Clustering Analysis of School Student Distribution in Bojonegoro Regency with Kernel K-Means

Background: Education is a fundamental aspect that plays an important role in determining the progress of a nation. In Indonesia, education equity remains a major challenge, particularly in relation to the gap between urban and rural areas. Bojonegoro District, with its diverse geographical and social characteristics, reflects this issue of uneven educational access. Objective: This study aims to examine the 2022 distribution of study groups at different education levels (kindergarten, elementary school, junior high school, high school, and vocational school) in Bojonegoro using descriptive statistics, normality testing, and the Kernel K-Means clustering algorithm. Methods: Data were tested for normality using the Kolmogorov-Smirnov method. The clustering was performed by comparing four kernel types (Dot, Polynomial, Gaussian, and Sigmoid) to determine the most effective approach based on the Average Within Cluster Distance (AWCD) and the elbow method principle. Results: The findings indicate that the distribution of study groups at the kindergarten and elementary school levels is relatively even and follows a normal pattern. In contrast, the distributions at the junior high school, high school, and vocational school levels remain uneven. The Kernel K-Means algorithm with the Dot kernel produced the most optimal results, identifying five main clusters that reflect regional disparities in educational participation. Conclusion: This study demonstrates the novelty of applying Kernel K-Means in the educational context to uncover spatial disparities. The resulting clusters offer valuable insights into education inequality in Bojonegoro. These insights can inform policymakers in designing more targeted, equitable, and data-driven education policies.