The academic performance of students is one of the most important characteristics of the educational activities of an educational institution, by which professors and education managers can judge the results achieved or the problems that exist. Each university has its own systems for assessing academic performance, including various indicators of academic activities (Elisabeta & Alexandru, 2018). The academic performance of students in mathematical disciplines is usually assessed through computer tests, expert evaluation of semester projects, preparation level for seminars, and attendance ((Zafar et al., 2020). The quality of students' work is then used for effective educational process management, in making decisions about awarding state academic and named scholarships, issuing diplomas with honors, and other tasks. Thus, the research covers the following tasks: (1) how to effectively use historical data to predict student performance; (2) predictive models that are the most understandable to education managers; (3) how to reduce the subjective influence of experts on the final grades of students.

The researchers (Zhang et al., 2021) state that predicting student performance helps all stakeholders in the educational process. For example, students can choose appropriate courses or exercises and make plans for the semester accordingly (Ibrahim & Rusli, 2007), discovering the relationships between courses. Professors can adjust educational materials and curricula depending on students' abilities and identify students at risk within the group (Kloft et al., 2014). Managers in the education sector can review the curriculum and optimize the set of disciplines. The prediction could guide course selection and early warning on student learning, but finding the key factors affecting most education behaviors is a more important task. That is because (1) the key feature could correspond to interventions of education; (2) the reason of success or failure could reflect the pattern of student learning; (3) understanding of these factors could provide plan settings, course assignments, and learning sequence with suggestions. As (Kahramanoğlu, 2018) notes, the same characteristics help to indirectly analyze the hard and soft skills of prospective teachers.

The article (Yağcı, 2022) proposes a machine learning model for predicting the final scores of undergraduate students, using their scores for midterm exams as the input data. To forecast the exam scores, the performance metrics of random forest, k-nearest neighbor, support vector machines, logistic regression, and naive Bayes algorithms are calculated and compared. The dataset consisted of the academic performance scores of 1854 students at a state university in Turkey during the autumn semester of 2019-2020. Predictions are made using three types of features: midterm exam scores, as well as department and faculty names. The proposed model achieved a classification accuracy of 70–75%. The insufficient accuracy of the model can be explained by the presence of low-variable features.

Authors of the study (Oluwadele et al., 2023) assessed academic performance in the field of medical education through indicators of students' acquisition and perception of knowledge, level of confidence, ease of use of the e-learning platform and willingness to recommend e-learning. The flaw of the proposed approach lies in the qualitative nature of the analyzed features, their strong dependence on the opinion of different experts.

Researchers (Liu & Yu, 2023) uses the online student actions that the e-learning platform allows you to collect, namely: the time it takes to answer a question or submit an assignment, the number of missed questions, excessive tardiness, cheating on tests, derogatory comments in online discussions. The disadvantage of this approach is that the data was taken without additional transformations that affect the performance of the model.

Exploration (Ye et al., 2022) offers a model for predicting the effectiveness of online learning, based on the selection and merging of features. The model uses the relationship between behaviors and examines whether combinations of behaviors are better predictors of academic performance.

The researchers (Yadav & Deshmukh, 2023) emphasize that the most significant factors influencing students' academic performance are low initial scores, family support, living arrangements, gender, previous performance, students' internal assessment, average academic performance, and students' activity in e-learning. They also note that the plan to improve students' academic performance should take into account additional consultations for students with low performance. This helps both students and teachers to overcome the challenges faced during education. The idea of selecting students for additional consultations formes the basis of the fourth stage of the proposed method.

Thus, it is possible to identify the following features that are used to predict academic performance: attendance coefficient; ratio of scores for work or campus activities to the total possible certification score; performance dynamics, the change in scores between the first and second certification. This change in estimates is the basis of the proposed method.

The authors (Yang et al., 2018) designed several week learning activity, includes homework, quizzes, video-based learning. They applied multiple linear regression model to predict students’ academic scores. They also reworked the well-known metrics for assessing the accuracy of the models, using data obtained during the cross-validation stage. They believe, however, that the models are applicable to the courses, learning activities and data attributes for which they were developed.

