction, the person inhaled deeply and then blew as much as possible to measure the vital capacity.


#### 2.2.3. Sit and Reach

The person faces the measuring instrument, sits on the cushion and straightens his legs forward; Keep his/her heels together, pedal on the baffle of the tester, and naturally separate the toes by about 10-15 cm. The subjects put their hands together, extend their palms downward, straighten their knees, bend their bodies forward, and push the cursor forward smoothly with the fingertips of the middle fingers of both hands at a constant speed until it can’t be pushed.


#### 2.2.4. Standing Long Jump

The two feet of the person are separated naturally. After standing on the jumper, both feet take off at the same time Measure the vertical distance from the trailing edge of the jumper to the trailing edge of the nearest landing point. Test 3 times and record the best score. The unit is cm, with 1 decimal place reserved.


#### 2.2.5. 0 Meter Sprint

5 subjects per group, standing start; Once hearing the start signal, started immediately and run to the finish line with their full strength. The timekeeper stood on the side of the finish line and opens the watch to count the time when the starting flag was waved; Stopped the watch when the subject’s chest reached the vertical plane of the finish line. The record was in seconds and one decimal place is reserved.


### 2.3. 1000 Meter Run

10 male subjects per group, standing start; Once hearing the start signal, started immediately and run to the finish line with their full strength. The timekeeper stood on the side of the finish line and opens the watch to count the time when the starting flag was waved; Stopped the watch when the subject’s chest reached the vertical plane of the finish line. The records are in seconds, rounded to the nearest whole number.


#### 2.3.1. 800 Meter Run

10 female subjects per group, standing start; Once hearing the start signal, started immediately and run to the finish line with their full strength. The timekeeper stood on the side of the finish line and opens the watch to count the time when the starting flag was waved; Stopped the watch when the subject’s chest reached the vertical plane of the finish line. The records are in seconds, rounded to the nearest whole number.


#### 2.3.2. One Minute Sit-ups

Female subjects lie on their backs on cushions, with their legs slightly separated, knees bent at 90°, and fingers of both hands crossed and pasted behind their heads. The companion presses his ankle to fix his lower limbs. When the tester issues the “start” password, open the meter to count the time, and record the number of times the subject completes within 1 minute. When the person sits up, her elbows touch or exceed her knees once. At the time of one minute, although the subject has sat up the elbow joint does not touch both knees, this number will not be counted. Record the number of times the subjects completed in one minute, accurate to one digit.


#### 2.3.3. Pull up

Male subjects face the horizontal bar and stand naturally; Then jump up and hold the bar with their forehand. Keep the hands shoulder-width apart, and the body is in a straight arm suspension position. When the body stops shaking, pull up with both arms at the same time; When pulling out, the body shall not have any additional movements. When the lower jaw exceeds the upper edge of the horizontal bar, it is restored to a straight arm suspension position, which is completed once. The tester recorded the number of times the subjects completed, accurate to one digit.


### 2.4. Data Mining

#### 2.4.1. Correlation Analysis

The SciPy 1.6.3 package was used to calculate the correlation coefficient and Pearson value between the above physical fitness indexes of male or female subjects.


#### 2.4.2. Association Rule Mining

The goal of association rule mining is to find the association or relationship between item sets. Discretization: association rule mining is usually applicable to scenarios where indicators take discrete values. However, if the index values in the original database are continuous, appropriate data discretization should be carried out before association rule mining (that is, the value of an interval should be mapped to a value). BMI is mapped into low weight, normal, overweight and obesity according to the “national student physical health standard (revised in 2014)”18], and other indicators are mapped into excellent, good, pass, and fail grades respectively.Apriori algorithm [19] is used in this experiment, and its main steps are as follows:first stage. This step needs to find all high-frequency itemsets from the original data set. The so-called high frequency means that the frequency of an item set reaches or exceeds a certain threshold relative to the overall data. The frequency of itemsets is called support, and the given threshold is called minimum support ms. A k-itemset satisfying the minimum support is called a high-frequency k-itemset (which can be expressed as frequency K). The algorithm generates frequency K + 1 from the subset of frequency K until it can no longer screen out a longer set of high-frequency items. Support is the proportion of the occurrence times of several associated data in the data set to the total data set. For the three itemsets X, Y, and Z, the corresponding support is defined as:(1)SupportX,Y,Z=PXYZ=numberXYZnumberAllSamples.second stage. This step needs to generate association rules. Association rules are generated by using the high-frequency k-itemset in the first stage. Under the constraint of minimum confidence mc, if the confidence obtained by a rule is not less than the minimum confidence, this rule is called association rules. The confidence is the conditional probability of the data. For example, the confidence of X for Y and Z is:(2)ConfidenceXYZ=P⇐X|YZ=PXYZPYZ.We set ms, mc to 0.5 and 0.6, respectively. Association rules are obtained according to the Apriori mining algorithm.


