Enhancing Urban and Peri-Urban Zoning Using Spatially Constrained Clustering: Evidence from the Jakarta–Bandung Mega-Urban Region

Abstract

Rapid urbanization in the Global South has intensified the formation of mega-urban regions, where conventional urban–rural classifications often fail to capture the complexity of peri-urban systems. In the Jakarta–Bandung Mega-Urban Region (JBMUR), rapid land-use change and socio-economic transformation have produced hybrid landscapes that challenge binary zoning approaches. This study aims to delineate urban, peri-urban, and rural spatial structures using a spatially constrained clustering framework and to evaluate the performance of the Rustiadi Quantitative Zoning Method-2 (RQZM-2) compared with conventional non-spatial clustering (Non-RQZM). Built-environment, accessibility, environmental, and socio-economic indicators derived from remote sensing and spatially disaggregated statistical data were analyzed using grid-based K-Means clustering. Comparative validation using internal metrics, stability analysis, spatial coherence diagnostics, and statistical differentiation tests indicates that RQZM-2 produces more stable, spatially coherent, and interpretable clusters than conventional clustering. The validated four-cluster solution identifies compact urban cores, extensive peri-urban transition belts, and two distinct rural sub-types, revealing a functionally differentiated regional structure across the JBMUR. These findings demonstrate that incorporating spatial contextualization into clustering improves the empirical representation of peri-urban spatial continuity and provides a robust analytical basis for spatial zoning and regional planning in rapidly urbanizing mega-urban regions.

1. Introduction

Urbanization continues to reshape global population patterns, with urban populations exceeding rural populations worldwide. According to United Nations projections, urban residents will account for approximately 68% of the global population by 2050, corresponding to an increase of around 2.5 billion people in urban areas since 2018 [1]. This transition has progressed more rapidly in the Global South [2], particularly in Asia, where accelerated urban growth has stimulated the emergence of Extended Metropolitan Regions (EMRs) [3]. Over time, several EMRs have expanded and merged, forming even larger urban agglomerations known as Mega-Urban Regions (MURs) or megalopolises, characterized by continuous urbanized zones that link multiple metropolitan centers [4]. These regions are characterized by continuous urbanized landscapes, intensified economic activity, strong urban–rural functional linkages, and rapid land-use transformation driven by population growth, industrialization, transportation infrastructure, and policy interventions [5,6,7].

Within this broader transformation, peri-urban or urban–rural fringe areas represent the most dynamic yet vulnerable spatial zones [8,9]. These transitional landscapes integrate rural and urban characteristics, exhibit mixed land-uses and livelihoods, and undergo rapid socio-ecological change. Despite their significance, the conceptual definition of peri-urban areas remains contested and ambiguously defined in both geographic and theoretical terms [10,11]. The traditional binary distinction between “urban” and “rural” is increasingly inadequate for capturing the spatial gradients and hybrid conditions that characterize contemporary settlement systems [12]. Peri-urban landscapes also perform critical ecological functions, including biodiversity conservation, ecosystem service regulation, and buffering urban environmental pressures [13,14], while simultaneously facing governance challenges arising from blurred boundaries and fragmented administrative jurisdictions [9,15].

A wide range of terminologies including rural–urban gradient, continuum, periphery, edge growth, rurban, exurban, urban sprawl, urban expansion, outskirts, semi-urban or semi-rural, as well as desakota in Asia, post-suburbia in North America, and technoburbia in both European and Asian cities have been used to describe the diverse manifestations of peri-urban areas [3,16,17,18]. Among these, the desakota phenomenon encompasses more than the conventional notion of peri-urban. It refers to closely interlinked rural–urban livelihoods and deeply integrated systems of communication, transport, and economic activity, forming hybrid spatial configurations in which agriculture, industry, services, and settlements coexist within a single functional landscape [19]. Embedded within McGee’s broader frameworks of EMRs and MURs, this perspective conceptualizes peri-urban transformation as a structurally integrated, functionally hybrid process driven by corridor-based, leap-frogging expansion, and socio-economic networks extending beyond administrative boundaries [3,20,21].

Despite these conceptual advances, many approaches to peri-urban identification continue to rely on administrative delineations or fixed empirical thresholds, limiting their ability to capture the multidimensional, spatially explicit, and dynamic nature of rural–peri-urban–urban (R–P–U) transitions. Early studies primarily relied on experiential and qualitative delineations, describing peri-urban areas as transitional zones extending several kilometers beyond urban cores, with spatial extents varying by regional context [22,23,24]. However, R-P-U zoning methodologies have progressively evolved toward quantitative approaches integrating remote sensing, spatial statistics, and geospatial analytics. Recent global studies illustrate this shift, for instance, China’s Pearl River Delta reveals hybrid desakota-like zones amid rapid industrialization [25]. In mature metropolitan corridors such as the Boston–Washington megalopolis, spatial modeling techniques have been employed to identify metropolitan patterns of urban sprawl [26]. Studies in Greater Tokyo demonstrate the scalability of advanced spatial analytics for analyzing highly dense metropolitan systems [27].

Within this evolving methodological landscape, land-use and land cover (LULC) change provides a critical analytical lens for understanding urban–rural interactions. Capturing peri-urban complexity, however, requires approaches that integrate physical, socio-economic, and spatial dimensions. Consequently, earlier qualitative delineations have gradually been complemented and replaced by a range of quantitative techniques, including threshold-based methods [28,29,30], breakpoint method [31,32], mutation detection and wavelet transformation [33,34,35], fuzzy logic functions [36], and spatial clustering approaches [37,38,39,40,41].