Researchers note (Troussas et al., 2013), that clustering users into groups with common interests is very useful when learning multiple languages. They used the k-means algorithm because of its simplicity. Authors (Bayazit et al., 2022) use the same clustering algorithm to identify students with low engagement. A known drawback of the algorithm is that the number of clusters is set a priori and does not sufficiently reflect students with a satisfactory level of interaction. Two clustering quality indexes are tested and compared in (Petrovic, 2006). Experimental results comparing the effectiveness of a multiple classifier with the two indexes implemented show that the system using the Silhouette index produces slightly more accurate results than the system that uses the Davies-Bouldin index.

Based on the literature review, it can be concluded that there is significant interest in predicting students' academic performance using machine learning methods. It has been established that academic performance prediction is carried out either through binary classification – whether a student will pass the exam or not, or through regression to predict the potential score for the exam. It has been identified that methods grouping students based on similarities in learning trajectories are not commonly applied.

The proposed methodology for predicting the final score includes five stages shown in Figure 6. The first stage involves performing a statistical analysis to identify imbalances, data omissions, high and low correlations. In the second stage, new features are formed, and the dataset is aggregated by student index and group number, forming a performance for each student. In the third stage, with a sufficient number of scores in the aggregate, a binary classification predictive model for students who passed and did not pass the exam is built along with an error assessment. There are several methods that implement a binary classification and the most effective methods are those derived from linear discriminant analysis (such as Quadratic Discriminant Analysis (QDA), Regularized Discriminant Analysis (RDA) and Logistic regression (Araveeporn, 2023). The choice of logistic regression is dictated by the fact that it does not assume normal distribution of independent variables and homogeneity of variation-covariance matrices. The quality of separation is evaluated using the F1 metric - the harmonic mean of accuracy and completeness:

, (1)

where TP, FP, FN – are true positive, false positive and false negative forecasts.

In the fourth stage performance is forecasted using linear regression. As a result, a trend and a predicted performance score are determined for each student. The quality of prediction is evaluated through mean absolute error (MAE), mean squared error (MSE), and root mean squared error (RMSE) (Aissaoui et al., 2020):

, , (2)

where yi is the prediction and xi is the true value, n – the observations number.

Finally, the fifth stage entails clustering students based on the similarity of their score set. The quality of clustering is determined by the silhouette coefficient. It measures how well an object matches its cluster compared to other clusters: a value close to 1 indicates that the object is well clustered, a value close to 0 indicates that the object is on the border between two clusters, a negative value indicates incorrect clustering.

The Silhouette Score can be calculated for each feature in the cluster and then averaged for an overall assessment of the clustering quality (Bonaccorso, 2018). The formula for calculating the silhouette coefficient for the individual object i is as follows:

(3)

where a(i) — The average distance from feature i to all other features in the same cluster. This value indicates how close the features within the cluster are to each other; b(i) — The minimum average distance from feature i to features in the nearest other cluster. This value indicates how close the feature is to other clusters.

The average value of the silhouette coefficients of all objects is calculated according to the formula:

, (4)

where n is the total number of objects.

The proposed method differs from known analogs in that, firstly, the dimensionality of the feature space increases due to the normalization of scores onto a single scale and the creation of new features: the index and rank of students, as well as the changes in performance across various activities for each student. Secondly, students at academic risk are forecasted, and the statistical significance of the features included in the model is evaluated. Thirdly, for each student, the final score for the semester is forecasted using an linear regressive model of academic performance. Fourthly, groups of students with similar learning trajectories are identified for customization of consultations.

The practical significance of this method lies in the possibility of obtaining new knowledge about the learning process.

To identify methods and key factors influencing academic performance we performed the literature review. To analyze, customize and predict academic performance based on the data from e-learning platforms we offered the multistage methodology. At the first and second stages it applies statistical methods to form new features and improve the predictive ability of models. Thus, correlation analysis revealed a strong relationship between a number of features. Therefore, the dynamic features introduced into the feature space, taking into account the change in academic performance over time. The problems of predicting exam grades, classifying students into passing and non-passing an exam, as well as clustering students by sets of grades are solved at the third, forth and fifth stages consequentially. The results of the classification of exam grades are as follows: the estimate of the harmonic mean value of accuracy and completeness for the initial data F1 is 82 %. The linear regression model demonstrated the following error values: MAE = 0.1, MSE = 0.02, RMSE = 0.1, R2 = 0.7.

