Spatial stratification and socio-spatial inequalities: the case of Seoul and Busan in South Korea

As social inequality worsens worldwide, its manifestation in complex urban environments has become a key policy issue. Prior work often measures inequality with economic, income, education, public service, and health indicators, or with subjective well-being, yet a better understanding of mechanisms shaping socio-spatial inequality is needed. This study focuses on opportunities and benefits conferred by space and measures spatial stratification via multifaceted factors that create disparities among spaces. Objectives are twofold: (1) to discuss methodological perspectives, approaches, and data for measuring spatial stratification using data-driven methods; and (2) to apply this approach to understand socio-spatial inequalities due to spatial stratification in South Korea, focusing on Seoul and Busan at the district/county level. The study conceptualizes socio-spatial inequality as uneven spatial distribution of opportunities, resources, and power that produces significant disparities across spaces. It adopts a data-driven social stratification perspective and applies a dissimilarity-based clustering algorithm (K-means++) to cluster regions and analyze disparities. Map visualization is used to identify spatial forms of inequality and inform policy. The study compiles multidimensional, country-specific indicators from 15 South Korean public institutions and applies data transformations to maximize similarity/dissimilarity for clustering. Tools: Python 3.7 and Scikit-learn 0.22.2.

Socio-spatial inequality is multidimensional and cannot be captured by income alone; studies also examine occupation, housing, education, and broader socioeconomic structure, yet often miss the processes by which inequality is reproduced. Spatial arrangement of economic and service facilities and class distributions structure urban space socioeconomically. Following George (1973), rising land values allow landlords to capture growth surplus; location and accessibility to facilities shape opportunities, advantages, and disadvantages, influencing economic performance and reproducing inequality. Spatial exclusivity and positional goods (Veblen) link coveted residential locations to class signaling, raising barriers to entry and excluding others. Class and social strata, pervasive across societies, reveal socioeconomic structure and underlie inequality dynamics, making them useful lenses for socio-spatial analysis. In the Korean context, dichotomies such as metropolitan vs rural, in-Seoul vs out-of-Seoul, and Gangnam vs Gangbuk encode identity, status, and class; spatially rigid class separation affects opportunities and can reproduce inequality if certain areas monopolize opportunities. Prior Korean regional inequality research emphasized metropolitan–rural economic gaps; however, multifaceted inequality factors concentrate in Seoul and Busan, making them apt cases to reflect broader social structure. Method choices in clustering: numerous algorithms exist with no definitive statistical criterion for preference; different methods can yield different outcomes. Many studies lack clear justification for algorithm selection. A problem-centric, data-driven selection aligned with objectives, context, and data characteristics is advised.

Design: Data-driven social stratification approach to measure spatial stratification via clustering based on similarity/dissimilarity in multidimensional indicators. Study area and units: Seoul Special City and Busan Metropolitan City, South Korea; analysis units are districts (gu) and county (gun) belonging to the two cities. Clustering method: K-means++ (Euclidean distance-based), chosen to directly optimize within-cluster similarity and assign each unit to exactly one cluster. Initialization via K-means++ improves centroid seeding and convergence relative to K-means. Number of clusters K selected using silhouette analysis; higher silhouette indicates better-separated clusters. Alternative methods considered: Hierarchical clustering and DBSCAN are discussed but not used, as the goal is not hierarchical nesting and the data do not require density-based approaches (no geographic coordinates used). Data selection: Indicators reflect spatial arrangement of economic and service facilities and socioeconomic class. Data drawn from 15 South Korean public institutions; variables include: - Economic and service facilities: Transportation (Subway stations; Public parking spaces; Road extension (m); Road extent (m²)); Culture (Cultural facilities: public libraries, museums, art galleries, centers, local culture centers; Movie theaters); Medical treatment (Tertiary hospitals); Safety (CCTV; Police stations including substations/community centers; Firehouses); Education (Enrollment rates of elite high schools; Number of private educational institutes); Economy (Large-scale stores: SSM, department stores, shopping centers, multi-shopping complexes, etc.). - Class: Education (High educational background: university/vocational college+ vs high school or below); Occupation (High professional skill: professional+ vs others); Income (High income: 4th quartile vs 1st quartile); Wealth (Average price of a condominium; district gross wage and salary based on location of withholding agent; unit for gross wage and salary is million KRW; condo price unit is 1,000 KRW). Ratios for upper vs lower tiers derived from national census/KEIS data. Data transformations: To emphasize ratios relevant to social stratification and maximize similarity/dissimilarity for distance-based clustering, log transformations applied to all non-ratio variables. Because zeros exist, transform as log(x + c), where c is selected per variable as a multiple of 10 one digit greater than that variable’s maximum value, to retain effective distances among small values while moderating large values. Ratio variables were not transformed. Illustrative comparison of c=1 vs variable-specific c shows improved clustering. Tools: Python 3.7; Scikit-learn 0.22.2. Visualization: socio-spatial maps for variables and cluster assignments. Model selection: Silhouette analysis conducted for K=2–6; K chosen per city based on highest silhouette and interpretability.

