Machine Learning Model Construction and Practice for Personalized Training Programs in Physical Education and Sport Teaching

The correlation problem assumes that there is an indeterminate interdependence between the variables, i.e., for every change in the value of the independent variable, the dependent variable will also change to a greater or lesser extent. However, due to the non-deterministic relationship between the independent variable and the dependent variable, it is unknown exactly how the dependent variable will change when the independent variable changes.

The Pearson linear correlation coefficient is a parameter that measures the degree and type of linear correlation between two random variables. The magnitude of the parameter characterizes the degree of linear correlation between the variables and takes a value between -1 and 1. The closer the value of the coefficient is to ±1, the greater the correlation between the two variables, close to +1 means that there is a strong positive linear correlation between the variables, close to -1 means that there is a strong negative linear correlation between the variables, and the smaller the coefficient is, the closer it is to 0 means that there is less correlation between the variables. Pearson correlation coefficient and the degree of correlation correspond to each other. For random variables X and Y, the Pearson correlation coefficient between them is calculated as follows: (1) ρ=cov(X,Y)var(x)var(Y)

The Spearman rank correlation coefficient provides a distribution-free measure of correlation between variables that does not require any transformation of the original data and does not force a linear relationship between the variables, but only a monotonic increase (or decrease) between the variables, i.e., a simultaneous increase (or simultaneous decrease). The Spearman rank correlation coefficient is less restrictive and more general than a linear relationship. Monotonic relationships are less restrictive and more common than linear relationships. The ordering of Spearman’s rank correlation coefficient is not determined by the actual data values, but depends mainly on the rank of the data sorted values, and the correlation of the data ranks can be calculated as long as the data are sorted according to certain rules. For two-dimensional random variables (X,Y) with the same distribution and (X1,Y1), (X2,Y2) and (X3,Y3) are independent of each other, the Spearman rank correlation coefficient is calculated as follows: (2) ρ=3{P[(X1−X2)(Y1−Y3)>0]−P[(X1−X2)(Y1−Y3)<0]}

Neural networks are the dominant solution for modern machine learning, achieving significantly better results than traditional machine learning solutions in many fields, and due to their powerful and almost foolproof fitting ability, they have seen a proliferation of research in academia and groundbreaking applications in industry. A neural network consists mainly of different layers, each of which has many nodes, each of which is associated with other nodes, and the input of one node becomes the output of another. The computation of a specific node can be depicted as: (3) y=f(∑i=1Nωixi) Where x_i denotes the output of the previous ind node and y denotes the output of the current node, which is equal to the weighted sum of each of the previous neurons, and the weight of each node is ω_i. Then, after the activation function f is that the system becomes a nonlinear system with the ability to fit the expression of nonlinear data.

There are various forms of activation functions, and it is generally sufficient to require a nonlinear function that is easy to compute. The weights ω_i of them are the parameters of the network. A complete network connects inputs and outputs, and the network is like a complex function without a specific form. The process of obtaining outputs from inputs can be expressed as: (4) y=ℕ(x) Where N indicates that after the calculation of the network, determine the parameters of the network has the ability to fit the data, the fitting effect to a certain extent, you can achieve a very high prediction accuracy on the test data, and in turn, you can also use the labeled data to test the classification and regression ability of this network.

The process of determining network parameters is called training. That is, the network parameters are adjusted by known input and output data. The general process is: 1)

Initialize the network parameters, which can be random values.

The principle of the BP algorithm is chain derivation, which gives the expression of the output as: (6) z=f2(∑ w2f1(∑ ω1x))

Then the gradient of z for node x can be calculated as shown in equation (7).

The actual neural networks used in production often have many more complex structures, but the basic algorithmic principle is still to learn the data through the BP algorithm and gradually adjust the network parameters. The role of the Loss function is to provide the error calculation guidelines of the neural network, which directly determines the direction of the neural network calculation, in addition to the squared error mentioned in Equation (5), the commonly used loss function also has a 0-1 loss, the loss of the absolute value and so on.

In this paper, we deal with one-dimensional vectors of specified length, and we do not need a complex neural network to fit the data, therefore, simple neural network structures such as Fully Connected Networks (FCNs) and Convolutional Neural Networks (CNNs) are used.

FCN is the simplest neural network, also known as multilayer perceptron, as the name suggests, it has many layers, and each layer has many nodes, and the nodes of the neighboring layers are connected two by two, while the number of nodes and the number of layers of the network can be continuously increased, the larger the whole network, the better the fitting and regression effect on the data, and the richer the information mined from the data.

