Based on the BP algorithm to determine the question bank test question score research: how to become an algorithm engineer

Abstract: This paper applies the BP (Back Propagation) neural network to the determination of the score of the question bank test questions, in order to solve the current irrationality of the determination of the score of the question bank test questions in the intelligent grouping research. When training the network, the standard BP algorithm is improved accordingly to adapt to the establishment of this intelligent model. Through the case test, it is verified that the accuracy of the intelligent model for determining the score value of the test questions is in line with the practical requirements, and to a certain extent, it lays the foundation for the intelligent grouping of papers.

Keywords: BP algorithm, question bank, test question score

Introduction

The question bank is an important means to ensure that the examination questions are of high quality and better meet the goals of educational measurement. With the promotion and application of computer and network technology, especially artificial intelligence technology in modern education, the educational field has paid great attention to e-assessment, paying more attention to the construction of question banks and the research and development of intelligent grouping.

A variety of question bank systems have appeared on the market. In fact, the question bank construction still lacks scientific theoretical guidance, especially in the determination of the parameters of the test questions, the subjective factors have a great influence, so that the question bank system can not be very good to achieve the desired goals. For example, there has not been a good solution for determining the score of test questions. The traditional practice is to use the difficulty assignment method and time assignment method [1], without considering the influence of other factors, such as the number of knowledge points and the importance of knowledge points. Considering the highly nonlinear relationship between the test score and the parameters affecting the test score, this paper utilizes the functions of simulating human thinking, nonlinear transformation and self-learning that BP neural network has to construct an intelligent determination model of test score in order to overcome the influence of various randomness and subjectivity on the score in the traditional practice.

1 Basic principles and methods

The use of known samples to train the BP network, so that it obtains expert experience and knowledge of determining the score of the test questions, and when new samples are processed, the network simulates human thinking and reproduces the expert knowledge and experience, and achieves the purpose of objectively determining the score of the test questions, and the specific steps are:

1) Extracting the parameters of the determination of the test scores. Quantitative processing for (0, 1) as the exact value of the network input.

② Use the existing expert knowledge base (sample library), through the BP algorithm to train the network, through the adjustment of network parameters and algorithm parameters to obtain a stable network parameters - score determination model. In order to be able to ensure acceptable computational accuracy in practical applications, we train the network so that it converges at a higher accuracy.

3) Input the parameters of the relevant test questions that need to determine the score, the network processes the input values based on the expert knowledge experience gained from self-study, and then outputs the value of (0, 1) as the final result (the score of the test question).

2 Structure of BP neural network for score determination

This paper analyzes and summarizes seven parameters (input vectors of the BP network) that affect the score of the test questions of the question bank, and as the first study of the problem in this field, in order to obtain enough representative training samples, this paper restricts the parameter "type of questions" to the following values. 1, 2, 3 and 4, which represent single-choice questions, multiple-choice questions, judgment and correction questions and fill-in-the-blank questions, respectively. According to the examination theory, the proposition design theory, belonging to these types of questions for each test question to examine the knowledge points generally no more than three, and the most suitable for the examination of literacy, comprehension and application of the three cognitive levels. Therefore, this paper also restricts the parameter "number of knowledge points" to take the integer between [1, 3], and restricts the parameter "cognitive level" to take the values of 1, 2 and 3, which represent knowledge, understanding and application respectively. The values of the seven parameters are shown in Table 1.

In the application of neural networks, the choice of network structure is very important, and a good network structure can reduce the number of network training times and improve the network learning accuracy. ［The more [2] hidden layers, the slower the neural network learning speed, according to Kosmogorov's theorem, under the condition of reasonable structure and proper weights, the 3-layer BP neural network can approximate the arbitrary continuous function, therefore, we selected the 3-layer BP network structure, as shown in Figure 1.

