Research on Classification of College Students’ Physical Fitness Test Scores Based on Neural Network

Along with the social development, people’s study area is getting more complicated. Using one property to describe something in detail is hard, and you need to think about it as a whole. So, the multiindicator assessment method emerged. A multi-indicator assessment is a more comprehensive and detailed description of the object using several properties. Multiple indicators have various properties, and there is a great difference in size and degree between them. If the dimensions of different properties are too big, and the former property is analyzed, it will greatly affect the result and reduce the effectiveness of the other properties. So, we need to regulate the properties of raw data to guarantee analytical results’ reliability.

There are a lot of ways to standardize data. One of the more common approaches is the standardization of the data, which is the uniform distribution of the data into the interval [0,1]. Commonly used standard approaches are Min - Max, Fuzzy Quantizing, Z Score, and Logarithm Function Transformation. Using Z - Z-score normalization, the measuring results of 8 QMS are normalized so that the cell limit and dimensional relation are removed, and the forecast time is shortened. Normalization of the Z Score is a way to standardize the data by using raw data’s average and standard deviation. Following is the standard calculation formula. The standardized approach can transform the raw data to a normal distribution with a median value of 0 and a variance of 1. (1)x=xi−E(x)si$$x = \frac{x_i - {\rm E}(x)}{s_i}$$

In the above formula, x_I is the original data, E(x) is the mean of the data, and s_i is the standard deviation of the data. Using normalization, the raw data are transformed into non-dimensional assessment indicators so that they are equal in value, which allows for weighing and weighing properties of various elements or degrees. As the data size is smaller, it can speed up some of the algorithms. A standardized approach helps to initialize, adjust the learning ratio, search for optimum solutions quickly, and make overall assessment more convenient.

In everyday learning, we may see some data sets listed before us. These data sets may have a particular association, which may be negative or no association. Therefore, we need a tool to measure correlations and analyze several data sets. That tool is data correlation analysis. Correlation between data refers to a specific relationship between data input attributes. Nowadays, in the Large Data Age, data relevance analysis can find inner relationships among objects rapidly and effectively. Relativity means a relation exists among two or more variables whose aim is to discover the hidden information within a dataset. Correlation analysis plays a very important role in data reduction and outlier repair. It is the core technology of data preprocessing. Without correlation analysis, the information expressed between the data may overlap to a certain extent, seriously affecting the accuracy of subsequent modeling and prediction.

The correlation coefficient can describe the relation among the variables. The sign of the correlative factor shows that the relation is positive or negative, and it shows the intensity of the relation. It has no correlation when it is 0, while it has a complete correlation when it is 1. The Pearson Correlation Coefficient, Spearman’s Correlation Factor, Part Correlation Factor, Kendall Correlation Factor, etc. The Pearson Relativity Factor was applied to compute the correlative degree of every property. Because the original data is normalized, the relationship among properties is not altered[5]. Therefore, the normalized data can compute the relationship among the properties. The method for calculating the correlation coefficient is given in the following equation: (2)r=∑i=1n(xi−x¯)(yi−y¯)∑i=1n(xi−x¯)2∑i=1n(yi−y¯)2$$r=\frac{\sum_{i=1}^n\left(x_i-\bar{x}\right)\left(y_i-\bar{y}\right)}{\sqrt{\sum_{i=1}^n\left(x_i-\bar{x}\right)^2} \sqrt{\sum_{i=1}^n\left(y_i-\bar{y}\right)^2}}$$

Take the data from the last year of 2019 in the dataset as an example, calculate the correlation between each attribute, and show the results in Table 3 below.

As shown in the table above, there is a strong correlation between the items measured in the fitness test results. The 50-meter running and standing long jump showed a negative correlation with a correlation coefficient 0.7478[6-7]. Because the 50-meter race data is time data, there is a negative correlation between time data and the score; the longer the time, the lower the score. A positive correlation exists between height, weight and lung capacity, and a strong negative correlation between height and strength events. Taller people require more force to measure than others, affecting the work speed. Since there is a strong correlation between attributes, this leads to redundant information affecting the accuracy of the model. If the correlation between the input data is too strong, the weights in the network connected to the input neurons play a similar role. The data correlation is too strong, the weight relationship trained in the network is not portable, and the model cannot be applied to other years’ data. So, PCA should be adopted to convert the raw data and remove the strong relativity before NN training.

A major problem with data handling is the complexity of the data. PCA is one of the most popular methods for minimizing the size of datasets. It can expose and simplify complicated relations among different variables[8]. Some primary variables with strong relativity are transformed into independent ones by means of coordinate conversion, and the computed independent variables are the main parts. PCA aims to substitute many relevant variables for a less significant number of non-relevant variables and retain as much raw data as possible. The main part is a linear combination of the initial variables, illustrated in the following diagram[9].

Figure 2.