### 2.5. Intelligent Forecasting model

#### 2.5.1. Dataset Processing

Female dataset: 2280 for training and 986 samples for validation. Male dataset: 780 samples for training and 343 samples for validation.Before feeding each indicator into the model, it is linearly normalized to 0～1 as follows:(3)xj′=xj−minxmaxx−minx.


#### 2.5.2. Artificial Neural Network (ANN)

Back propagation neural network is a mathematical modeling method to simulate the function of human neurons. It can automatically update the parameters by using the error return mechanism. The network structures usually include the input layer, hidden layer, and output layer [20]. Back propagation neural network has a strong fitting ability. In the Anaconda virtual environment, the framework of the neural network is built by using PyTorch 1.7.1, in which the first hidden layer contains 12 nodes, the second hidden layer contains 12 nodes, the output layer has only 1 node, and the number of nodes in the input layer depends on the dimensions of features (indicators). And relu function is selected as the activation function and mean square error (MSE) as the loss function, which is optimized by the Adam algorithm.Thus, the forward propagation of the neural network is:(4)y^=FW•X+b.where in (4), W is weight matrix [w1, w2, ..., wn] T, X is input variables [x1, x2, ..., xn], y^ is the predicted value, F is the activation function, and b represents the bias.In the process of back propagation, the update of the link weightwi of a node i in each iteration can be expressed as:(5)wi′=wi−η∂∑i=1n1/ny−y^2∂wi.where in (5), wi′ represents the updated weight of the node, and y is the real value, η is the learning rate.Similarly, the biasb′ updated in this epoch is:(6)b′=b−η∂∑i=1n1/ny−y^2∂b.


#### 2.5.3. Random Forest Regressor

Random forest (RF) samples the original data set many times, and extracts as many observations as the sample size each time. Because it is put back sampling, some observations are not drawn every time, and some observations will be drawn repeatedly. In this way, many different data sets will be obtained, and then a decision tree will be established for each data set, resulting in a large number of decision trees. Because for each node of each tree in a random forest, the split variables are competed by a few randomly selected variables. The limitation of the number of candidates for splitting variables can avoid the details in the data relationship being ignored due to the dominance of strong variables, which greatly improves the performance of the model. The prediction of a random forest is the average of the results of all trees, that is, for a new observation value, n prediction values are obtained from many trees (such as n trees), and finally, the average of these n prediction values is used as the final result. The random forest regression in this experiment is based on scikit-learn 0.24.2.


## 2.1. ．Participants

This experiment was conducted at Zibo Normal College in Shandong Province, China. The ethics committee of Zibo Normal College approved this study. 1123 male college students and 3266 female college students were tested (age = 20Y ± 2). All participants were healthy and free from major diseases.


## 2.2. ．Data Collection

Obey the “national student physical health standard (revised in 2014)” [18], the various 80 physical fitness indicators of participants were recorded.


### 2.2.1. Body Mass Index

Height measurement: the measured person stands barefoot on the base plate of the height meter in a “stand at attention” posture, whose heels, sacral and two shoulders are close to the column of the height meter; Adjust the head so that the upper edge of the tragus is flush with the lowest point of the lower edge of the orbit. Weight measurement: the examinee takes off his shoes, stands on the base of the weight measuring instrument, stands in a correct position and stands upright. Read and record the reading of the pointer on the weight measuring instrument, that is, the subject’s weight, expressed in kg. According to the body mass index (BMI) = weight / height2. The BMI of all the participants was calculated and recorded.


### 2.2.2. Vital Capacity

The vital capacity was measured with the spirometers (HJ-101 of Ningbo huajuhe Electronic Technology Co., Ltd.). After the measuring instrument issued the measurement instruction, the person inhaled deeply and then blew as much as possible to measure the vital capacity.


### 2.2.3. Sit and Reach

The person faces the measuring instrument, sits on the cushion and straightens his legs forward; Keep his/her heels together, pedal on the baffle of the tester, and naturally separate the toes by about 10-15 cm. The subjects put their hands together, extend their palms downward, straighten their knees, bend their bodies forward, and push the cursor forward smoothly with the fingertips of the middle fingers of both hands at a constant speed until it can’t be pushed.


### 2.2.4. Standing Long Jump

The two feet of the person are separated naturally. After standing on the jumper, both feet take off at the same time Measure the vertical distance from the trailing edge of the jumper to the trailing edge of the nearest landing point. Test 3 times and record the best score. The unit is cm, with 1 decimal place reserved.


