Analysis on Course Scores of Learners of Online Teaching Platforms Based on Data Mining

The rapid development of information technology (IT) and the Internet has greatly promoted the reform and innovation of traditional teaching models, resulting in better teaching effect [1-4]. More and more schools and teachers have turned to online teaching platforms (OLPs) that integrate online and offline teaching based on Internet Plus. After years of development, OLPs have accumulated a huge amount of data on student scores. To optimize the teaching strategies, contents, and plans, it is not enough to conduct simple statistical analysis and summary of these data [5-9]. Instead, the massive data on student scores need to be analyzed by big data technology, aiming to cluster the students and extract group features. This will enable the teachers to propose pertinent teaching strategies, and design effective teaching contents and plans, thereby improving the learning methods and scores of students.

Data mining is widely used in such fields as finance, science and technology, and agriculture. It is also increasingly applied in education and teaching [10-14]. The existing studies on data mining of education data mainly focus on the prediction of student scores, and the correlation between course scores [15-18].

On the prediction of student scores, Dahri et al. [19] constructed a total score prediction model based on long short-term memory (LSTM) network, and compared it with Bayesian algorithm and decision tree (DT) to verify its accuracy in predicting the scores of graduate and undergraduate students. Using effectively collected enrollment data, Syahidi and Asyikin [20] contrasted the effects of DT, logistic regression, and backpropagation neural network (BPNN) in freshman scores, and discovered that the BPNN achieved the highest prediction accuracy. Hamdi and Kartowagiran [21] preprocessed enrollment data (e.g. enrollment rate) through linear regression, and combined DT with naive Bayes to predict undergraduate scores on the Weka machine learning workbench.

On the correlation between course scores, Arami and Wiyarsi [22] identified the key factors affecting the student scores of universities for nationalities by k-means clustering (KMC), and obtained the highly correlated course scores. With the aid of association rules, Wibawa [23] analyzed the correlations between the factors affecting the total score of students, mined out the useful rules, and optimized the current allocation of teaching resources. Gkontzis et al. [24] applied the improved association rule Apriori algorithm to evaluate the correlations between course scores of computer application majors, and quantified the degrees of correlation between the scores of professional courses. Northey et al. [25] relied on the Iterative Dichotomiser 3 (ID3), a DT algorithm, to examine the factors affecting student scores, and optimized the design of student score mining system, using improved association rule mining and clustering algorithms.

Based on data mining, this paper puts forward a course score analysis model for OLP learners. The purpose is to effectively mine out the useful knowledge and information behind the massive data on OLP learner scores, and to accurately evaluate the rationality of teaching plans, the distribution of course scores, and the importance of each course.

The remainder of this paper is organized as follows: Section 2 classifies the score features of OLP learners, and details the calculation method of the computational features; Section 3 analyzes the learner scores through expectation maximization (EM) clustering, which has the advantage of unsupervised learning, and obtains the salient features by principal component analysis (PCA); Section 4 combines the clustering algorithm with the support vector machine (SVM), a supervised learning method, to accurately categorize the features of OLP learner scores; Section 5 verifies the effectiveness of our method through experiment; Section 6 puts forward the conclusions.

The scores on OLPs are private data of the learners. The acquisition of these data brings certain risks and difficulties. Considering the universality of relevant analysis methods and the predefined features of OLP learner scores, this paper decides to analyze learner scores through EM clustering, which has the advantages of unsupervised learning. The workflow of EM clustering is explained in Figure 3.

The EM clustering is an iterative algorithm based on maximum posterior probability and maximum likelihood estimation. Suppose dataset Z=(X, Y) encompasses observed data X and unobserved data Y, and JPD(X,Y|Ψ) be the joint probability density of these data. Then, finding the maximum of the likelihood function LF (X; Ψ) of X is to make the maximum likelihood estimation of Ψ:

$LF(X;\Psi )=\log JPD(X\left| \Psi  \right.)=\int{\log JPD(X,Y\left| \Psi )dY \right.}$            (20)

2222.png

Figure 2. The model of score features for OLP learners

3.png

Figure 3. The workflow of EM clustering

In EM clustering, the EM of LF^*(X; Ψ) is iteratively calculated to maximize the log likelihood function of X:

$L{{F}^{*}}(X;\Psi )=\log JPD(X,Y\left| \Psi ) \right.$           (21)

After t iterations, the likelihood estimate of Ψ can be expressed by Ψ(t). During the t+1-th iteration, the likelihood function expectation of Z during the calculation of the posterior probability of each sample belonging to each class can be described as:

$LFE(\Psi \left| \Psi (t) \right.)=PPC\{L{{F}^{*}}(\Psi ;Z)\left| X \right.\left| \Psi (t)\} \right.$          (22)

where, PPC {} is the posterior probability calculation function. During the updating of the probability distribution function of each class through maximum likelihood estimation, LFE (Ψ|Ψ|(t)) is maximized, and Ψ is updated.

The above steps are repeated iteratively to optimize and update model parameters. In this way, the likelihood probability of the training samples and model parameters continues to increase until reaching the extreme point.

After clustering, it is necessary to select suitable features of OLP learner scores. Otherwise, there will be no basis for subsequent data mining. Inspired by the idea of dimensionality reduction, this paper transforms multiple features of OLP learner scores into a few representative features through PCA.

