The college students' psychological health education dataset downloaded from China national knowledge infrastructure (CNKI, https://www.cnki.net), consisted of 865 articles. The terms “college students' psychological” and “education” were used as retrieve articles based on the Chinese social sciences citation Index (CSSCI), the Chinese science citation database (CSCD) and the Chinese core journal criterion of PKU. The time range was set between 1994 and 2024. We excluded the articles that were irrelevant to the current research or not an original research article (e.g., reviews, newsletters, or conference reports). Finally, 676 articles with bibliographic data including titles, keywords, authors and publish data were retained, and then these data were imported into the Bibliographic items co-occurrence matrix builder (Bicomb) software (Guo et al., 2015; Li and Cheng, 2021). Via Bicomb we extracted keywords from these articles, and generated a term-document matrix and a term-term co-occurrence matrix that were used to conduct downstream analysis tasks.

The student life dataset downloaded from Kaggle site (https://www.kaggle.com/datasets) comprised survey results from 100 computer science students. Demographic data, depression status, and performance variables, such as academic performance, taking notes in class, and presentation frequency, were collected. These variables have been measured before this study and are publicly accessibly (https://www.kaggle.com/datasets).

For the college students' psychological health education dataset, we implemented statistical analysis on keywords that appeared in each record, and obtained keyword rankings, in which high frequency indicated close attentions on the corresponding field. Keywords that occurred <2 times across all records were removed. For student life dataset, the Python toolkit package Scikit-learn was used to transform numerical variables and categorical variables.

Different from traditional graph where an edge can only connect to two nodes, in hypergraph an edge can connect more than two nodes. This mechanism of hypergraph effectively handles with information loss problem. For example, to group a set of articles into different topics, the common practice is to first construct a pairwise interaction network (simple graph) where two nodes are linked with an edge if there is at least one common author writes them, and then graph clustering method is implemented on this graph to obtain the final cluster assignments (Zhou et al., 2006). However, the graph constructing strategy above obviously ignore some useful information when the same author contributes more than two articles. Such unexpected lost information is important to clustering or knowledge findings.

A natural approach to address information loss issue is to use hypergraph to organize data relationships. Figure 2 gives an illustrative example to construct hypergraph. Given the weighted hypergraph G = (V, E, W), where V is the set of nodes and E denotes the of hyperedges. For each hyperedge e, we used w(e) to represent its weight. In this manuscript, the gaussian kernel function is used to compute the weights of hyperedges. The incidence matrix P∈R^{|V| × |E|} corresponding to G with entry p(v, e) is defined as follows:

where |V| and |E| represent the number of nodes and hyperedges, respectively. The degree of node v is defined as d(v)=∑e∈Ew(e)p(v,e). The degree of hyperedge e is defined as δ(e)=∑v∈Vp(v,e). Let D_v and D_e denote degree matrices of nodes and hyperedges, respectively. The hypergraph Laplacian matrix L_hg can be defined as follows:

Note that in this manuscript we used Louvain community detection algorithm (Blondel et al., 2008) instead of k-nearest neighbors (KNN) to generate hyperedges, i.e., each cluster represents a hyperedge. By using this strategy, noisy information or outliers are filtered out to some extent. The hypergraph captures the high-order interaction among nodes. The hypergraph regularization can be defined as follows:

Here, H denotes the low-dimensional representation matrix of nodes.

Next, we will introduce the proposed HSNMF algorithm by integrating hypergraph into this objective.

To identify the college students' psychological health education research topics, we introduce hypergraph induced semi-orthogonal non-negative matrix factorization (HSNMF) model. Let X∈R+p×n denote the original data matrix, HSNMF aims to learn two low-dimensional representation matrices W∈R+p×k (basis matrix) and H∈R+k×n (coefficient matrix), and a feature similarity matrix S∈R+p×p, where p, n denote the numbers of features and samples, respectively. k≪min(p, n) is the rank of factorized matrix. The objective function of HSNMF can be written as follows:

where I is identity matrix, 1 is a column vector with all its elements to be 1s. S is the learned feature similarity matrix that can be used for clustering and data visualization. α, β and γ are hyperparameters to be tuned. We will discuss how to select their values in the later section.

