Growing global social inequality, particularly its manifestation in urban environments, necessitates policy research. Existing studies often focus on economic indicators like income, education, and public services to measure urban inequality. However, a deeper understanding of the mechanisms shaping socio-spatial inequality is needed. This study addresses this gap by focusing on the opportunities and benefits derived from space, measuring spatial stratification through multifaceted factors contributing to disparities among spaces. The study's objectives are twofold: a methodological discussion on measuring spatial stratification using data-driven methods, and the application of this approach to understand socio-spatial inequalities in Seoul and Busan, South Korea. Socio-spatial inequality, defined as uneven distribution of opportunities, resources, and power across different spaces, is central to the study. The research uses a data-driven method, the K-means++ clustering algorithm, to analyze regional clusters and disparities. Map visualization is employed to interpret clustering results and to gain insights for policy.

Existing literature on urban inequality often relies heavily on income data, overlooking the multifaceted nature of inequality. While studies incorporating occupation, housing, and education offer insights into socioeconomic structures, they often fall short in explaining the reproduction of inequality. Multi-dimensional analyses of space provide a more comprehensive understanding of socioeconomic structures. The study builds on existing research by highlighting the spatial organization of urban inequality, focusing on the spatial arrangement of economic and service facilities and its influence on socioeconomic class. It draws upon George's (1973) work on land value and rent in understanding how landowners can monopolize surplus, increasing inequality. Furthermore, the concept of positional goods (Veblen, 1994), where location represents social status, is relevant to the analysis. The study examines the Korean context, where spatial terms reflect social status and economic class, further highlighting the close relationship between space and social stratification. The study also addresses methodological limitations in previous studies that use clustering algorithms without clear justification for algorithm selection.

This study employs a data-based social stratification approach, using data-driven methods to measure social stratification. It utilizes the K-means++ clustering algorithm, a dissimilarity-based method, for clustering regions and analyzing disparities. The selection of K-means++ over other algorithms like hierarchical clustering and DBSCAN is justified based on the study's objectives and data characteristics. K-means++ addresses the limitations of the standard K-means algorithm by strategically initializing centroids, leading to more optimal cluster formation and faster convergence. Silhouette analysis is used to determine the optimal number of clusters (K). Data selection is crucial in this approach. The study uses data from 15 public institutions in South Korea, reflecting the multifaceted characteristics of spaces. The data includes indicators related to economic and service facilities (transportation, culture, safety, medical treatment, education, and economy) and socioeconomic class (educational background, occupation, income, and wealth). Specifically, the data encompass factors like the number of subway stations, public parking spaces, road infrastructure, cultural facilities, medical facilities, safety features (CCTV, police stations, firehouses), educational institutions (elite high schools, private institutes), large-scale stores, and indicators of socioeconomic class (gross wage, educational attainment, professional skills, income, condominium prices). Log transformations, log(x+c), are applied to the data to maximize similarity and dissimilarity for optimal clustering. The value of 'c' is strategically chosen for each variable, considering minimum and maximum values to improve clustering efficiency. Map visualization is used to present and interpret the clustering results.

Socio-spatial maps of Seoul and Busan provide intuitive visualizations of the distribution of economic and service facilities and social classes. In Seoul, these elements are heavily concentrated in the southern area, while in Busan, the concentration is less pronounced but still concentrated in the southeast. Silhouette analysis indicates K=2 as the optimal number of clusters for Seoul and K=4 for Busan. In Seoul, the two clusters reveal significant disparities. Cluster 1 (Gangnam, Seocho, and Songpa districts) shows significantly higher values for all indicators compared to Cluster 0, indicating a concentration of opportunities and resources in this area. Cluster 1 has substantially more subway stations, public parking, roads, cultural facilities, theaters, medical facilities, safety features, and elite schools. It also has much higher average income, educational attainment, professional skills, and condominium prices. In Busan, the four clusters show less pronounced but still evident disparities. Cluster 2 (Haeundae district) stands out with superior values across most sectors. The study reveals distinct spatial patterns of social inequality in both cities, with specific regions offering higher levels of benefits and opportunities to residents.

The findings highlight the existence of significant socio-spatial inequalities in Seoul and Busan. The spatial clustering clearly shows how opportunities and resources are concentrated in certain areas, leading to disparities in the quality of life and access to essential services. The concentration of benefits and opportunities in specific areas, especially in Seoul's Gangnam area and Busan's Haeundae district, reflects and reinforces existing socioeconomic inequalities. These findings confirm the existence of spatial stratification, where socioeconomic status is closely linked to geographical location. The significant disparity in elite high school enrollment rates between these areas and the rest of the cities underscores the reproduction of social class through education. The study's results provide strong support for the hypothesis that socio-spatial inequality is deeply ingrained in the spatial structure of these cities.

This study demonstrates the utility of data-driven methods, specifically K-means++ clustering, in identifying and visualizing socio-spatial inequalities. The findings reveal significant disparities in Seoul and Busan, highlighting the concentration of resources and opportunities in specific areas. The results have strong implications for urban planning and policy, advocating for strategies to address these inequalities by promoting a multi-centric city structure that decentralizes opportunities. Future research could expand this analysis to other cities in South Korea, include more comprehensive data, and explore longitudinal changes in socio-spatial structures to track the evolution of these inequalities.

The study acknowledges limitations. The causal explanation linking location, benefits, opportunities, and socio-spatial inequality requires further investigation. The analysis relies on available data, and there may be missing data that could affect the results. The lack of time-series data prevents analysis of the evolution of these inequalities over time. Methodologically, while K-means++ was chosen based on a data-driven approach, comparing results using different clustering algorithms would strengthen the analysis. Finally, the analysis focuses on opportunities and resources but does not address political inequality from a spatial perspective and also does not cover the entire country.