Let Z=(z₁,z₂,…,z_g)^T be a g-dimensional random vector obtained by standardizing the original observed data. Then, a matrix of U samples z_i=(z_i1,z_i2,…,z_ig)^T was constructed, and the matrix elements were standardized by:

${{S}_{ij}}=\frac{{{z}_{ij}}-{{{\bar{z}}}_{j}}}{\sqrt{\frac{\sum\limits_{j=1}^{U}{{{({{z}_{ij}}-{{{\bar{z}}}_{j}})}^{2}}}}{U-1}}}$         (23)

${{\bar{z}}_{j}}=\frac{\sum\limits_{i=1}^{U}{{{z}_{ij}}}}{U}$           (24)

The correlation coefficient matrix can be established as:

$R={{[{{r}_{ij}}]}_{g}}=\frac{{{S}^{T}}S}{U-1}={{\left[ \frac{\sum{{{s}_{kj}}\cdot {{s}_{jk}}}}{U-1} \right]}_{g}}$            (25)

Solving the characteristic equation |R-λI_g| of formula (25), a total of g characteristic roots can be obtained. The PCA needs to satisfy the following inequality:

${\sum\limits_{j=1}^{d}{{{\lambda }_{j}}}}/{\sum\limits_{j=1}^{g}{{{\lambda }_{j}}}}\;\ge 0.8$        (26)

Then, the d value of principal components with a utilization rate greater than 0.8 was calculated. Solving the equation set Rb=λ_jb, the unit eigenvector σ⁰_j was obtained. Next, the standardized data features were converted into principal components:

$P{{C}_{ij}}=S_{i}^{T}\sigma _{j}^{0}$        (27)

Taking the variance contribution rate as the weight, the d principal component features were weighted and summed to derive the comprehensive evaluation of OLP learner scores.

The massive data on OLP learner behaviors were collected and processed through the flow in Figure 5, and the preprocessed features were stored in a non-relational database. The learner behavior data involve attributes like StudentID, SessionID, Verb, Object, and Context, which help to judge whether a learner enters a session or exit the system.

5.png

Figure 5. The collection and preprocessing of learner behavior data

The originally extracted data contain lots of redundant information. The high-quality features need to be selected from the original data, such that the model will not face problems induced by the curse of dimensionality: poor generalization, high complexity, and long training. Here, the correlation coefficients of score features in each category are calculated by the correlation coefficient method. The calculated results are recorded in Table 2.

If the Pearson correlation coefficient falls in 0.5-1.0, the features are strongly correlated; if the coefficient falls in 0.3-0.5, the features are moderately correlated; if the coefficient falls in 0.1-0.3, the features are slightly correlated; if the coefficient falls in 0-0.1, the features are basically uncorrelated. This paper chooses the features with Pearson correlation coefficient greater than 0.3 for clustering analysis.

Table 2. The salient features of OLP learner scores and their Pearson correlation coefficients

6a.png

(a) Two classes

6b.png

(b) Three classes

Figure 6. The visualized results of EM clustering of selected features

From the multi-source data of OLP learners throughout the 20-week semester, the features closely correlated with learner scores were extracted, and grouped by EM clustering into two classes (I and II) or three classes (I, II, and III). To give a visual display of the clustering results, the features to be clustered were subject to PCA and dimensionality reduction. The visualized results of EM clustering are displayed in Figure 6.

Following the idea of equal division, the results of three-class EM clustering before and after feature selection were divided into three levels, namely, 1-200, 200-400, and 400-600, and the clustering accuracy in each level was calculated in turn. Table 3 compares the accuracies of EM clustering before and after feature selection.

From Figure 6 and Table 3, the EM clustering achieved a good effect on the OLP learner scores. The accuracy before feature selection was higher than that after feature selection. The three-class clustering was more accurate than two-class clustering, with accuracy falling between 82.76% and 86.74%. Therefore, our clustering analysis method excels in distinguishing fine-grained features of learner scores.

Next, three SVM classifiers were designed by integrating multiple binary classifiers through one-against-one. Their performance was cross validated, and evaluated. Then, the SVM classifiers were adopted to predict the multiple classes of learner scores, based on the feature subset of the multi-source data on OLP learner scores and the features closely correlated with learner scores. Table 4 compares the classification results of the three SVM classifiers.

It can be seen that the three-class SVM classifier achieved an accuracy of 82-91%, slightly higher than that of two-class SVM classifier. This classifier effectively distinguished between the scores of learners in different levels, suggesting that it is suitable for analyzing and managing OLP learner scores.

Furthermore, the scores of electrical automation majors on 13 professional courses were clustered by the proposed SVM classifier and the rule-based classifier. As shown in Figure 7, the proposed SVM classifier outshined the rule-based classifier in accuracy and recall, despite a slight lag in efficiency. The results demonstrate the accuracy and effectiveness of our method in the classification of OLP learners and their score features.

Table 3. The EM clustering accuracies before and after feature selection

Table 4. The classification results of the 3 SVM classifiers before and after feature extraction

7.png

Figure 7. The classification results on professional course scores of rule-based classifier and SVM classifier

Note: ECT is Electrical Control Technology, EET is Electrical and Electronic Technology, PC is Programmable Controller, SDT is Sensing and Detection Technology, ACNCMT is Application of Computer Numerically Controlled (CNC) Machine Tools, PAC is Principle of Automatic Control, PAPLC is Principle and Application of Programmable Logic Controller (PLC), ESD is Electronic System Design, AET is Analog Electronic Technology, DET is Digital Electronic Technology, ATC is Application of Computer Technology, FET is Fundamentals for Electrical Towage, PECT is Power Electronic Conversion Technology.