Intelligent Analytics for Educational Big Data and Its Application to Instructional Management

The fundamental principle of the DBSCAN density clustering algorithm is that the sample points within each cluster are closely related to each other, and the density of a point inside the cluster must be greater than the density of the point outside the cluster, that is, the points within the same category must be related [26]. The density is defined as a set of parameters (ε, minPts), ε represents the maximum value of the distance between sample points, i.e., the distance between sample points can not exceed this maximum value, which is also equivalent to the radius. minPts describes the number of sample points clustered in the smallest of clusters within a region of density, i.e., the number of sample points contained in this range of distances from a certain point. dbscan algorithm The core idea is to find the core object, and then the object as the center to find the sample points falling within a specific distance (ε), and finally, all the sample points in series to form a cluster. Let the set of sample points be D, some basic parameters of the algorithm are defined as follows.

The ε -neighborhood of a point: The ε -neighborhood of a A -point denotes the set of sample points where the distance between the points in the sample set and the A -point is less than ε, as defined in Equation (1): 1 Nε(A)={B∈D∣dist(A,B)≤ε}

In a sample set, assuming that the distance between the data point A and data point B is less than ε, it is said that point A is in the ε -neighborhood of point B, and of course, point B is in the ε -neighborhood of point A.

Core object: if there are no less than minPts sample points within a distance of ε, and this sample point belongs to it, then the sample point is a core object point, such as point P in Fig. 1 is the core object.

Figure 1.

DBSCAN clustering principle

Direct density reachability: if data points A and B satisfy the following constraints: 1)

Data point B falls within the ε -neighborhood of data point A.

Density reachability: If a sample point is connectable to another sample point, and the distance between these two sample points is less than ε. For example, in Figure 1, data points P and Q, there is a density reachability relationship between them, and the density reachability can actually be transferred by direct density, and point Q in the figure can be density reachable by point P.

Density connected: for data points A and B, if there exists another core object K such that B and A are density reachable through K, then points A and B are density connected. As shown in Figure 1, points A and B can be density-connected through point K.

Boundary point: a sample point is called a boundary point if it belongs to a certain class, but the ε - neighborhood of the sample point does not contain the rest of the points. For example, the C -points in Fig. 1.

Noise point: if there exists a point that is not in all the clusters and all other core objects are density unreachable for this point, the point is called a noise point. For example, the red point in Fig. 1 is labeled as a noise point.

Based on the above definition, the steps of the DBSCAN clustering algorithm can be described in such a way that the category obtained by executing the algorithm is the largest set of samples that are connected by the density reachable and density connected between the sample points, and the specific process can be described as: 1)

Mark all sample points as not visited.

The student academic alert model was created to inform students about future academic performance. The student academic alert results were categorized into three categories: incomplete, deferred completion, and successful completion. If a student took more than four additional years to earn a degree or did not finish it, it is considered incomplete. Extended completion means that the student took between one and three additional years to earn a degree. Successful completion means that the student has graduated with a degree. The XGBoost-based academic alert model for college students is shown in Figure 2, which contains three main parts: data preprocessing, student academic alert algorithm, and student academic alert characterization. 1)

Data preprocessing. In order to improve the performance and warning accuracy of the student academic alert algorithm, the raw data set needs to be processed. Processing the original dataset is necessary to use it directly in the model for training as it may have missing data, outliers, and feature attribute redundancy. Data cleaning, feature selection, data transformation, and imbalance processing are the main aspects of data preprocessing in this paper.

Figure 2.

Student aca demic warning model

The XGBoost algorithm, whose full name is “Extreme Gradient Boosting”, was proposed in 2016 as a boosting learning algorithm. The algorithm is improved on the basis of the GBDT algorithm, which adopts the second-order Taylor expansion and the regular term to effectively avoid overfitting and accelerate the convergence speed [27]. Compared with other algorithms, the XGBoost algorithm has the advantages of being fast, efficient, generalizable, and suitable for dealing with large-scale tabular data, so it has been widely used in the fields of statistics and machine learning.

The integrated idea of the XGBoost algorithm is to establish multiple weak evaluators through residual fitting and eventually accumulate the weak evaluators to get strong evaluators, and each additional weak evaluator is expected to improve the effect of the model so that the final prediction results of the model can be maximally close to the real value and have as much as possible generalization ability to the unknown samples.

