Data mining is a way to obtain useful information from a large amount of data, and the rapid growth of data worldwide has increased the importance of data mining. It can be simply stated that data mining refers to the extraction of knowledge from a large amount of data, for this reason many people consider this term a synonym for the word discovery of knowledge [23]. Data mining is used to identify new, correct, comprehensible and potentially useful relationships and patterns within data, by combining data sets and extracting complex patterns for humans. Data mining is an important step in discovering and extracting knowledge. This term means exploring large data sets to extract unknown patterns between data [24]
2 − 1 Educational data mining
Educational data mining is a branch of data mining that seeks to discover the knowledge contained in the data of the educational system. One of the applications of educational data mining is to predict the academic performance of students. Predicting the academic performance of students in order to know the academic status and prevent poor performance and then to improve it, is of particular importance in the success of educational systems and in the knowledge and correct decision-making of managers and trainers to increase the efficiency of the educational system and better performance of students. It can play an effective role. In the field of data mining, Baker and Yasef [25] have identified data prediction based on educational data mining as the most widely used field. Also, Pina Ayala [26] conducted a comprehensive review research in the field of educational data mining, which studies and researches of the type they identified forecasting as the most common research in this field. Educational data mining is the process of transforming raw educational data into information that can be useful in design decisions or answers to research questions. The purpose of educational data mining depends entirely on who is going to use the results. For example: education director, lecturer, student or other officials. The used techniques are diverse and sometimes combined and have been designed and implemented according to different goals [27].The use of different data mining techniques is considered as a potential field for a systemic change that can help higher education institutions to have the most significant positive impact [28]. Therefore, the results of data mining programs can provide valuable support for the decision-making process [29].
2–2 Recommender Systems
Today, due to the ever-increasing growth of the Internet and the massive amount of information, we need systems that can offer the most suitable services to the user. The systems that perform this task are called recommender systems. One of the important challenges in this field is the existence of little knowledge against a large amount of data; therefore, the existence of a strong tool to extract useful information from mass data is a vital issue [30]. There are two ways to use the recommender systems, one way is to use the existing data of the system directly, which is called the memory-based method, and the other way, which is a little smarter, is to use a model in the system and to It is called the model-based method (using genetic algorithms, neural networks, fuzzy) [31].In this research, to create a recommender system, we use a model-based method, using a neural network, which is an intelligent solution, to predict the academic status of students.
2-3Neural Networks
Neural networks are mathematical computational models that simulate the learning mechanism like the natural neural network of the human brain structure. A neural network forms a layer by putting several neurons together. The neural network calculates the calculation of the function by propagating the calculated values from the input neurons to the output neurons and using the weights as intermediate parameters. By analyzing data and the relationship between input and real outputs, neural networks can discover hidden aspects of science and hidden relationships in data [32]. The block-mathematical model of a neural network is shown in Fig. 1 [33–43].
In Fig. 2, the variables p, w, b, f, and a are the input matrix, the weight matrix of the neurons, the bias value, the transfer function, and the output matrix, respectively. Also, the neural network can have multiple inputs or multiple layers or multiple outputs. be Neural networks are used in two types and feed-forward, where in the feed-forward network, the signal is only allowed to move in one direction and cannot return to the neuron of the previous layer. In fact, the processing of input data is forward and the processing path does not return to the neurons of the previous layer, and the output of each layer will only affect the next layer, and in feedback networks it has at least one feedback signal, that is, the output of the neuron, except for the current input, depends on its previous output. Therefore, in this type of network, the signal can move in two directions and all connections between neurons are allowed, that's why loops are used a lot in this type of network.
2-3-1 Transfer function
Transfer functions can be a linear or non-linear function depending on the variable n, which are:Hard limiting function, Hardlims function, linear function, Log-Sigmoid function, Tan-Sigmoid function.The selection of the transfer function affects the accuracy of the network output, therefore, in order to determine the best combination of transfer functions in a neural network with one or more hidden layers, different transfer functions are used to develop the network. Table 1 shows transfer functions with conventional signs [33].
Name of function
|
Input/output
|
Symbol
|
Function
|
Hard Limit
|
a = 0, n < 0
a = 1, n ≥ 0
|
![image](data:image/png;base64,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)
|
hardlim
|
Symmetrical Hard Limit
|
a = –1, n < 0
a = +1, n ≥ 0
|
![image](data:image/png;base64,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)
|
hardlims
|
Linear
|
a = n
|
![image](data:image/png;base64,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)
|
purelin
|
Symmetric Saturating Linear
|
a = –1, n < –1
a = n, –1 ≤ n ≤ 1
a = 1, n > 1
|
![image](data:image/png;base64,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)
|
satlins
|
Log-Sigmoid
|
a=
|
![image](data:image/png;base64,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)
|
logsig
|
Hyperbolic Tangent Sigmoid
|
|
![image](data:image/png;base64,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)
|
tansig
|
2-3-2 Neural network learning
Working with the neural network becomes possible through teaching and learning in line with the goals. Learnability means the ability to adjust time-varying parameters, with the aim that the network can be efficient for new conditions with brief training. In most neural networks, learning rules are used to train the network, and neural network learning is done in two types, supervised and unsupervised, which is shown in Table 2 comparing these two learning methods [34], [35], [36], [37].
2-3-3 Mean Square Error
The mean square error is a method to estimate the amount of error and is one of the most famous error functions that calculates the mean squared difference between the actual and predicted values by the following Eq. (1)
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The real data is the simulated (predicted) data and N is the total data in which performs the averaging operation and calculates the squared error value of Each data. The MSE result is always positive, and the closer its value is to zero, the lower the error; Therefore, in an accurate model, the MSE value is close to zero
2-3-4 Average Absolute Error
This function calculates the average absolute value difference between the actual and predicted values by the following equation:
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The performance of the proposed model in the paper is evaluated using the mean squared error (MSE), mean absolute error (MAE).