However, the number of network layers and the number of nodes can not be increased indefinitely, on the one hand, it will bring an exponential increase in the amount of computation, the training time is prolonged, on the other hand, the network’s descriptive ability will not be increased indefinitely, on the contrary, it may “remember” all the samples, the formation of overfitting, so we can not unlimitedly increase the size of the network to improve the performance of the network, and should expand the design of new network structures. Therefore, the network size should not be increased indefinitely to improve network performance, but rather expanded to design a new network structure.

Convolutional neural networks introduce convolutional computation into the network, and the one-dimensional convolutional discretization is defined as follows: (8) yt=∑k−1Kwkxt−k+1⇔y=w*x Where * denotes the convolution operator. Where ω is called the convolution kernel and x is the input sequence, the output sequence is obtained by sliding the convolution kernel through the input sequence, this structure can better extract the features of the data. In the backpropagation process after this operation, assuming that f is a scalar activation function, the relationship between the output and the input is expressed as: (9) y=f(ω*x)

By the nature of the convolution, the derivative can be calculated: (10) ∂f(y)∂ω=∂f(y)∂y*x

There are also mechanisms in convolutional neural networks to reduce model parameters, including local connectivity, weight sharing, and a typical convolutional neural network will also work with a fully-connected network after multiple convolutions, and after this is obtained, the final result is output by the activation function.

Principal component analysis method is a comprehensive statistical analysis method, which can achieve the purpose of making the original data dimensionality reduction, simplify and condense the data, make the problem become simpler, delete the repetitive information of the original data variables, and extract the concise data information. The basic idea of principal component analysis method is to transform the dimensions, through orthogonal changes, convert the correlated variables into new uncorrelated variables, convert the covariance matrix of the original data variables into diagonal matrix, convert the original data variables into new orthogonal system, and reduce the dimensionality through multidimensional variables.

Take the two-dimensional space as an example. Let the number of samples be 50, each sample contains two variables x₁ and x₂, and the two-dimensional plane is defined by x₁ and x₂.

The distribution direction of the sample data is not the x₁-axis and x₂-axis, but its distribution trend has a certain regularity, so consider that there may be some connection between the two, and other variables can be used to replace x₁ and x₂. However, if any of these dimensions is used to replace them, it will surely result in the loss of the original data information. Therefore, the coordinate system is rotated counterclockwise by a certain angle Θ so that the direction of maximum dispersion of the sample points is the z₁ axis and its orthogonal direction is the z₂ axis.

The z₁ and z₂ rotation equations are: (11) { z1=x1cosΘ+x2sinΘz2=−x1sinΘ+x2cosΘ

Its matrix form is: (12) (z1z2)=(cosΘsinΘ−sinΘcosΘ)(x1x2)=PTX where P^T is an orthogonal matrix.

The coordinate system has the following properties after rotation: 1)

Variables z₁ and z₂ are orthogonal to each other, and the sample points are uncorrelated in both directions, which prevents information overlap due to multicollinearity between the original data variables.

The calculation steps of the principal component analysis method are as follows: 1)

Standardize the original data and unify the data scale and order of magnitude.

K-means clustering algorithm is one of the most commonly used clustering algorithms in cluster analysis and one of the widely used clustering algorithms. K-means clustering algorithm has high efficiency and simplicity and hence it is a highly researchable divisive clustering algorithm. The algorithm takes the number of K cluster classes as a parameter and divides n data objects into K cluster classes, resulting in low similarity between different clusters and high similarity within the same cluster.

The basic steps of K-means clustering algorithm are as follows: 1)

In the data set X, randomly select k data objects as the initial clustering centers.

With the progress of technology, how to utilize the vivid subjective evaluation data to provide support for the evaluation of teachers’ teaching effectiveness is a problem we need to solve. Natural language processing is an important direction in the field of computer science and artificial intelligence, and subjective evaluation data can be fully analyzed and mined by using NLP natural language processing technology for teaching management. Natural Language Toolkit (NLTK) is a class library based on Python language, and it is also the most popular natural language programming and development tool. When conducting natural language processing research and applications, proper utilization of the functions in NLTK can dramatically improve efficiency and achieve work goals.

Natural language sentiment analysis can currently be performed using either lexical analysis or machine learning. Dictionary matching is used to directly calculate sentiment words in the text and derive their sentiment tendency scores. While the idea of machine learning method is to first select a part of the text that expresses positive sentiment and a part of the text that expresses negative sentiment, and train them with machine learning method to obtain a sentiment classifier. Then all texts are dichotomously categorized positively and negatively by this sentiment classifier, and the final categorization can either give a category like 0 or 1 for the text, or a probability value.