### 2.2.5. 0 Meter Sprint

5 subjects per group, standing start; Once hearing the start signal, started immediately and run to the finish line with their full strength. The timekeeper stood on the side of the finish line and opens the watch to count the time when the starting flag was waved; Stopped the watch when the subject’s chest reached the vertical plane of the finish line. The record was in seconds and one decimal place is reserved.


## 2.2.1. Body Mass Index

Height measurement: the measured person stands barefoot on the base plate of the height meter in a “stand at attention” posture, whose heels, sacral and two shoulders are close to the column of the height meter; Adjust the head so that the upper edge of the tragus is flush with the lowest point of the lower edge of the orbit. Weight measurement: the examinee takes off his shoes, stands on the base of the weight measuring instrument, stands in a correct position and stands upright. Read and record the reading of the pointer on the weight measuring instrument, that is, the subject’s weight, expressed in kg. According to the body mass index (BMI) = weight / height2. The BMI of all the participants was calculated and recorded.


## 2.2.2. Vital Capacity

The vital capacity was measured with the spirometers (HJ-101 of Ningbo huajuhe Electronic Technology Co., Ltd.). After the measuring instrument issued the measurement instruction, the person inhaled deeply and then blew as much as possible to measure the vital capacity.


## 2.2.3. Sit and Reach

The person faces the measuring instrument, sits on the cushion and straightens his legs forward; Keep his/her heels together, pedal on the baffle of the tester, and naturally separate the toes by about 10-15 cm. The subjects put their hands together, extend their palms downward, straighten their knees, bend their bodies forward, and push the cursor forward smoothly with the fingertips of the middle fingers of both hands at a constant speed until it can’t be pushed.


## 2.2.4. Standing Long Jump

The two feet of the person are separated naturally. After standing on the jumper, both feet take off at the same time Measure the vertical distance from the trailing edge of the jumper to the trailing edge of the nearest landing point. Test 3 times and record the best score. The unit is cm, with 1 decimal place reserved.


## 2.2.5. 0 Meter Sprint

5 subjects per group, standing start; Once hearing the start signal, started immediately and run to the finish line with their full strength. The timekeeper stood on the side of the finish line and opens the watch to count the time when the starting flag was waved; Stopped the watch when the subject’s chest reached the vertical plane of the finish line. The record was in seconds and one decimal place is reserved.


## 2.3. 1000 Meter Run

10 male subjects per group, standing start; Once hearing the start signal, started immediately and run to the finish line with their full strength. The timekeeper stood on the side of the finish line and opens the watch to count the time when the starting flag was waved; Stopped the watch when the subject’s chest reached the vertical plane of the finish line. The records are in seconds, rounded to the nearest whole number.


### 2.3.1. 800 Meter Run

10 female subjects per group, standing start; Once hearing the start signal, started immediately and run to the finish line with their full strength. The timekeeper stood on the side of the finish line and opens the watch to count the time when the starting flag was waved; Stopped the watch when the subject’s chest reached the vertical plane of the finish line. The records are in seconds, rounded to the nearest whole number.


### 2.3.2. One Minute Sit-ups

Female subjects lie on their backs on cushions, with their legs slightly separated, knees bent at 90°, and fingers of both hands crossed and pasted behind their heads. The companion presses his ankle to fix his lower limbs. When the tester issues the “start” password, open the meter to count the time, and record the number of times the subject completes within 1 minute. When the person sits up, her elbows touch or exceed her knees once. At the time of one minute, although the subject has sat up the elbow joint does not touch both knees, this number will not be counted. Record the number of times the subjects completed in one minute, accurate to one digit.


### 2.3.3. Pull up

Male subjects face the horizontal bar and stand naturally; Then jump up and hold the bar with their forehand. Keep the hands shoulder-width apart, and the body is in a straight arm suspension position. When the body stops shaking, pull up with both arms at the same time; When pulling out, the body shall not have any additional movements. When the lower jaw exceeds the upper edge of the horizontal bar, it is restored to a straight arm suspension position, which is completed once. The tester recorded the number of times the subjects completed, accurate to one digit.


## 2.3.1. 800 Meter Run

10 female subjects per group, standing start; Once hearing the start signal, started immediately and run to the finish line with their full strength. The timekeeper stood on the side of the finish line and opens the watch to count the time when the starting flag was waved; Stopped the watch when the subject’s chest reached the vertical plane of the finish line. The records are in seconds, rounded to the nearest whole number.


## 2.3.2. One Minute Sit-ups

Female subjects lie on their backs on cushions, with their legs slightly separated, knees bent at 90°, and fingers of both hands crossed and pasted behind their heads. The companion presses his ankle to fix his lower limbs. When the tester issues the “start” password, open the meter to count the time, and record the number of times the subject completes within 1 minute. When the person sits up, her elbows touch or exceed her knees once. At the time of one minute, although the subject has sat up the elbow joint does not touch both knees, this number will not be counted. Record the number of times the subjects completed in one minute, accurate to one digit.