Classifying, clustering, and predicting academic performance can be useful for multiple stakeholders such as teachers, students, and institutions. For teachers, these tools help identify at-risk students, adapt curricula, and design targeted interventions. Students benefit by gaining insights into their performance trends, enabling better planning of study strategies and group work. Institutions can use these models to identify program-wide trends, evaluate curriculum effectiveness, and allocate resources to address systemic issues.

This article explores the use of machine learning methods to predict student performance, emphasizing several critical steps in the process. To ensure that all features are on a comparable scale, missing data is addressed, and normalization is applied. Key academic components—such as homework, projects, midterm scores, and test scores—serve as predictors, while new features are created to enhance the models' predictive power. The study employs clustering to analyze student behavior, multiple linear regression for performance prediction, and logistic regression for binary classification, such as pass/fail outcomes. The models are evaluated using metrics like mean absolute error (MAE), mean squared error (MSE), and root mean squared error (RMSE) to assess their accuracy. Additionally, Principal Component Analysis (PCA) and Kernel Density Estimation (KDE) are used to visualize the data, providing deeper insights into its structure and distribution. Together, these methods offer a robust framework for understanding and predicting academic performance.

At the same time, the proposed multi-method has a number of limitations. For example, when performing the first two stages, which include statistical analysis and generation of additional features, it is necessary to make some efforts to normalize the data, set a threshold for excluding strongly correlated features, and correctly specify pairs of different-temporal features of the same name that are converted into dynamic ones. In addition, when using methodology in universities of a humanitarian orientation, the Programming skills attribute can be replaced, for example, by attendance.

At the last stage, the k-means clustering method is used to divide students into groups. This is a simple and straightforward method, which, unlike more modern clustering methods (e.g., DBSCAN (Vladova, 2024), DBCLASD (Sheikholeslami & Zhang, 1998), WaveClaster (Sheikholeslami & Zhang, 1998)) involves a separate expert study on the number of clusters. This study includes an estimate of the inertia, silhouette index, and Davis-Baldwin index and results in a recommended cluster count interval. Within this interval, the educational manager must select one number – the exact number of clusters. Such a choice requires a certain expertise from the decision-maker, but at the same time allows him to take into account the administrative restrictions on the number of groups of students studying in different programs.

In the subsequent study, it is proposed to exclude from further consideration students at academic risk identified at the first stage (Shou et al., 2024), and also to investigate the impact on academic performance of signs of IP address coincidences when doing homework (Komosny & Rehman, 2022), duration of work, start and end time of work. In addition, it is necessary to develop dashboards that greatly facilitate model settings and decision-making for managers and teachers of educational institutions.

The literature review highlights various approaches to predicting student academic performance using machine learning and statistical methods. Researchers emphasize the importance of identifying key factors influencing performance, such as prior academic scores, and engagement in e-learning platforms. Various models, including regression analysis and classification techniques, have been utilized, demonstrating mixed success rates, while suggesting the need for further feature selection and data transformation to enhance predictive accuracy. The weaknesses of the approaches include insufficient accuracy of the models, the use of qualitative features, and the influence of experts

The study carried out a comprehensive statistical analysis of students' scores for a math discipline. This involved assessing data imbalance, identifying gaps, constructing score distribution densities, and exploring the correlation matrix of scores. These analyses provide valuable insights into the distribution and relationships of student scores, laying a strong foundation for further modeling and predictions.

The study changed the dimensionality of the feature space by normalizing scores to a common scale and creating new features such as student indexes, ranks, and differences between scores at different time points. This expansion of the feature space enhances the richness of the dataset and can potentially lead to more robust and accurate predictive models.

By developing models to predict students at academic risk and evaluating the statistical significance of the included features, the study addresses the crucial issue of identifying and supporting students who may be at risk of underperforming. This proactive approach can help institutions tailor interventions and support to students who need it most.

The study's plan to customize consultations for student groups with similar learning trajectories reflects a student-centric approach to enhancing academic performance. By recognizing the diverse needs of student cohorts and tailoring support accordingly, the study aims to foster a more personalized and effective learning environment.

The approach of predicting exam scores for individual students demonstrates a commitment to providing comprehensive support beyond mere assessment. By leveraging analysis, modeling, and customization of consultations, the study aims to proactively improve students' academic performance levels within university settings.

The proposed multi-method to the analysis of data from electronic platforms shows a picture of student engagement close to reality. The progress track, predictive assessment and clustering allows educational managers and teachers to assign consultations to groups of students at academic risk and with deteriorating academic performance.