Principal component analysis (PCA) model

The mathematical model expression is shown in the following formula. (3){ y1=μ11x1+μ12x2+⋯+μ1ixi+⋯+μ1pxp y2=μ21x1+μ22x2+⋯+μ2ixi+⋯+μ2pxp ⋮ yi=μi1x1+μi2x2+⋯+μiixi+⋯+μipxp ⋮ yp=μp1x1+μp2x2+⋯+μpixi+⋯+μppxp$$\left\{\begin{array}{c} y_1=\mu_{11} x_1+\mu_{12} x_2+\cdots+\mu_{1 i} x_i+\cdots+\mu_{1 p} x_p \\ y_2=\mu_{21} x_1+\mu_{22} x_2+\cdots+\mu_{2 i} x_i+\cdots+\mu_{2 p} x_p \\ \vdots \\ y_i=\mu_{i 1} x_1+\mu_{i 2} x_2+\cdots+\mu_{i i} x_i+\cdots+\mu_{i p} x_p \\ \vdots \\ y_p=\mu_{p 1} x_1+\mu_{p 2} x_2+\cdots+\mu_{p i} x_i+\cdots+\mu_{p p} x_p \end{array}\right.$$

After the model is changed into a matrix form, the following formula is shown: (4)y=[ μ11 μ12 ⋯ μ1p μ21 μ22 ⋯ μ2p ⋮ ⋮ ⋮ ⋮ μp1 μp2 ⋯ μpp][ x1 x2 ⋮ xp]=Ux$$y=\left[\begin{array}{cccc} \mu_{11} & \mu_{12} & \cdots & \mu_{1 p} \\ \mu_{21} & \mu_{22} & \cdots & \mu_{2 p} \\ \vdots & \vdots & \vdots & \vdots \\ \mu_{p 1} & \mu_{p 2} & \cdots & \mu_{p p} \end{array}\right]\left[\begin{array}{c} x_1 \\ x_2 \\ \vdots \\ x_p \end{array}\right]=U x$$ (5)μi12+μi22+⋯+μip2=1$$\mu_{i 1}{ }^2+\mu_{i 2}^2+\cdots+\mu_{i p}^2=1 $$ (6)cov=1n∑i=1n(xi−x¯)(yi−y¯)$$cov=\frac{1}{n} \sum_{i=1}^n\left(x_i-\bar{x}\right)\left(y_i-\bar{y}\right) $$

See the following formula: (7)s2=1n∑i=1n(xi−x¯)2=1$$s^2 = \frac{1}{n} \sum_{i=1}^n (x_i - \bar x)^2= 1$$

At this time, the following formula can be obtained: (8)r=∑i=1n(xi−x¯)(yi−y¯)∑i=1n(xi−x¯)2∑i=1n(yi−y¯)2=∑i=1n(xi−x¯)(yi−y¯)nn=cov$$r=\frac{\sum_{i=1}^n\left(x_i-\bar{x}\right)\left(y_i-\bar{y}\right)}{\sqrt{\sum_{i=1}^n\left(x_i-\bar{x}\right)^2} \sqrt{\sum_{i=1}^n\left(y_i-\bar{y}\right)^2}}=\frac{\sum_{i=1}^n\left(x_i-\bar{x}\right)\left(y_i-\bar{y}\right)}{\sqrt{n} \sqrt{n}}={cov}$$

Part of a nerve net [10-12]. The model uses an error-back learning method based on multiple layers of nonlinear feed-forward networks. The network consists of three levels: the entry-level, concealed, and output. The BP study method consists of the error signal’s forward and backward transmission.

Connections among neurons create a connectivity model among nerve networks randomly allocated to each link by a computer. The forward transmission phase means that the raw data signal is transmitted via a hidden level from an input to an output level. In other words, the output of a preceding node serves as an input for the next one. The following diagram illustrates the fundamental architecture of BP Neural Network’s forward propagation[13-15].

Figure 3.

Basic structure of forward propagation stage BP neural network

Each neuron cell y_i has its own calculated weight w_ik, as illustrated in the drawing. (9)net1k=∑i=1nwikyi+bk=w1ky1+w2ky2+⋯wnkyn+bk$$net1_k=\sum_{i=1}^n w_{ik}y_i + b_k = w_{1k}y_1 + w_{2k}y_2 + \cdots w_{nk}y_n + b_k$$

It is possible to get a better forecast precision during the forecast by using the activation function. Activation functions have various types, such as Sigmoid, Hyperbola, and ReLU. The Sigmoidogram function is utilized to activate the output message. The activation function activates the input layer’s output value as f(net1k), and the following formula obtains the hidden layer z_k (10)zk=f(net1k)=11+exp(−net1k)$$z_k = f(net1_k) = \frac{1}{1+exp (-net 1_k)}$$