Visual socio-spatial patterns: - Seoul: Transportation, culture, safety, education, economy, and class factors concentrate south of the Han River; highly educated, professional, high-income, wealthy classes predominantly reside there. - Busan: Concentrations are weaker than Seoul but many facilities cluster in the southeast (East Busan); gross wage and salary appear higher in the west (linked to port/logistics), while higher-class residents are more concentrated in the southeast. Silhouette analyses: - Seoul: Highest silhouette at K=2 (0.59); scores decrease with K=3 (0.511), K=4 (0.445), K=5 (0.437), K=6 (0.415). - Busan: Best at K=4 (0.364); K=2 and K=3 have clusters with negative silhouette segments; scores decrease for K=5 (0.300) and K=6 (0.255). Seoul clustering (K=2): - Cluster composition: Cluster 1 = Gangnam, Seocho, Songpa (3 districts); Cluster 0 = remaining 22 districts. - Mean disparities (Cluster 1 vs Cluster 0): Subway stations 26.32 vs 12.72; Public parking spaces 13,717.45 vs 6,534.79; Road extension (m) 397,962.4 vs 306,319.4; Road extent (m²) 5,408,973 vs 3,086,839; Cultural facilities 21.21 vs 12.48; Theaters 3.58 vs 2.74; Tertiary hospitals 1.29 vs 0.31; CCTV 2,863.44 vs 1,954.38; Police stations 22.26 vs 16.75; Firehouses 6.00 vs 4.41; Elite high school enrollment rate 9.77 vs 3.17; Private educational institutes 1,146.15 vs 311.94; Large-scale stores 27.03 vs 15.55; Gross wage and salary (million KRW) 19,541,940 vs 4,255,825; High educational background (%) 70.32 vs 52.17; High professional skill (%) 42.77 vs 28.06; High income (%) 43.49 vs 25.99; Average condominium price (1,000 KRW) 1,303,537 vs 554,130. Overall, Cluster 1 dominates across all sectors. Busan clustering (K=4): - Cluster geography: Cluster 2 = Haeundae (single-district elite cluster); Cluster 1 = six adjacent central-eastern districts (Geumjeong, Dongnae, Yeonje, Busanjin, Nam, Suyeong); Cluster 0 = seven western/central districts (Buk, Sasang, Saha, Seo, Jung, Dong, Yeongdo); Cluster 3 = edge districts (Gangseo, Gijang). - Mean disparities (selected): Subway stations: C2 15.00; C1 9.46; C3 8.38; C0 4.73. Public parking spaces: C2 3,495.76 highest. Cultural facilities: C2 10.00 vs C1 6.50 vs C0 5.59 vs C3 4.66. Theaters: C2 6.00 vs C1 1.38 vs C0 0.79 vs C3 1.00. Police stations: C2 16.00; C1 14.21; C0 9.91; C3 7.77. Firehouses: C2 7.00 vs others lower. Education: Elite high school enrollment C2 24.6 vs C1 5.63 vs C0 3.83 vs C3 2.75; Private institutes C2 602.00 vs C1 317.79 vs C3 167.88 vs C0 115.08. Economy: Large-scale stores C2 26.00 vs C1 12.74 vs C0 7.17 vs C3 6.42; Gross wage and salary (million KRW) C2 2,696,997; C3 2,571,038; C1 1,851,498; C0 1,570,900. Class: High education (%) C2 49.27; C1 48.16; C3 41.04; C0 38.58. High professional skill (%) C2 24.79; C1 22.42; C3 17.44; C0 16.83. High income (%) C2 29.03; C3 27.72; C1 21.36; C0 16.08. Average condo price (1,000 KRW): C2 376,242; C1 320,561; C3 272,477; C0 199,462. Disparities are smaller than Seoul but still pronounced, with Haeundae (Cluster 2) most advantaged on most indicators. Overall: Certain regions densely populated by socioeconomically upper-class residents concentrate facilities, opportunities, and benefits, revealing clear socio-spatial stratification in both cities.

The findings address the research goal by empirically uncovering spatial stratification patterns via clustering and visualization. In Seoul, a stark bifurcation emerges: Gangnam, Seocho, and Songpa form a highly advantaged cluster across transportation, safety, culture, education, economy, and class, contrasted with the rest of the city. In Busan, while disparities are milder, Haeundae stands out as a concentrated node of opportunities and higher-class residency. These patterns substantiate the proposed mechanism whereby the spatial arrangement of facilities and class composition shape socio-spatial inequality by differentially distributing access to benefits and opportunities. The maps and cluster statistics provide interpretable, policy-relevant evidence of where inequalities are concentrated and how they align with popular socio-spatial identities (e.g., Gangnam vs. others; East vs. West Busan). The results are consistent with theories of positional goods, accessibility-driven opportunity structures, and the reproduction of class advantage through educational pipelines (e.g., elite high school enrollment).

Methodologically, the study demonstrates a data-driven approach to measuring spatial stratification using K-means++ with tailored log(x+c) transformations and silhouette-based K selection, coupled with map visualizations for interpretation. Empirically, Seoul is optimally partitioned into two clusters with large disparities concentrated in Gangnam–Seocho–Songpa, while Busan partitions into four clusters with Haeundae most advantaged. These results indicate that regions with concentrations of upper-class residents offer higher levels of public transport, safety, medical treatment, culture, education, and economic opportunities and benefits. Policy implications include recognizing and addressing the geography of opportunities: reducing gaps by decentralizing economic and service facilities and developing multi-centric urban structures so that education, culture, transportation, and industry are not mono-centrically concentrated. Expanding the geography of opportunities can improve access in underserved living areas. Future research should incorporate time-series data to assess changes in socio-spatial structures and compare multiple clustering algorithms for robustness and comprehensive interpretation.

The causal chain linking location, benefits/opportunities, class, and socio-spatial inequality is tentative. Data selection entails some arbitrariness and is constrained by availability; important dimensions were missing. Time-series data were unavailable, limiting dynamic analysis. The approach captures opportunities and resources but not political inequality spatially. The analysis covers Seoul and Busan only, not national-scale inequalities, which may be larger between Seoul and other regions. Methodologically, only K-means++ was applied; results were not compared across alternative clustering algorithms, which should be explored in follow-up studies.