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Analysis and Research on Provincial Postgraduate Cultivation 
Performance Based on BP Neural Network 

Shuai Wu a, Peiyu Li, Xi Chen, and Hui Wang 

School of Information Engineering, Henan University of Science and Technology, Henan, China. 

aheixue@live.com 

Abstract. According to relevant data, the comprehensive competitiveness and quality of graduate 
education in Henan Province are in the middle of the 31 provinces in China, and its graduate 
education has a great room for improvement. Through the research on the current situation of 
educational performance evaluation at home and abroad, and the analysis of the limitations in the 
evaluation process of postgraduate training in Henan province, we proposed a performance 
evaluation method based on BP neural network. This method uses the theory and technology of 
information theory, analytic hierarchy process, and BP neural network to establish an educational 
performance evaluation model. Through this model, the shortcomings of the existing performance 
evaluation methods of graduate student training are overcome, and performance evaluation 
methods that are closer to the actual situation are excavated, which provides a scientific decision-
making reference for the performance evaluation of graduate education in Henan Province. This 
experiment uses the university education data of Henan Province as the experimental data test set. 
The experimental results show that this model has good generalization ability and can provide 
reference for the reform and construction of postgraduate education in Henan province. 

Keywords: Performance analysis, BP neural network, neighborhood mutual information, analytic 
hierarchy process, information entropy theory. 

1. Introduction  

At present, the main methods for the performance of graduate students at home and abroad are 

linear weight method, analytic hierarchy process, mathematical statistics method, fuzzy 

comprehensive evaluation method and other multi-index comprehensive evaluation methods. Most 

of these methods start from the perspective of overall scale, rather than evaluate performance from 

the perspective of input-output efficiency. This is not conducive to guiding the improvement of the 

utilization rate of educational resources, and it is also difficult to provide a decision-making basis for 

the optimal allocation of educational resources. 

Data Envelopment Analysis (DEA) is a commonly used method to study the performance of 

multiple inputs and outputs [1-3].This method attempts to comprehensively compare the input-output 

efficiency among universities, but only considers the overall efficiency, technical efficiency and scale 

efficiency of each decision-making unit.Without analyzing the specific reasons for the decision 

making unit falling into the invalid state from a single index, it cannot provide an effective basis for 

performance improvement. 

In recent years, with the rapid development of education informatization, the number of 

postgraduate education data in our province has increased dramatically. These massive data have 

made it possible for us to adopt some new mining methods. 

In view of the defects of traditional methods, as well as some current situations, and taking full 

account of various human and subjective factors, this paper introduces information theory into the 

mining process of performance analysis. Through the method of mutual information, BP neural 

network and hierarchical analysis, good mining results are obtained. 

This research involves pedagogy, statistics, informatics, computer science and other multi-

disciplinary research fields. It is a method of mining and predicting unknown performance evaluation 

results based on existing education data. It has a good reference role for graduate education evaluation 

in Henan Province. 



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2. Basic concepts and related principles  

2.1 Analytic Hierarchy Process (AHP) 

AHP was proposed by an American operations researcher and is currently relatively mature and 

effective in solving complex problems with multiple goals [4]. This is a typical systematic 

engineering method from qualitative analysis to quantitative analysis. In the process of graduate 

performance evaluation, this method can mathematicise people's complex thinking processes, 

quantify subjective judgments, and digitize various differences, which can effectively reduce the 

impact of human factors. 

This article mainly uses the analytic hierarchy process to determine the weight of each output 

indicator used to determine performance. The main operation is divided into the following four steps: 

Determine the index system 

Through the comparison between the two indicators by experts, the comparison results are 

quantified with numbers from 1 to 9, and the average value is taken to form a judgment matrix 
 

Table 1. Consistency index 
 

Comparison results (compared between the two, the former is better than the latter) Scaling 

Equally important 1 

Slightly stronger 3 

Obviously important 5 

Strongly important 7 

Extremely important 9 

2, 4, 6, 8 Between the front and back 

Check the consistency of the matrix. When the CR consistency ratio is less than 0.1, the degree of 

inconsistency is considered to be within the allowable range 

Calculate the matrix to obtain the eigenvalues and eigenvectors satisfying the formula 

𝐴𝑊 = 𝜆𝑚𝑎𝑥, and the components of W are the weights of the corresponding elements. 