Then, it takes the hidden level data as the input level and transmits it to the output level. The output value net2j is the weighted sum of the hidden level and the link weight of the hidden layer and the output layer vkj, and the threshold bj. (11)net2j=∑k=1nvkjzk+bj=v1jz1+v2jz2+⋯vnyn+bj$$net2_j=\sum_{k=1}^n v_{kj} z_k + b_j = v_{1j} z_1 + v_{2j}z_2 + \cdots v_n y_n + b_j$$

The following formula activates the output value to obtain the final output layer data. (12)Oj=f(net2j)=11+exp(−net2j)$$O_j =f(net2_j) = \frac{1}{1+exp(-net2j)}$$

Based on the 2016 Physique Test Data, 80% of the Student Sample is taken as the Training Set, and the other 20% is the Model Assessment Kit. There are differences in the standards and grading methods between boys and girls. For this reason, male and female test data are divided into two groups, each constructed to predict the results. Based on 80 percent of the training data, continuous adjustment and optimization were carried out, and the results were presented in the table[16].

The threshold is taken as a condition to terminate the training, as illustrated in the chart above, and it is expressed as a default in the error function. If it is impossible to achieve a predefined value, then the maximal iteration count will force the training to halt when it is impossible to stop the iteration. The arithmetic of “prop +” is based on the weight of the error backpropagation method and the BP NN[17-18]. Then, an error function “sse” is applied to compute the value of the error at the termination of the forward transmission. The activation function uses the parameter “logistic” as the Sigmoid activation function. The Neural Count of the Hidden Level is calculated based on the Average Square Error (MSE) and the Equation below. (13)h=m+n+α$$h =\sqrt{m+n} + \alpha$$ (14)AE=oi−oj MSE=1n∑i=1n(oi−oj)2$$\begin{array}{c} {\rm AE} = o_i - o_j \\ {\rm MSE} = \frac{1}{n} \sum_{i=1}^n \left( o_i - o_j\right)^2 \end{array}$$

Based on the PCA, the ANN model is built for 80% of the data input model. To increase the precision of the model, a forecast model for boys and girls was built, and the experiment results were assessed[19-20]. Experimental data not involved in the model’s training were entered into the model. At last, the forecast effect of male and female was combined with that of male and female, and the forecast capability of the entire model was observed. Based on a random sample of 40 participants from the 2016 dataset, the following graph illustrates the discrepancy between the results obtained from those 40 participants and those of the model[21-23].

The following row diagram compares the predictions with the results obtained from a sample of 40 random pupils. The solid line indicates the real value, while the dotted line indicates the prediction. The results indicate that both lines are highly coincident with each other, and only a small number of samples exhibit remarkable errors. Experimental results indicate that the forecasting model of QMS has high accuracy and excellent performance. The MSE (MSE) is 1.361713.

Figure 4.

Comparison of predicted data with actual data samples

Figure 5.

Error value frequency distribution

The absolute error is in the range of [-1, 1], which takes up approximately two-thirds of the data set. The highest error rate is about 0. The error rate is so low that it is below 0. 01 when the absolute error is larger than 3. In this diagram, the dotted line is the density profile of the error distribution, which is close to that of the normal distribution. Visual results indicate that the forecast capability of this model is quite good, which will help forecast the synthetic performance of the PE test.

The absolute error absolute value of the 20% test set in 2016 and the data prediction result in 2019 is binned into six intervals, which are [0,1), [1,2), [2,3), [3,4), [4,5), [5, ∞), their distribution is shown in the following table.

As can be seen from the chart above, the 2016 prediction was excellent, with an absolute error below 2 for 92.95 percent of the figures and a mere 0.06 percent higher than 4. This shows that this model has a good prediction ability. When the models created by the 2016 scoring criteria were applied to 2019, the predictive accuracy of the models declined. The percent absolute error rate decreased by 23.54 percent on a 0-to-1 scale, but the total predicted outcome remains significant. The standard for 2016 should be suitable for 2019 if the standard is strict, and the forecast precision of the model will be similar to that of 2016. A significant reduction in the forecast impact suggests that manual calculations have resulted in differences in the 2016 and 2019 scoring criteria.

Based on 2016 data, this model is based on 2016, and the weight of each model is based on 2016. When the 2016 rating scale was used to predict the 2019 total score, the results showed a difference in the rating scale. Because the teacher’s hand is involved in the computation, the standard of the full marks is not unified. Because of the differences in the past classification criteria, the full score cannot be used to describe the variation in the fundamental body quality of the students. It’s hard to tell if a student’s body quality has increased or declined with time. Not making the best use of data for many years. Based on this model, we can find a stable relationship between project data and overall score and ensure the model can be studied. That’s a great method to eliminate all of the complex conventional fitness tests, and it can also save you the time needed to calculate the overall points. Based on the uniform classification criterion, we can get a clearer view of the variation in students’ body quality by using the Radar Chart. Thus, the model’s prediction of fitness test results is essential.