## 2.3.3. Pull up

Male subjects face the horizontal bar and stand naturally; Then jump up and hold the bar with their forehand. Keep the hands shoulder-width apart, and the body is in a straight arm suspension position. When the body stops shaking, pull up with both arms at the same time; When pulling out, the body shall not have any additional movements. When the lower jaw exceeds the upper edge of the horizontal bar, it is restored to a straight arm suspension position, which is completed once. The tester recorded the number of times the subjects completed, accurate to one digit.


## 2.4. Data Mining

### 2.4.1. Correlation Analysis

The SciPy 1.6.3 package was used to calculate the correlation coefficient and Pearson value between the above physical fitness indexes of male or female subjects.


### 2.4.2. Association Rule Mining

The goal of association rule mining is to find the association or relationship between item sets. Discretization: association rule mining is usually applicable to scenarios where indicators take discrete values. However, if the index values in the original database are continuous, appropriate data discretization should be carried out before association rule mining (that is, the value of an interval should be mapped to a value). BMI is mapped into low weight, normal, overweight and obesity according to the “national student physical health standard (revised in 2014)”18], and other indicators are mapped into excellent, good, pass, and fail grades respectively.Apriori algorithm [19] is used in this experiment, and its main steps are as follows:first stage. This step needs to find all high-frequency itemsets from the original data set. The so-called high frequency means that the frequency of an item set reaches or exceeds a certain threshold relative to the overall data. The frequency of itemsets is called support, and the given threshold is called minimum support ms. A k-itemset satisfying the minimum support is called a high-frequency k-itemset (which can be expressed as frequency K). The algorithm generates frequency K + 1 from the subset of frequency K until it can no longer screen out a longer set of high-frequency items. Support is the proportion of the occurrence times of several associated data in the data set to the total data set. For the three itemsets X, Y, and Z, the corresponding support is defined as:(1)SupportX,Y,Z=PXYZ=numberXYZnumberAllSamples.second stage. This step needs to generate association rules. Association rules are generated by using the high-frequency k-itemset in the first stage. Under the constraint of minimum confidence mc, if the confidence obtained by a rule is not less than the minimum confidence, this rule is called association rules. The confidence is the conditional probability of the data. For example, the confidence of X for Y and Z is:(2)ConfidenceXYZ=P⇐X|YZ=PXYZPYZ.We set ms, mc to 0.5 and 0.6, respectively. Association rules are obtained according to the Apriori mining algorithm.


## 2.4.1. Correlation Analysis

The SciPy 1.6.3 package was used to calculate the correlation coefficient and Pearson value between the above physical fitness indexes of male or female subjects.


## 2.4.2. Association Rule Mining

The goal of association rule mining is to find the association or relationship between item sets. Discretization: association rule mining is usually applicable to scenarios where indicators take discrete values. However, if the index values in the original database are continuous, appropriate data discretization should be carried out before association rule mining (that is, the value of an interval should be mapped to a value). BMI is mapped into low weight, normal, overweight and obesity according to the “national student physical health standard (revised in 2014)”18], and other indicators are mapped into excellent, good, pass, and fail grades respectively.Apriori algorithm [19] is used in this experiment, and its main steps are as follows:first stage. This step needs to find all high-frequency itemsets from the original data set. The so-called high frequency means that the frequency of an item set reaches or exceeds a certain threshold relative to the overall data. The frequency of itemsets is called support, and the given threshold is called minimum support ms. A k-itemset satisfying the minimum support is called a high-frequency k-itemset (which can be expressed as frequency K). The algorithm generates frequency K + 1 from the subset of frequency K until it can no longer screen out a longer set of high-frequency items. Support is the proportion of the occurrence times of several associated data in the data set to the total data set. For the three itemsets X, Y, and Z, the corresponding support is defined as:(1)SupportX,Y,Z=PXYZ=numberXYZnumberAllSamples.second stage. This step needs to generate association rules. Association rules are generated by using the high-frequency k-itemset in the first stage. Under the constraint of minimum confidence mc, if the confidence obtained by a rule is not less than the minimum confidence, this rule is called association rules. The confidence is the conditional probability of the data. For example, the confidence of X for Y and Z is:(2)ConfidenceXYZ=P⇐X|YZ=PXYZPYZ.We set ms, mc to 0.5 and 0.6, respectively. Association rules are obtained according to the Apriori mining algorithm.


## 2.5. Intelligent Forecasting model

### 2.5.1. Dataset Processing

Female dataset: 2280 for training and 986 samples for validation. Male dataset: 780 samples for training and 343 samples for validation.Before feeding each indicator into the model, it is linearly normalized to 0～1 as follows:(3)xj′=xj−minxmaxx−minx.