After the weight is obtained, the value used to measure performance can be obtained according to 

the weight and the index value. 

2.2 Neighborhood Mutual Information (NMI) 

Mutual information is a useful information measure in information theory, which can be used to 

measure the correlation between two sets of events. In information theory, the higher the entropy, the 

more information that can be transmitted, and the lower the entropy, the less information that can be 

transmitted[5]. 
 

H(X)
H(Y)

H(X,Y)

H(X|Y) H(Y|X)I(X;Y)

 

Fig. 1 Mutual information 



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At the same time, mutual information can be used to measure the degree of interdependence 

between two variables. In this project, the entropy principle in information theory is used to mine the 

correlation between input indicators to maximize the retention of input information 

The mutual information calculation formula is as follows: 

𝐼(𝑋; 𝑌) = ∑∑𝑝(𝑥, 𝑦) 𝑙𝑜𝑔(
𝑝(𝑥, 𝑦)

𝑞(𝑥)𝑞(𝑦)
)

𝑦∈𝑌𝑥∈𝑋

 

Mutual information is a useful information measure in information theory, which can be used to 

measure the correlation between two sets of events. In information theory, the higher the entropy, the 

more information that can be transmitted, and the lower the entropy, the less information that can be 

transmitted. 

At the same time, mutual information can be used to measure the degree of interdependence 

between two variables. In this project, the entropy principle in information theory is used to mine the 

correlation between input indicators to maximize the retention of input information 

The mutual information calculation formula is as follows: When the variables X and Y are 

completely unrelated or independent of each other, the mutual information is the smallest, which 

means that the information entropy is the largest at this time, the overlapping information is the 

smallest, and the degree of dependence is the smallest. 

Mutual information is generally used for discrete variables and cannot measure the nonlinear 

relationship between two variables. The education-related data used in the performance evaluation 

process is continuous data, so this paper chooses neighborhood mutual information to solve this 

problem. 

In rough set theory, the neighborhood rough set model granulates the domain of the mixed 

information system by establishing neighborhood relations, so as to achieve an approximate 

approximation to the target knowledge [6-7]. 

The theorem of neighborhood mutual information is as follows: 
Definition 1 

Suppose that the set M is not empty. If  ∀𝑥𝑎, 𝑥𝑏, 𝑥𝑘 ∈ 𝑈 , there exists a uniquely certain real 

function P corresponding to it, and satisfies: 

𝑃(𝑥𝑎, 𝑥𝑏) ≥ 0 If and only if the condition  𝑥𝑖 = 𝑥𝑗  is met, there is 𝑃(𝑥𝑎, 𝑥𝑏) = 0 

𝑃(𝑥𝑎, 𝑥𝑏) = 𝑃(𝑥𝑏 , 𝑥𝑎) 
𝑃(𝑥𝑎, 𝑥𝑘) < 𝑃(𝑥𝑎, 𝑥𝑏) + 𝑃(𝑥𝑏 , 𝑥𝑘) 

Then, P is the distance function on U. < 𝑀, 𝑃 > is the metric space. In general, the commonly 

used distance functions are Manhattan distance and Euclidean distance. 

 
Definition 2 

Let < 𝑀,𝑃 > be non-empty, then 𝑥 ∈ 𝑀, 𝜕 ≥ 0  is called a point set. 

𝛿(𝑥) = {𝑦|𝑃(𝑥, 𝑦) ≤ 𝛿, 𝑦 ∈ 𝑈}  

is the neighborhood of x in the metric space < 𝑀, 𝑃 > 
 

Definition 3 

Given domain P, C refers to the conditional attribute describing P, and D is the decision-making 

attribute. According to C, a set of neighborhood relations R on the universe of discourse can be 

generated, and then 𝑁𝐷𝑇 ≤< 𝑃, 𝑅, 𝐷 > is called the neighborhood approximation space. 
 

