Clustering of Higher Education Institutions Based on Tuition Fee and Living Cost of International Students Using the Gaussian Mixture Models Method

Abstract

The wide variation in tuition fees and living costs among higher education institutions across different countries creates significant challenges for prospective international students in making informed enrollment decisions. This study applies the Gaussian Mixture Models (GMM) method to cluster higher education institutions based on the financial burden of international students. The dataset was obtained from the Kaggle platform, comprising 1,407 records covering multiple universities worldwide, with four primary features: Tuition_USD, Living_Cost_Index, Rent_USD, and Visa_Fee_USD. The research methodology encompassed data collection, preprocessing with Z-Score normalization, determination of the optimal number of clusters using the Bayesian Information Criterion (BIC) and Akaike Information Criterion (AIC), and parameter estimation via the Expectation-Maximization (EM) algorithm. The GMM method was selected for its probabilistic approach, which is well-suited to modeling complex and multivariate data distributions. The experimental results demonstrate that the GMM model with K=7 clusters effectively identifies seven distinct university groups with meaningfully differentiated cost profiles, converging at iteration 139 with BIC = 11,196.28 and AIC = 10,650.36. The identified clusters range from affordable public universities to exclusive elite institutions, offering nuanced insights into the financial landscape of international higher education. These findings confirm that GMM-based soft clustering adequately uncovers latent structural patterns in right-skewed, asymmetric international student cost data, outperforming hard clustering methods such as K-Means in handling distributional complexity.