### 2.5.2. Artificial Neural Network (ANN)

Back propagation neural network is a mathematical modeling method to simulate the function of human neurons. It can automatically update the parameters by using the error return mechanism. The network structures usually include the input layer, hidden layer, and output layer [20]. Back propagation neural network has a strong fitting ability. In the Anaconda virtual environment, the framework of the neural network is built by using PyTorch 1.7.1, in which the first hidden layer contains 12 nodes, the second hidden layer contains 12 nodes, the output layer has only 1 node, and the number of nodes in the input layer depends on the dimensions of features (indicators). And relu function is selected as the activation function and mean square error (MSE) as the loss function, which is optimized by the Adam algorithm.Thus, the forward propagation of the neural network is:(4)y^=FW•X+b.where in (4), W is weight matrix [w1, w2, ..., wn] T, X is input variables [x1, x2, ..., xn], y^ is the predicted value, F is the activation function, and b represents the bias.In the process of back propagation, the update of the link weightwi of a node i in each iteration can be expressed as:(5)wi′=wi−η∂∑i=1n1/ny−y^2∂wi.where in (5), wi′ represents the updated weight of the node, and y is the real value, η is the learning rate.Similarly, the biasb′ updated in this epoch is:(6)b′=b−η∂∑i=1n1/ny−y^2∂b.


### 2.5.3. Random Forest Regressor

Random forest (RF) samples the original data set many times, and extracts as many observations as the sample size each time. Because it is put back sampling, some observations are not drawn every time, and some observations will be drawn repeatedly. In this way, many different data sets will be obtained, and then a decision tree will be established for each data set, resulting in a large number of decision trees. Because for each node of each tree in a random forest, the split variables are competed by a few randomly selected variables. The limitation of the number of candidates for splitting variables can avoid the details in the data relationship being ignored due to the dominance of strong variables, which greatly improves the performance of the model. The prediction of a random forest is the average of the results of all trees, that is, for a new observation value, n prediction values are obtained from many trees (such as n trees), and finally, the average of these n prediction values is used as the final result. The random forest regression in this experiment is based on scikit-learn 0.24.2.


## 2.5.1. Dataset Processing

Female dataset: 2280 for training and 986 samples for validation. Male dataset: 780 samples for training and 343 samples for validation.Before feeding each indicator into the model, it is linearly normalized to 0～1 as follows:(3)xj′=xj−minxmaxx−minx.


## 2.5.2. Artificial Neural Network (ANN)

Back propagation neural network is a mathematical modeling method to simulate the function of human neurons. It can automatically update the parameters by using the error return mechanism. The network structures usually include the input layer, hidden layer, and output layer [20]. Back propagation neural network has a strong fitting ability. In the Anaconda virtual environment, the framework of the neural network is built by using PyTorch 1.7.1, in which the first hidden layer contains 12 nodes, the second hidden layer contains 12 nodes, the output layer has only 1 node, and the number of nodes in the input layer depends on the dimensions of features (indicators). And relu function is selected as the activation function and mean square error (MSE) as the loss function, which is optimized by the Adam algorithm.Thus, the forward propagation of the neural network is:(4)y^=FW•X+b.where in (4), W is weight matrix [w1, w2, ..., wn] T, X is input variables [x1, x2, ..., xn], y^ is the predicted value, F is the activation function, and b represents the bias.In the process of back propagation, the update of the link weightwi of a node i in each iteration can be expressed as:(5)wi′=wi−η∂∑i=1n1/ny−y^2∂wi.where in (5), wi′ represents the updated weight of the node, and y is the real value, η is the learning rate.Similarly, the biasb′ updated in this epoch is:(6)b′=b−η∂∑i=1n1/ny−y^2∂b.


## 2.5.3. Random Forest Regressor

Random forest (RF) samples the original data set many times, and extracts as many observations as the sample size each time. Because it is put back sampling, some observations are not drawn every time, and some observations will be drawn repeatedly. In this way, many different data sets will be obtained, and then a decision tree will be established for each data set, resulting in a large number of decision trees. Because for each node of each tree in a random forest, the split variables are competed by a few randomly selected variables. The limitation of the number of candidates for splitting variables can avoid the details in the data relationship being ignored due to the dominance of strong variables, which greatly improves the performance of the model. The prediction of a random forest is the average of the results of all trees, that is, for a new observation value, n prediction values are obtained from many trees (such as n trees), and finally, the average of these n prediction values is used as the final result. The random forest regression in this experiment is based on scikit-learn 0.24.2.