The XGBoost algorithm can be expressed as an additive form as:2 y^i = ∑​Kfk(xi),fk∈F

Where ŷ_i denotes the predicted value of the model. K denotes the number of decision trees: f_k denotes the k th submodel. x_i denotes the i th input sample. F denotes the set of all decision trees. The objective function of XGBoost consists of two parts: loss function and regular term: 3 L(ϕ)t=∑i=1nl(yi,y^i(t−1)+ft(xi))+Ω(fk) $$L{\left( \phi \right)^t}\, = \,\sum\limits_{i = 1}^n {l\left( {{y_i},\hat y_i^{\left( {t - 1} \right)} + {f_t}\left( {{x_i}} \right)} \right) + \Omega \left( {{f_k}} \right)} $$ 4 Ω(fk)=γT+12λ‖ω‖2

Where L(ϕ)^t is the objective function for the t th iteration: ŷ_i^{(t – 1)} is the predicted value for the first t–1 iterations. Ω(f_k) is the regular term of the model for the t th iteration, which is used to reduce overfitting. γ and λ denote the regular term coefficients to prevent the decision tree from being too complex. T denotes the number of leaf nodes in the model. To further optimize the objective function, the expansion of equation (3) using Taylor’s formula can be obtained: 5 L(ϕ)t≅∑i=1n[ gift(xi)+12hift2(xi) ]+γT+12λ∑j=1Tωj2≅∑j=1T[ (∑i∈Ijgi)ωj+12(∑i∈Ijhi+λ)ωj2 ]+γT

Where g_i is the first-order derivative of sample x_i ; h_i is the second-order derivative of sample x_i ; ω_j is the output value of the j th leaf node, and I_j is a subset of the samples of the j th leaf node values. From this formula, we can see that the objective function is a convex function, and by taking the derivative of ω_j and making the derivative function equal to zero, we can find the ω_j that minimizes the objective function, i.e.: 6 ωj* = −∑i∈ljgi∑iljhi+λ 7 L(ϕ)min=−12∑j=1T(∑i∈ljgi)2∑i∈ljhi+λ+γT $$L{\left( \phi \right)_{\min }}\, = \, - \,{1 \over 2}\,\sum\limits_{j = 1}^T {{{{{\left( {\mathop \sum \limits_{i \in {l_j}} {g_i}} \right)}^2}} \over {\mathop \sum \limits_{i \in {l_j}} {h_i} + \lambda }}\, + \,\gamma T} $$

Equation (7) can be used to evaluate the goodness of the tree model, with smaller values indicating a better model. From this, the score formula (8) used for the tree to perform node splitting can be derived, and finally, the Gain value of each feature is ranked to find the optimal feature and the optimal cut-off point.8 Gain=12[ (∑i∈∫Lgi)2∑i∈∫Lhi+λ+(∑i∫IRgi)2∑i∫IRhi+λ−(∑i∫Igi)2∑i∫Ihi+λ ]−λ

Student behavior data contains student achievement, book borrowing data, and campus card consumption data three-dimensional data using the DBSCAN algorithm for this three-dimensional data were clustering analysis, student achievement, and book borrowing as shown in Figure 3, student achievement and consumption amount clustering analysis as shown in Figure 4, the number of students borrowing and consumption data clustering as shown in Figure 5. 1)

Cluster analysis of student achievement and borrowing amount

The analysis is carried out using the DBSCAN clustering algorithm, the number of data clusters k is set to 4, and the distance from the data object to the central cluster is calculated using the Euclidean distance and the clustering results obtained are shown in Figure 3. The horizontal axis in Fig. 3 represents the students’ performance information, and the vertical axis represents the information on the number of students borrowing in a semester. Four different colors are used in the figure to represent four different data clusters, where the red part represents that the number of books borrowed by students with grades of 0-65 in a semester ranges from 1-8 books, and most of the students have a number of borrowing data of 1 book. The green portion represents students with grades of 63-73 who borrowed between 1-17 books in a semester. The blue section represents the number of books borrowed in a semester by students with grades of 75-80 ranging from 0-16. The orange portion represents the number of books borrowed in a semester by students with grades between 80-100 ranging from 1-24. Synthesizing the results of the cluster analysis reveals that the number of books borrowed by undergraduate students is small, with most students borrowing only one book. Visualization of the clustering results shows that the number of books borrowed by students with good grades is about two times more than that of students with failing grades. Therefore, the number of books borrowed can also tell how good a student’s grades are. For example, a student who borrows 17 books in a semester will have an academic grade of 78 or more and will definitely have a passing academic grade.

Figure 3.

Student achievement and borrowing number clustering

Figure 4.

Student achievement and borrowing number clustering

Figure 5.

Student borrowing number and consumer data clustering

For the four algorithms, RF, GBDT, XGBoost, and LGB, the training parameters need to be adjusted before all training to improve the prediction performance of the model. By testing multiple training parameter combinations, the combination with the best prediction effect is chosen as the final parameter combination. Since the prediction of academic warning in this paper is a classification problem, classification precision, prediction accuracy and recall, and F1 score are used as the evaluation indexes of model performance, and the results of the four algorithms are shown in Table 1.

Table 1 shows that the XGBoos algorithm achieves 96% classification precision, 89% prediction accuracy, 88% recall, and 92% F1 score. Next RF algorithm is better, and the GBDT algorithm has the worst performance. The GBDT algorithm has a difference of 4.7%, 1.7%, 4.0%, and 7.0% compared to the XGBoos algorithm. Thus, it shows that out of these 4 algorithms, the XGBoos algorithm classifies the dataset used in this paper well, so this algorithm is chosen for student academic prediction.