In the object of HSNMF, the first term, ||X-WH||F2, is standard non-negative matrix factorization (NMF) loss function for student psychological education or student life data. The second term, ||S-WWT||F2, is a consensus graph factorization strategy which regularizes kernel WW^T toward a consensus graph S, and generating a meaningful factorization. Through iterative training, the first two terms in Equation 4 can learned the low-dimensional representation for samples and features, however, the high-order relationships among nodes may be ignored. For example, the depression level of student may be correlated to the mixed effects of academic pressure, numerous work, and family responsibilities (Opoku et al., 2021; Wang et al., 2014). Hence, modeling high-order interactions among variables with hypergraph is important to mine the latent feature associations. Therefore, we include the third term, tr(WTLhgW), in HSNMF model. The fourth term, ||WTW-I||F2, encourages W to be column-orthogonal. One of the advantages is the uniqueness and interpretability of solution W. The term, S1=1, is a constraint term on S that enforces each row of S to have summation close to 1.

Unlike other clustering methods based on spectral graph theory including spectral clustering and its variants which used the eigenvectors corresponding to large eigenvalues to conduct clustering (White and Smyth, 2005; Ng et al., 2001; Law et al., 2017), HSNMF adopts hypergraph Laplacian to explore the complicated interaction relationships among variables. The low-dimensional factor matrices obtained from HSNMF own stronger representation ability. In addition, orthogonal constraints on basis matrix W leads to better clustering solution and interpretability: the columns in W will tend to be sparse. The optimization algorithm of HSNMF is presented in the next subsection.

The optimal problem of objective function (Equation 4) can be divided into three sub-problems and can be solved alternately.

In HSNMF, there are three parameters α, β and γ that need to be determined. First, we used NNDSVD (Boutsidis and Gallopoulos, 2008) to solved the optimization problem ||X-WH||F2 and obtain the initial solutions W^ and H^. Second, we used Ochiai coefficients (Vancraeynest et al., 2024; Kalgotra et al., 2020) to set the initial value S^ of S. Finally, α, β and γ are set as:

Noting that for the sake of fairness we adopted parameter selection rules defined in Equations 10–12 across all the experiments. The ablation experiments in the following subsection also demonstrated the effectiveness of the objection of HSNMF algorithm.

Unsupervised clustering metric silhouette coefficient (Kaufman and Rousseeuw, 2009), Calinski-Harabasz index (CHI; José-García and Gómez-Flores, 2023; Caliński and Harabasz, 1974), and Davies-Bouldin index (DBI; José-García and Gómez-Flores, 2023; Davies and Bouldin, 1979) are used to evaluate the performance of the clustering methods.

Let a(i) denote the average distance of data point i to all other data within the same cluster with i, and b(i) denote the average distance of i to all data points to the neighboring cluster, i.e., the smallest average distance to the cluster of i. The silhouette coefficient for data point i is defined as:

High silhouette score indicates good clustering performance. The average values of silhouette scores of all the data points are reported.

Let n, k denote the number of data points and clusters, respectively, the CHI is defined as follows:

where n_i is the number of data points belonging to ith cluster, C_i is the data set belonging to ith cluster, c_i is the centroid of ith cluster, c is the centroid of all data points.

The DBI is defined as follows:

where |C_i| denotes the number of data points in C_i, d(x, c_i) denotes the distance between x and c_i.

In the college students' psychology health education dataset, we used the term-document matrix and the term-term co-occurrence matrix as inputs for HSNMF, and obtained the low-dimensional representation matrices W, H and a similarity matrix S. Clustering and data visualization were implemented using S. We compared the HSNMF algorithm with other competing methods, including NMF (Lee and Seung, 2000, 1999), spectral clustering (SC; White and Smyth, 2005; Jia et al., 2014), and symmetric non-negative matrix factorization (SNMF; Kuang et al., 2012; Ma et al., 2020), for the topic analysis of students' psychological health research. For SC, we first constructed similarity matrix with the cosine function, and then implemented spectral clustering on the similarity matrix. For HSNMF, we first constructed a k-nearest neighbor (KNN) graph based on the learned similarity matrix S, and then implemented Louvain clustering on the KNN graph.