Definition 4 

Given the universe of space {𝑥1, 𝑥2, . . . . . . , 𝑥𝑛}, conditional attributes C, 𝐴 ⊆ 𝐶,𝑁𝐴 are expressed 

as the neighborhood relations induced by feature subset A. Let 𝑥𝑖 calculate the neighborhood based 

on A as 𝛿𝐴(𝑥𝑖), then the uncertainty of the neighborhood particle is:  

𝑁𝐻𝛿
𝑥𝑖(𝐴) = −𝑙𝑏

|𝛿𝐴(𝑥𝑖)|

𝑛
 



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The formula is based on 2. Correspondingly, the uncertainty of the neighborhood approximation 

space < 𝑀,𝑁𝐴 > is: 

𝑁𝐻𝛿(𝐴) = −
1

𝑛
𝑙𝑏
|𝛿𝐴(𝑥𝑖)|

𝑛
 

Because of ∀𝑥𝑖 ，𝛿𝐴 ∈ 𝑈 and 
|𝛿𝐴(𝑥𝑖)|

𝑛
≤ 1, 𝑙𝑏𝑛 ≥ 𝑁𝐻𝛿(𝐴) ≥ 0 is obtained. If and only if ∀𝑥𝑖 

and  𝛿𝐴(𝑥𝑖) = 1, there is 𝑁𝐻𝛿 = 𝑙𝑏𝑛. If and only if ∀𝑥𝑖 and 𝛿𝐴(𝑥𝑖) = 𝑛, there is  𝑁𝐻𝛿 = 0. 
 

Definition 5 

If and only if 𝐴, 𝐵 ∈ 𝐶  are two sets of feature subsets describing the universe, and the 

neighborhood of 𝑥𝑖 on 𝐴 ∪ 𝐵 is denoted as 𝛿𝐴∪𝐵(𝑥𝑖), then the joint entropy of A and B can be 

defined as: 

𝑁𝐻𝛿(𝐴, 𝐵) = −
1

𝑛
∑𝑙𝑏

|𝛿𝐴∪𝐵(𝑥𝑖)|

𝑛

𝑛

𝑖=1

 

When C is a decision attribute, 𝛿𝐴∪𝐵(𝑥𝑖) = 𝛿𝐴(𝑥𝑖) ∩ 𝑐𝑥𝑖 can be obtained, at this time: 

𝑁𝐻𝛿(𝐴, 𝐶) = −
1

𝑛
∑𝑙𝑏

|𝛿𝐴(𝑥𝑖) ∩ 𝑐𝑥𝑖|

𝑛

𝑛

𝑖=1

 

 

Definition 6 

𝐴, 𝐵 ⊆ 𝐶 is the two sets of feature subsets describing the universe. Given feature subset A, the 

neighborhood conditional entropy of B relative to A is: 

𝑁𝐻𝛿(𝐵|𝐴) = −
1

𝑛
∑𝑙𝑏

|𝛿𝐴∪𝐵(𝑥𝑖)|

|𝛿𝐴(𝑥𝑖)|

𝑛

𝑖=1

 

 

Definition 7 

𝐴, 𝐵 ⊆ 𝐶 is the two sets of feature subsets describing the universe. The neighborhood mutual 

information of A and B can be defined as: 

𝑁𝑀𝐼𝛿(𝐴; 𝐵) = −
1

𝑛
∑𝑙𝑏

|𝛿𝐴(𝑥𝑖)|. |𝛿𝐵(𝑥𝑖)|

𝑛|𝛿𝐴∪𝐵(𝑥𝑖)|

𝑛

𝑖=1

 

2.3 BP neural network 

Neural network is a technology that abstracts and simulates the general characteristics of the 

human brain or nature. In recent years, the application of neural network in the field of prediction and 

empirical research has achieved remarkable results. BP neural network has a fairly strong ability to 

process information, and has self-learning and self-adaptive capabilities in the process of processing 

data, which can better explain the non-linear characteristics contained in the data.[8] 

1

1

2

D

b

 f

1x

2x

Dx
weight

The activation 
function

a  

Fig. 2 Neurons 



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Neurons are the basic units that form neural networks. In a biological neural network, each neuron 

is connected to other neurons. When it is "excited", it will send chemicals to the connected neuron to 

transmit information to the next neuron. In an artificial neural network, a neuron receives input signals 

from n other neurons. These input signals are transmitted through a weighted connection. The total 

input value received by the neuron will be compared with the neuron threshold, and then Through the 

"activation function" processing to generate neuron output. 