Figure 1

In which, the number of nodes in the input layer n is determined by the number of parameters affecting the score of the test question, here n=7, and the number of output nodes is m=1 because the output result is a score of a test question; on the basis of summarizing a large number of network structures, we have derived the empirical formula for the number of neurons in the hidden layer as

Thereby this paper preliminarily determines the number of neurons in the hidden layer as s=5. In the experimental simulation, we will dynamically adjust the number of neurons in the hidden layer to obtain the network

3 Adjusting the BP algorithm

3.1 Dynamically adjusting the number of units in the hidden layer and the learning step size

As mentioned above, the number of neurons in the hidden layer is initially determined to be 5, and then, through the human-computer interaction, the number of neurons in the hidden layer will be increased or decreased, and analyzed and compared with the global error of the The number of hidden layer neurons is determined by analyzing and comparing the degree of oscillation, the degree of error decreasing, the degree of network accuracy after error stabilization and the convergence performance of the network. In this paper, the training of the network is neither fixed step size nor adaptive adjustment of the step size, but the method of human-computer interaction dynamic adjustment, the author believes that this is troublesome, but the adjustment of the step size is more intelligent.

3.2 The method of selecting pattern pairs and the calculation of global error

In this paper, all the samples are stored in the database, and 2/3 of the samples are used as the training samples, and when selecting the pattern pairs, it starts from the first record of the training samples all the way to the last one, and so on. After repeated experiments, it is verified that this method is more effective than the method of random selection, which is manifested in the network error decreasing obviously, basically there is no oscillation. Through analysis, the author believes that in the random selection method, due to randomness, can not guarantee that all the representative samples are selected, so that the sample no longer represents the whole, losing the significance of the sample, resulting in a slow decrease in error, the shock is obvious, the training shall not converge. The following formula is used to calculate the global error:

Where, fp is the actual output of the output layer, y is the desired output, M is the total number of training samples, E is the global error, N is a positive integer, the choice of the value should be reasonable, otherwise it will cause the network to enter the local minima, or the error decreases slowly, the oscillation is obvious, and it is difficult to converge the training.

4 Examples and analysis of determining the test score of the question bank

4.1 Sample selection

The sample should represent the whole well, which requires that there must be enough training samples, otherwise the samples can only represent a part of the whole, so that even if the network is trained to a high degree of accuracy, when the actual application of the network will find that the network error sometimes becomes so large that it can not be used at all. According to this principle and determine the number of parameters and the value of each parameter, we need at least 22,500 training samples. Considering the difficulty of obtaining samples and the actual accuracy required for score determination, this paper extracts highly representative 800 training samples and 400 test samples from the intelligent question bank of the Computer Culture Fundamentals course that we are developing, because the difficulty, differentiation, and other parameters of the questions in the question bank have been tested and obtained, so they are more credible, and the answering time and the scores have been estimated artificially based on experience. The answer time and scores are estimated empirically. In order to improve the network precision, we organized a special group (three professors of related majors and seven master's degree students of information technology pedagogy) to estimate the estimated answering time and scores of the 1200 samples more rigorously, and the estimation value was accurate to 0.1. The estimation method is that ten members of the group estimated the answering time and scores of each sample separately, and then removed one highest score and one lowest score, and put the remaining eight estimated scores into the sample. The method of estimation is that ten panelists estimated the answer time and score for each sample, then removed a maximum score and a minimum score, and calculated the weighted average of the remaining eight estimates, and the resulting value is the final answer time or score.

4.2 Sample Normalization

In order to make the results of the normalization process as evenly distributed as possible between [0, 1], this paper adopts the normalization method shown in the following equation:

4.3 Determine the Accuracy of the Training Network

In practice, we usually take the integer multiples of 0.5 as the scores of a certain test question, so if the obtained BP network model can be as accurate as 0.1 is enough, and then according to the class rounding method to deal with it as an integer multiple of 0.5 a value. When the decimal part of the result is less than 0.25, it is rounded off, and when it is between [0.25, 0.75], it is processed as 0.5, and if it is greater than or equal to 0.75, it is rounded to the nearest integer. this is in line with the practical requirements. However, trained to achieve a certain accuracy of the network in practice, its error is always around a fixed value up and down. This is especially true when the representativeness of the sample is poor. For this reason, we set the global error of the network to be smaller than what is actually required when training the samples. In this study, it is set to 10-5.

