3.1

Principle of k-means algorithm

K-means is an iteratively solved cluster analysis algorithm, where k refers to the number of clusters and means is understood as the mean of the data in each class. K-means clustering is one of the most popular and simple clustering algorithms, and is still widely used in many fields today due to its simplicity, efficiency, and ease of implementation.

The basic idea of the k-means algorithm is that for a given sample set X={x₁,x₂,…, x_m} the sample set is divided into k clusters according to the distance d between samples. The calculation method of the least square error of the cluster C={C₁, C₂, …, C_k} obtained by the k-means algorithm is as follows.

The distance calculation between sample objects is generally measured by Euclidean distance. The calculation method of Euclidean distance is as follows.

The flow chart of the k-means algorithm is shown in Figure 2.

Figure 2.

Flow chart of k-means algorithm.

3.2

Improved k-means algorithm

The k value of the traditional k-means algorithm needs to be preset, and the selection of the initial cluster center is random, so the result of the algorithm changes with the selection of the center point, which may lead to a local optimum. The canopy algorithm is a fast clustering technique. Although the accuracy is low, it cannot give accurate cluster results, but it can give the optimal number of clusters. You can use canopy clustering to first perform coarse clustering on the data, and use the number of clusters and cluster centers of the canopy algorithm as the input parameters of the k-means algorithm to complete the fine clustering of the data set. The process of using the canopy algorithm to help the k-means algorithm to select the initial cluster center is shown in Figure 3.

Figure 3.

Canopy algorithm to determine cluster centers.

The specific algorithm is as follows:

Input: dataset X = {x₁, x₂, …, x_n}

Step 1: Determine two distance thresholds T₁ and T₂ through cross-validation tuning or prior knowledge, where T₁ > T₂.

Step 2: Randomly select a sample point P from the dataset X as the first canopy cluster center, and add P to the set C. Remove P from L.

Step 3: Randomly select a sample Q from set X, and calculate the Euclidean distance from Q to each canopy cluster center in set C, and select the minimum value d among these distances.

Step 4: Compare T₁ with distance d. If d < T₁, add the sample point Q to the canopy with the smallest distance from it, and label a weak marker. If d > T₁, set Q as the new canopy distance center, add sample point Q to set C, and remove Q from dataset X.

Step 5: Compare T₂ with distance d. If d<T₂, attach a strong label to it, update the center position of all strongly labeled samples to the cluster center of this canopy, and delete the sample point Q from the dataset X.

Step 6: Repeat steps 3, 4 and 5 until dataset X is empty.

Output: Cluster center set C

4.1

Data collection

This paper desensitizes the collected student behavior data. The original data includes the one-card consumption data of some undergraduates in a university in Henan, library access control data and educational administration system data. For details, see Table 1-3.

Table 1.

Student card canteen consumption data.

Table 2.

Library loan data.

Table 3.

Academic affairs system grade data.

4.2

Data processing

The raw data of students’ behavior recorded in various information systems of the school are too large and cumbersome to directly mine knowledge. In this paper, statistical methods are used to compress, generalize and normalize the student behavior data to make the data more valuable for analysis. For example, for the student card data, this paper first uses statistical methods to calculate the average monthly consumption amount, consumption frequency and consumption peak of students using a monthly cycle. After preprocessing, the evaluation indicators of students are shown in Table 4.

Table 4.

Student evaluation metrics.

4.3

Experimental result

Due to space limitations, here we only use canopy and k-means algorithm to cluster student consumption data, analyze students’ consumption patterns, and construct the consumption portrait of students on campus. The result is shown in Table 5.

Table 5.

Clustering results of students’ consumption.

The monthly average consumption of students in group 1 is the lowest among all groups, but it cannot be simply judged that the overall consumption level of this group of students is low. The consumption frequency of such students is lower, and the average single consumption is higher among all groups. Therefore, it can be inferred that such students like off-campus consumption, and the overall consumption level is relatively high.

For the second group of students, the peak monthly consumption of these students is relatively close to the average monthly consumption, and the average monthly consumption and single consumption are in the middle level of each group. According to the consumption characteristics of such students, it can be seen that their consumption is relatively regular, basically solved in schools, and the overall consumption level is at a moderate level.

Group 3 students make up 16% of the total. Average monthly consumption, monthly consumption frequency and single consumption are relatively high. It can be inferred that their overall consumption level is relatively high and their living expenses are relatively sufficient.

Group 4 students, the average monthly consumption and single consumption are lower. It can be seen that the overall consumption level of such students is relatively low, and they belong to economically poor students. Schools should prioritize these students in financial aid evaluations.

4.4

Student portrait

According to the clustering results of the three indicators of consumption law, life law and effort level, the student categories with different behavior characteristics are summarized, categorized, and labeled, and the label of each indicator and the basic information of the student are integrated to describe the student Behavioral portraits. The portrait of the student is shown in figure 4.

Figure 4.

Student image.