The clustering performance evaluated by CHI, DBI and silhouette scores are presented in Figure 3.

As shown in Figure 3, HSNMF achieved the best performance on the college students' psychological health education dataset in terms of CHI, DBI and silhouette scores. NMF achieves the second-best performance in terms of CHI. SC also performed well in terms of silhouette score. The results demonstrate that the proposed HSNMF algorithm is effective on students' psychological health education dataset. One of the possible reasons is that the introducing hypergraph regularization term and the semi-orthogonal constraints on the low-dimensional representation W into the HSNMF objective function.

We further validate the effectiveness of HSNMF via ablation experiments. We set α, β and γ to 0 in turn. When α = 0, the values of CHI and DBI were 2.7e-5 and 45.87, respectively. When β = 0, the values of CHI and DBI were 0.0075 and 17.51, respectively. When γ = 0, the values of CHI and DBI were 0.0082 and 19.05, respectively, and the averaged silhouette score was 0.7206. The results demonstrate that the effectiveness of introducing the hypergraph regularization term, consensus graph factorization strategy, and semi-orthogonal constraints on the columns of W into the object of the HSNMF algorithm.

HSNMF can not only be used to cluster, but also be used to data visualization. Based on the learned the low-dimensional factor matrix W, the term similarity matrix S, and the clustering indices of all terms, we implemented visualization analysis, and the term clusters were represented in Figures 4a, b. We can see that the learned the low-dimensional factor matrix W and similarity matrix S had clear clustering structures. The terms in pink box in the figure consist of research topics related to psychological health education. As Figure 4 shown, W and S had consistent clustering structures in some topics.

We conducted further investigation into the five topics and found that they primarily focused on the following several fields: 1) Psychological health problem, including psychological characteristics, psychological capital, and psychological stress. 2) Psychological health education and teaching, including psychological health education for college students, teaching reform, psychological counseling, art education, curriculum system, moral education, frustration education. 3) Strategy and service system, including growth path, student psychological health services, and education strategy.

We further validated the performance of HSNMF on student life dataset. Figures 5a, b show the visualization results for the original data matrix and the learned low-dimensional factor matrix W (the averaged silhouette score equals 0.9128). We can see that the individuals with different depression levels show the clearly clustering structure (Figure 5b). Additional analysis was conducted on the factor matrices W and H, where we inspected the rows of H with the large entries, and identified several features related to student depression status. The experimental results showed that three kinds of behaviors including “Academic performance,” “Taking note in class” and “Number of friends” were related to student depression status (depression). “Gender,” “Taking note in class” and “Like presentation” are related to student depression status (sometimes depression).

Next, we implemented an association analysis between depression levels and student class behaviors based on student life data. Logistic regression analysis (LogisticRegression function in Sklearn package) was implemented to measure the associations between student depression level and behavior variables. The regression coefficients for features “Number of friends,” “Gender” and “Taking note in class” are −1.32 (p-value = 0.000598), −0.97(p-value = 0.000034) and −0.27(p-value = 0.03), respectively. The results indicate that students' depression level is significantly correlated to their class performance and social communication strength (number of friends).

HSNMF can not only be used for sample clustering, but also be used for classification. We further validate the effectiveness of HSNMF via cross-validation where the original data are divided into two parts. The one is used to train model, the other is used to test. The results were presented in Figures 5c, d. We can see that “HSNMF + random forest” achieves the best performance compared to other competing methods in terms of accuracy, F1, and AUC metrics. Different from random forest, we used the low-dimensional factor matrix W obtained from HSNMF to train classification models, and obtain the better performance (random forest, accuracy 0.85). The results demonstrate that integrating HSNMF into the traditional machine learning algorithms can effectively improves the model's performance. One of the possible reasons is that the learned low-dimensional latent variable W contain more semantic information that can guide the training process for more effective classification tasks.

Although HSNMF achieves better performance in terms of accuracy, F1, and AUC metrics, it still needs to be further validated in more student life data. In this manuscript, we aimed to develop a novel algorithm to analyze the students' behaivour, and explored the relationships between depression levels and student class behaviors. For other questions, such as population study and behavior variables measurement, they are beyond the scope of our research.