## 3. Results

### 3.1. Correlation Analysis

Considering the correlation between vital capacity and body weight, we adopted the vital capacity weight index (hereinafter referred to as VCWI), where VCWI = vital capacity (ml) / body weight (kg)×100%.The correlation coefficient matrix and Pearson coefficient matrix among various indicators of female and male participants are obtained through correlation analysis, which is shown in Figure1 and Figure 2, respectively. For female participants, most indicators show different degrees of correlation with each other except BMI and sit & reach; For male participants, sit & reach had no significant correlation with BMI, 50m sprint, and standing long jump. What’s more, male vital capacity showed no significant correlation between 50m sprint and 1000m run. However, compared with vital capacity, male vital capacity weight index had more correlation with 1000m running.Figure 1
Correlation analysis for female participants. (a) Correlation coefficient matrix among various indexes of female participates; (b) The Pearson coefficient matrix among various indexes of female subjects, black block P > 0.05, rose block 0.01 < p < 0.05, canary yellow block P < 0.001. Most indicators show different degrees of correlation with each other.
(a)(b)Figure 2
Correlation analysis for male participants. (a) Correlation coefficient matrix among various indexes of male participates; (b) The Pearson coefficient matrix among various indexes of male subjects, canary yellow block P < 0.001, orange block 0.001 < P < 0.01, rose block 0.01 < p < 0.05, black block P > 0.05. It can be seen that 1000m is positively correlated with vital capacity weight index, but not with vital capacity.
(a)(b)


### 3.2. Association Rules

For female college students, all association rules are shown in Table1. For male college students, all association rules are shown in Table 2.Table 1
Association rules for female subjects.
No.Left ruleRight ruleConf (L⟶R)Conf (R⟶L)Support1BMI normalpass the 50 m sprint0.61570.81860.50512pass the 50 m sprintpass the sit-up test0.81880.63980.50523BMI normalpass the sit-up test0.79330.82420.65084BMI normalpass the standing long jump0.75700.82240.62105pass the standing long jumppass the sit-up test0.82160.78580.62046BMI normalpass the sit-up test, pass the standing long jump0.6219_0.51027pass the standing long jumppass the sit-up test, BMI normal0.6757_0.51028pass the sit-up testpass the standing long jump, BMI normal0.6462_0.5102Table 2
Association rules for male subjects.
No.Left ruleRight ruleConf (L⟶R)Conf (R⟶L)Support1excellent vital capacityBMI normal0.67090.92890.62722excellent vital capacitypass the sit and reach0.58960.93840.55123excellent vital capacitypass the 1000 m run0.62860.94020.58774excellent vital capacitypass the 50 m sprint0.67770.94040.63365excellent vital capacityfail the pull up test0.66050.93810.61756excellent vital capacitypass the standing long jump0.60980.95760.5701


### 3.3. Intelligent Prediction Model

In order to further explore the relationship between vital capacity, vital capacity body mass index and male 1000m run, the relationship between standing long jump, BMI, sit-ups and female 50m sprint was studied. Eight different prediction models using artificial neural networks and random forests were constructed.The true value and model’s prediction of the four ANN models which predict the time of 50m sprint or 1000m running can be seen in Figure3. The true value and model’s prediction of the 4 RF models which predict the time of 50m sprint or 1000m running can be seen in Figure 4. To better compare these models, we calculated their average error (shown in Table 3) and mean square error (shown in Table 4) on the valid set. For the male 1000m run, the RF models perform better than the ANN models, The two models that used VCWI have weak advantages in precision over the two models that used vital capacity. The prediction models for the female 50m sprint are of relatively high precision. That takes only 3 features as inputs causing a slight precision loss of the two 50m sprint prediction models.Figure 3
(a) The true value and model’s prediction of the ANN model for predicting 1000m, which takes vital capacity, BMI, sit & reach, standing long jump, pull-up and 50m sprint as inputs; (b) The true value and model’s prediction of the ANN model for predicting 1000 m, which takes VCWI, BMI, sit & reach, standing long jump, pull-up and 50m sprint as inputs; (c) The true value and model’s prediction of the ANN model for predicting female 50 m, which takes vital capacity, BMI, one minute sit-ups, sit & reach, standing long jump and 800 m running as inputs; (d) The true value and model’s prediction of the ANN model for predicting female 50 m, which takes BMI, standing long jump, and one minute sit-ups as inputs.
(a)(b)(c)(d)Figure 4
(a) The true value and model’s prediction of the RF model for predicting 1000 m, which takes vital capacity, BMI, sit & reach, standing long jump, pull-up and 50 m sprint as inputs; (b) The true value and model’s prediction of the RF model for predicting 1000 m, which takes VCWI, BMI, sit & reach, standing long jump, pull-up and 50 m sprint as inputs; (c) The true value and model’s prediction of the RF model for predicting female 50 m, which takes vital capacity, BMI, sit-ups, sit & reach, standing long jump and 800 m running as inputs; (d) The true value and model’s prediction of the RF model for predicting female 50m, which takes BMI, standing long jump, and sit-ups as inputs.
(a)(b)(c)(d)Table 3
The average error of different prediction models on the valid set.
Male 1000 mFemale 50 mwith vital capacitywith VCWI6 input features3 input featuresANN28.470927.01460.57230.5775RF26.609926.37840.57760.6207Table 4
The mean square error (MSE) of different prediction models on the valid set.
Male 1000 mFemale 50 mwith vital capacitywith VCWI6 input features3 input featuresANN1781.28141729.61850.59960.5702RF1503.16891446.17230.57970.6625