Backpropagation neural network is a three-layer feedforward network, including input layer, 

hidden layer, and output layer. For the input signal, it must first propagate forward to the hidden node, 

and then pass the output information of the hidden node to the output node after the function action, 

and finally get the output variable result.[9] 

1x

2x

nx

...

1S

nS

...

The input layer Hidden layer Output layer
 

Fig. 3 Neural Network 

The learning process of the algorithm consists of forward propagation and back propagation. The 

input information is processed by the hidden layer unit and passed to the output layer. If the desired 

output cannot be obtained in the output layer, it enters back propagation and modifies the weight of 

the neuron. Make the error signal reduce. The system continuously loops these two processes, 

repeating the learning, until the error between the output value and the expected value is reduced to 

the specified range, the system stops learning. 

In this experiment, pytouch is used to realize the related calculation of BP neural network. pytouch 

is Facebook's open source machine learning library. It is a python-based sustainable calculation 

package with powerful GPU accelerated tensor calculation, which can effectively improve the 

calculation speed. 

3. Selection of evaluation indicators 

In the performance analysis process, the input and output indicators are mainly based on the data 

available in the current process of college graduate training. In the initial selection, it is necessary to 

include as much as possible the statistical index data. 

3.1 Confirmation of input indicators 

Combining the data characteristics of colleges and universities in our province and the status quo 

of postgraduate training, the selected investment is mainly divided into three aspects, capital 

investment, manpower investment and equipment investment. They are: number of teachers, teaching 

volume, doctoral degree teachers, full-time teachers, project funding, unit talent training personnel 

funding, unit scientific research personnel funding, teaching staff funding, unit talent training room 

area, unit room area, unit science Research room area, teacher team room area, unit personnel training 

equipment investment, unit scientific research equipment investment, faculty equipment investment, 

unit scientific research total, unit equipment funding, key laboratory, natural science fund, etc. 19 

inputs Indicators are used as raw input data. 



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After the dimensionless normalization of the indicator data, in order to avoid excessive substitution 

between the selected indicators, the information theory is used to analyze the relevance of the input 

indicators. 

According to the principle of information theory, mutual information can measure the mutual 

relationship between two variables, and can measure the amount of information between message 

sets. This method can reduce the dimensionality while preserving the overall characteristics as much 

as possible. 

Calculate the information entropy of 19 input indicators, then delete individual indicators in turn, 

calculate and compare the information entropy of the remaining indicators. Compare and observe the 

calculation results, delete the index items that have the least impact on the entropy value after deletion, 

and then cycle. 

The information entropy value change after each deletion is shown in Figure 4. 

 

Fig. 4 Entropy Value 

It can be seen from the figure that when the tenth indicator is deleted, the entropy value has 

changed significantly, and when the first 10 indicators are deleted, the amount of information has 

little effect. 

Therefore, the input indicators selected in this article are: Natural Science Foundation, Key 

Laboratory, Unit Scientific Research, Unit Personnel Training Area, Unit Personnel Training 

Personnel Expenses, Teaching Staff Housing Area, Teaching Staff Expenses, Unit Subject Research 

Staff funding, number of PhD teachers. 

3.2  Determination of output indicators 

The output data indicators mainly include the following 7: intellectual property rights and works, 

employment rate, graduation rate, number of students, journal papers, competition awards, and 

outstanding alumni. 

Here, we use the analytic hierarchy process. The analytic hierarchy process quantifies people's 

subjective evaluation of performance, this complex system of thinking process, and helps people 

maintain the consistency of their thinking models, thereby reducing the influence of factors that are 

considered. 

Find 10 experienced university professors to set the output index weights, and assign values 

according to the comparison of the two indexes according to the 1-9 scale method, and then discuss 

the results. The final result is shown in the Figure6.  

Check the consistency of the matrix. When the CR consistency ratio is less than 0.1, the degree of 

inconsistency is considered to be within the allowable range. After testing, the judgment matrix can 

pass the consistency test.  



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Table 2. Index Value 

After each group of data is normalized, multiplied by the weight, the final measurement value for 

performance evaluation can be obtained. 

According to the metric value obtained in the final calculation, the result value is evaluated 

according to the following grades, among which the good and the difference are represented by the 

numbers 3, 2, 1, and 0, and are used as the output result of the system. 