4.4 Network Training Process

In this study, the number of hidden layer units is dynamically adjusted during network training to get a more appropriate number of hidden layer units. The momentum term is not used (it is tested that it works better without it), and the step size is dynamically adjusted by setting its initial value to 1, and then adjusting it between [0, 1] with a magnitude of 0.05 according to the error decrement. Cyclic selection of 800 training samples to train the network, every cycle m times to calculate the global error, every cycle n (n is an integer multiple of m) times to observe and record the change of the error, through the analysis and comparison to determine the direction of the step size adjustment. The main program code (c#) to train the network is as follows:

button3_Click(object sender, EventArgs e)

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// Dynamically specify the number of cells in the implied layer

wj=new double[h_num];//output-implied weights

wij=new double[7, h_num];//implied-input-weights

hvj=new double[h_num]; //implicit-layer threshold

int i, j;

netj=new double[h_num]; //implicit-layer input vector

xi=new double[7]; //input-layer input vector

comm2=conn1.CreateCommand();

hoj=new double[h_num]; //implicit layer output vector

ej=new double[h_num]; //implicit layer general error

//Initialize weights, thresholds, step sizes, and momentum factors

a=double.Parse(textBox2.Text.ToString());

//Initialize output node threshold

double e1=0.00001, E1=e1+1, E2=0;

int count=0, count1=0;

for(i=0; i=yb_count+1) ybbh=1;

ybbh=rand.Next(1, yb_count+1);

comm2.CommandText = "select * from gyhVIEW

where Sample number="" + " '" + ybbh + " '";

dr1 = comm2.ExecuteReader();

if (dr1.Read())

{for (i = 0; i = 3*yb_count)

{ E1 = E2 /3*yb_count; count = 0; count1 += 1;

if (count1 >= 1000)

{if (MessageBox.Show(E1.ToString() + " a="+ a.ToString() + "Decrease step size?" , "Prompt message",

MessageBoxButtons.OKCancel,

MessageBoxIcon.Question) == DialogResult.OK)

{ a -= 0.05;}

if (MessageBox. Show(E1.ToString() + "Increase step size?" , "Prompt message",

MessageBoxButtons.OKCancel,

MessageBoxIcon.Question) == DialogResult.OK)

{ a += 0.05; } count1 = 0; }}}

By Repeated training and comparative analysis, finally the number of network implicit layer units is determined as 6, every cycle 3 times to calculate the global error, the second every cycle 3000 times to observe and record the change of the error once, the learning step size is adjusted from 1 to 0.65, and finally converge at 0.65. *** trained 11.28 million times. After the model is stabilized, the connection weights between the input layer and the implied layer are shown in Figure 3 (where i indicates the input layer unit serial number, and wij indicates the connection weights between the input layer unit i and the implied layer unit j), and the connection weights between the implied layer and the output layer and the threshold of the implied layer are shown in Figure 4 (where j indicates the unit serial number of the implied layer), and the threshold of the output layer is -33.05475.

Observations to analyze the network The testing error of the model is basically less than 0.005, with the minimum value of 0.0001399517 and the maximum value of 0.01044011, which fully meets the accuracy required for the determination of the score of the question bank test questions (0.1), and is in line with the practical needs.

Conclusion

This paper applies the BP neural network to the determination of question bank test score, which provides a feasible method for the determination of question bank test score. In applying the BP algorithm, the number of hidden layer units is dynamically adjusted, the learning step size is dynamically adjusted, the pattern pair selection method of cyclically selecting training samples is used, and the global error is calculated once after a specific number of cycles of training. All these are derived from the accurate construction of this model. In addition, if the training samples represent the whole well, intelligent models for determining test scores with higher accuracy will be built with this method.

References:

[1] C.F. Hu, F. Li. Educational Measurement and Evaluation [M]. Guangdong Higher Education Press, 2003.7.

[2] Hadi, MuhammadN.S. Neuralnetworks applications in concrete structures. Computers and Structures Volume: 81, Issue: 6 March, 2003, pp. 373-381.

[3] Jiang H., Zhao J.. Learning behavior evaluation model and implementation based on BP neural network [J]. Computer Application and Software, 2005.22, (8): 89-91.

[4] Dai Y.W., Lei C.Y. Research on BP network learning algorithm and its application to image recognition [J]. Computer and Modernization, 2006.11: 68-70.

[5] Naihua Song, Qinghua Xing. A new BP network learning algorithm based on granular cluster optimization [J]. Computer Engineering, 2006.14:181-183.

Funded Projects: National Education Science "Eleventh Five-Year Plan" Key Research Project on Educational Examination (2006JKS3017); Shanxi Province Education Science "Eleventh Five-Year Plan" Project (GHG). "Planning Project (GH-06106).

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