## 3.1. Correlation Analysis

Considering the correlation between vital capacity and body weight, we adopted the vital capacity weight index (hereinafter referred to as VCWI), where VCWI = vital capacity (ml) / body weight (kg)×100%.The correlation coefficient matrix and Pearson coefficient matrix among various indicators of female and male participants are obtained through correlation analysis, which is shown in Figure1 and Figure 2, respectively. For female participants, most indicators show different degrees of correlation with each other except BMI and sit & reach; For male participants, sit & reach had no significant correlation with BMI, 50m sprint, and standing long jump. What’s more, male vital capacity showed no significant correlation between 50m sprint and 1000m run. However, compared with vital capacity, male vital capacity weight index had more correlation with 1000m running.Figure 1
Correlation analysis for female participants. (a) Correlation coefficient matrix among various indexes of female participates; (b) The Pearson coefficient matrix among various indexes of female subjects, black block P > 0.05, rose block 0.01 < p < 0.05, canary yellow block P < 0.001. Most indicators show different degrees of correlation with each other.
(a)(b)Figure 2
Correlation analysis for male participants. (a) Correlation coefficient matrix among various indexes of male participates; (b) The Pearson coefficient matrix among various indexes of male subjects, canary yellow block P < 0.001, orange block 0.001 < P < 0.01, rose block 0.01 < p < 0.05, black block P > 0.05. It can be seen that 1000m is positively correlated with vital capacity weight index, but not with vital capacity.
(a)(b)


## 3.2. Association Rules

For female college students, all association rules are shown in Table1. For male college students, all association rules are shown in Table 2.Table 1
Association rules for female subjects.
No.Left ruleRight ruleConf (L⟶R)Conf (R⟶L)Support1BMI normalpass the 50 m sprint0.61570.81860.50512pass the 50 m sprintpass the sit-up test0.81880.63980.50523BMI normalpass the sit-up test0.79330.82420.65084BMI normalpass the standing long jump0.75700.82240.62105pass the standing long jumppass the sit-up test0.82160.78580.62046BMI normalpass the sit-up test, pass the standing long jump0.6219_0.51027pass the standing long jumppass the sit-up test, BMI normal0.6757_0.51028pass the sit-up testpass the standing long jump, BMI normal0.6462_0.5102Table 2
Association rules for male subjects.
No.Left ruleRight ruleConf (L⟶R)Conf (R⟶L)Support1excellent vital capacityBMI normal0.67090.92890.62722excellent vital capacitypass the sit and reach0.58960.93840.55123excellent vital capacitypass the 1000 m run0.62860.94020.58774excellent vital capacitypass the 50 m sprint0.67770.94040.63365excellent vital capacityfail the pull up test0.66050.93810.61756excellent vital capacitypass the standing long jump0.60980.95760.5701