Table 3. Performance evaluation grade 

Performance evaluation grade Scaling 

excellent 0.75-1 

good 0.5-0.75 

medium 0.25-0.5 

difference 0-0.25 

After each group of data is normalized, multiplied by the weight, the final measurement value for 

performance evaluation can be obtained. 

4. Construction of bp neural network performance index evaluation model  

4.1 Abbreviations and Acronyms 

The experimental data were obtained from universities in Henan Province and the network , and 

the experimental data were divided into training set and test set.  

The experimental environment is Windows10 + Anaconda + Mysql + Pytoch + VisualStudio. 

Anaconda provides a Python environment for experiments , while PyTouch provides library functions 

for training BP netural networks. 

4.2 Input layer  

Using the neighborhood mutual information interest rate , the selected input indexes were reduced 

from 19 to 9 after correlation analysis .  

Table 4. Index Input 
number Input indicators 

1 Natural science fund 

2 Key laboratories 

3 Total amount of scientific research 

4 Room area for talent training 

5 Funds for personnel training 

6 Room area for teachers 

7 Faculty staff funds 

8 Funding for discipline researchers 

9 Number of teachers with doctoral degrees 

 Books Job_rate Graduate_rage Num Article Award Outstanding_graduate 

Books 1 1/2 8 3 6 3 1/2 

Job_rate 2 1 7 8 5 4 1 

Graduate_rage 1/8 1/7 1 3 1/3 1/5 1/8 

Num 1/3 1/8 1/3 1 1/5 1/7 1/8 

Article 1/6 1/5 3 5 1 1/2 1/6 

Award 1/3 1/4 5 7 2 1 1/5 

Outstanding_graduate 2 1 8 8 6 5 1 



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4.3 Hidden layer 

In the training process of BP neural network, the number of hidden nodes can affect the 

performance of the training model. At present, there is no definite calculation formula for the number 

of hidden layer nodes. According to the traditional empirical formula  

ℎ = √𝑚 + 𝑛 + 𝑎(0 < 𝑎 < 10) 
The approximate reasonable range can be calculated. 

Where, H is the number of nodes in the hidden layer, M is the number of nodes in the input layer, 

and N is the number of nodes in the output layer. A is the regulation constant between 1 and 10. 

In this paper, m=9, n=4, the number range of nodes in the hidden layer can be determined as [3, 

13]. 

Through experimental comparison and comprehensive consideration of factors such as time cost, 

iteration number and error size of machine learning, the number of hidden layer nodes is set as 8. 

4.4 Output layer 

According to the performance evaluation system of domestic graduate students, it is divided into 

four levels: excellent, good, medium and poor, so the number of output neurons is set as 4 

The activation function of the hidden layer adopts the ReLU function, and the step size of the 

training process is 0.02  

4.5 Training model 

The selected input index data and output index data are de-dimensionalized as the training data of 

BP neural network model. 

 
Fig. 5 Cross entropy 

Cross entropy can be used to determine the degree of proximity between the actual output and the 

expected output. The smaller the value of cross entropy is, the closer the two probability distributions 

are. 

As shown in the figure above, after 3000 times of training, the cross entropy change is no longer 

obvious. 

The trained model is saved for further verification. 

4.6 Validation 

The trained model is verified by the validation set, and the results show that the prediction accuracy 

is over 90%, which is in line with the expectation. 



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5. Conclusion 

This paper conducts a comprehensive study on the performance evaluation of colleges and 

universities in Henan Province, aiming to analyze the current situation and influencing factors of the 

performance of postgraduate training in colleges and universities in Henan Province, and carries out 

simulation on relevant data through machine learning model BP neural network to verify the 

generalization ability. 

The weight of performance related indicators was determined by the chromatography analysis 

method, and the input indicators were screened by the information entropy theory, so as to effectively 

avoid the influence of human subjective factors and reasonably simplify the input indicators in a more 

scientific way. 

BP neural network has the ability of self-learning and self-adaptation, which reduces the influence 

of human factors. Increases the credibility of the results. 

Due to limited data sources and incomplete data of some colleges and universities, the selection 

of qualitative indicators has certain limitations. In the follow-up research, with the improvement of 

databases of colleges and universities, this evaluation model can also achieve better results. 

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