## 3.3. Intelligent Prediction Model

In order to further explore the relationship between vital capacity, vital capacity body mass index and male 1000m run, the relationship between standing long jump, BMI, sit-ups and female 50m sprint was studied. Eight different prediction models using artificial neural networks and random forests were constructed.The true value and model’s prediction of the four ANN models which predict the time of 50m sprint or 1000m running can be seen in Figure3. The true value and model’s prediction of the 4 RF models which predict the time of 50m sprint or 1000m running can be seen in Figure 4. To better compare these models, we calculated their average error (shown in Table 3) and mean square error (shown in Table 4) on the valid set. For the male 1000m run, the RF models perform better than the ANN models, The two models that used VCWI have weak advantages in precision over the two models that used vital capacity. The prediction models for the female 50m sprint are of relatively high precision. That takes only 3 features as inputs causing a slight precision loss of the two 50m sprint prediction models.Figure 3
(a) The true value and model’s prediction of the ANN model for predicting 1000m, which takes vital capacity, BMI, sit & reach, standing long jump, pull-up and 50m sprint as inputs; (b) The true value and model’s prediction of the ANN model for predicting 1000 m, which takes VCWI, BMI, sit & reach, standing long jump, pull-up and 50m sprint as inputs; (c) The true value and model’s prediction of the ANN model for predicting female 50 m, which takes vital capacity, BMI, one minute sit-ups, sit & reach, standing long jump and 800 m running as inputs; (d) The true value and model’s prediction of the ANN model for predicting female 50 m, which takes BMI, standing long jump, and one minute sit-ups as inputs.
(a)(b)(c)(d)Figure 4
(a) The true value and model’s prediction of the RF model for predicting 1000 m, which takes vital capacity, BMI, sit & reach, standing long jump, pull-up and 50 m sprint as inputs; (b) The true value and model’s prediction of the RF model for predicting 1000 m, which takes VCWI, BMI, sit & reach, standing long jump, pull-up and 50 m sprint as inputs; (c) The true value and model’s prediction of the RF model for predicting female 50 m, which takes vital capacity, BMI, sit-ups, sit & reach, standing long jump and 800 m running as inputs; (d) The true value and model’s prediction of the RF model for predicting female 50m, which takes BMI, standing long jump, and sit-ups as inputs.
(a)(b)(c)(d)Table 3
The average error of different prediction models on the valid set.
Male 1000 mFemale 50 mwith vital capacitywith VCWI6 input features3 input featuresANN28.470927.01460.57230.5775RF26.609926.37840.57760.6207Table 4
The mean square error (MSE) of different prediction models on the valid set.
Male 1000 mFemale 50 mwith vital capacitywith VCWI6 input features3 input featuresANN1781.28141729.61850.59960.5702RF1503.16891446.17230.57970.6625


## 4. Discussion

The measured indicators in this study, including lower limb explosive power, muscle endurance, core strength, respiratory function, back and upper limb strength, etc., can be used to reflect the physical fitness of college students. For male college students, vital capacity does not show a direct correlation with 1000m running (P > 0.05), while VCWI indicates a high correlation with 1000m running performance (P < 0.001). The reason may be that heavier people tend to have a larger vital capacity, because Wang et al. [21] indicated that there was a high correlation between the students’ vital capacity and height, weight, sitting height, chest circumference, waist circumference, shoulder skinfold thickness, upper arm skinfold thickness, abdominal skinfold thickness.Although there is an association rule that male students have excellent vital capacity but fail the pull-up test, the correlation coefficient matrix tells us that vital capacity is positively correlated with the pull-up. Taller college students tend to have a larger vital capacity; The literature [22] states that: the person with taller stature generally has longer arms, every time he pulls up, the actual distance his body’s center of gravity moves upward is greater than the person with short stature. Overall, the pull-up presented a weak positive correlation with vital capacity.Several association rules are found between BMI, standing long jump, one minute sitting up, and BMI in female participants. Both the standing long jump and sit-up require abdominal strength, though the former is in favor of explosive power and the latter is biased toward endurance. Both correlation analysis and association rule mining reveal, for female subjects, that lower limb explosive power, core strength, and well-proportioned body shape play important roles in sprint running. The abdominal strength and hip flexion strength are helpful for sprint running, which are reflected by one minute sit up. When the velocity force of the hip muscle group is large enough, the lift height of the thigh can be well adjusted, which facilitates a well-established kinetic mode. The thigh is raised to a higher height under a fixed kinetic stereotypic mode, and the stride is increased without affecting the steps frequency [23]. According to Li [24], core strength can stabilize the core part of the human body, control the center of gravity of the body, and transmit the strength of the upper and lower limbs. Xu [25] improved 100m sprint performance among high school female students through a sit-up exercise intervention.Based on the information found by data mining, we make 8 prediction models utilizing ANN and RF algorithms. For the male 1000m run, the RF models performed better than the ANN models, The two models that used VCWI have weak advantages in precision over the two models that used vital capacity. The “National Standards for Physical Health of Students (revised 2014)” take vital capacity as a test item, which may not well represent the dynamic function of the respiratory system [26].Since vital capacity and VCWI only reflect the static function of the respiratory system and the chest morphology among students, if future studies can introduce timed vital capacity, it is expected to further improve prediction accuracy. While the prediction model for the female 50m sprint has outstanding performance, all four models are of high accuracy. The two 50m sprint prediction models used only 3-input features, greatly reducing the parameters and computational complexity, and the precision loss is still within the acceptable range. This also verifies that lower limb explosive power, core strength, and body shape are key important factors for speed quality.


## 5. Conclusions

This study reveals the relationship between physical fitness indicators of normal college students by using data mining and machine learning. These findings suggest that: For male students, the ostensibly paradoxical relationships between vital capacity and the 1000m run and between vital capacity and pull-up were actually due to body shape; Body shape, lower limb explosive power, and core strength play key roles in female college students’ speed quality; BMI, standing long jump and one minute sit-up can be used to predict the 50m sprint performance of general female college students.[16]



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*Source: 3320942-2022-09-26.xml*