Spatial clustering partitions geographic data into a set of meaningful subgroups by grouping spatial units that exhibit similar attributes or are located in close proximity, while separating those that are dissimilar or spatially distant. This principle is theoretically grounded in Tobler’s First Law of Geography, which states that “everything is related to everything else, but near things are more related than distant things” [42]. Recent advances in spatial analysis have increasingly emphasized the importance of spatially constrained clustering techniques for zoning. Traditional clustering methods, including K-Means, have been widely used to identify spatial zoning based on multivariate attributes; however, these approaches often ignore spatial dependence and may produce fragmented spatial patterns that are difficult to interpret in geographic contexts [43]. To address this limitation, several spatially constrained clustering approaches have been developed in spatial analysis and regional science, including methods such as SKATER [44], AZP (Automatic Zoning Procedure) [45], and REDCAP [46]. These approaches incorporate spatial contiguity and adjacency relationships during the clustering process, enabling the formation of spatially coherent regions that simultaneously satisfy attribute similarity and geographic connectivity. Consequently, spatial zoning outcomes become more interpretable and analytically meaningful, particularly in studies of urban systems, regional development, and peri-urban transformation.

Among the spatial zoning approaches that incorporate these principles, the Rustiadi Quantitative Zoning Method 2 (RQZM-2) integrates multivariate clustering with explicit spatial contiguity and compactness constraints [47,48]. Contiguity denotes the connectedness of its constituent spatial units, meaning that each unit shares a boundary with at least one other unit within the same region, while compactness refers to the spatial density or tightness of a region. To incorporate these spatial properties into the clustering process, RQZM-2 introduces spatial contextual influence by adjusting variable values based on neighborhood relationships [49]. This contextualization is operationalized through an aggregation function that integrates attribute similarity with spatial adjacency among neighboring spatial units, thereby embedding spatial dependence directly within the clustering process rather than imposing it as a post hoc constraint [47]. Implemented through Rustiadi Quantitative Zoning Method Contiguous II (C”) framework [49], this approach enables K-Means-based zoning to generate spatially coherent R–P–U zones. Recent applications of the RQZM approach further demonstrate its potential: Jatayu [41] employed RQZM to capture detailed spatial and socio-economic dynamics, including changes in urban form, while Kurnia [48] applied it to identify priority zones for industrial, residential, and agricultural protection using a comprehensive set of indicators framed within an urban–rural development perspective.

This study applies the RQZM-2 framework to the Jakarta–Bandung Mega Urban Region (JBMUR), an emerging mega-urban corridor in Indonesia characterized by strong spatial spillover effects and rapid peri-urban transformation. Early empirical studies in the Jakarta Metropolitan Area, commonly referred to as Jabodetabek, have documented rapid land-use conversion and corridor-based urban expansion, reflecting intensive peri-urban transformation associated with metropolitan spillovers [50,51]. Similar patterns are evident in the Bandung Metropolitan Area, where sustained growth of built-up land, declining agricultural areas, and increasing differentiation between urban cores, suburban, and rural hinterlands have been widely reported [52,53]. Subsequent studies examining the EMRs of the Jakarta and Bandung metropolitan areas further demonstrate substantial physical and functional integration dynamics between these metropolitan areas, forming a continuous urbanized corridor across the region [54,55,56]. These dynamics represent an early manifestation of mega-urban formation in Indonesia, in which peri-urbanization emerges as a structurally embedded and spatially continuous phenomenon rather than a residual transition zone [57].

To analyze these dynamics, this study applies the RQZM-2 framework as a spatially constrained clustering approach that incorporates spatial contiguity and neighborhood effects. By integrating physical and socio-economic variables with spatial contextual influence, the approach aims to produce a more spatially coherent representation of peri-urban dynamics in the JBMUR. The objectives of this study are (1) to delineate urban, peri-urban, and rural spatial structures using a spatially constrained clustering framework, and (2) to empirically evaluate the performance of the spatially constrained RQZM-2 method compared with a conventional non-spatial clustering approach (Non-RQZM). This approach provides a methodological contribution by demonstrating how spatially constrained clustering improves the empirical representation of peri-urban spatial continuity relative to conventional clustering techniques.

2. Materials and Methods

2.1. Study Area

The case study was conducted in the Jakarta–Bandung Mega-Urban Region or JBMUR, widely recognized as the largest mega-urban region in Indonesia. JBMUR comprises a rapidly expanding ~200 km urban corridor that functionally integrates urban and rural systems while connecting the two major metropolitan centers of Jakarta and Bandung [58]. Spatially, the region encompasses a complex assemblage of cities and regencies spanning Banten Province, Special Capital Region of Jakarta, and West Java Province. The Jakarta Metropolitan Area consists of Jakarta as the core city, surrounded by adjacent cities and regencies collectively known as Bodetabek (Bogor, Depok, Tangerang, and Bekasi). In parallel, the Bandung Metropolitan Area includes Bandung City as the core, along with Cimahi City and the regencies of Bandung and West Bandung. These two extended metropolitan systems are linked by three intermediary regencies (Karawang, Purwakarta, and Cianjur) forming a continuous mega-urban corridor [59] (Figure 1).

2.2. Variables and Indicators

This study utilized remotely sensed LULC classification derived from Landsat 9 satellite imagery for the year 2025, acquired from the USGS Earth Explorer. The study area is covered by Landsat path/row combinations 122/064, 122/065, and 121/065, ensuring complete spatial coverage of the JBMUR. To delineate R–P–U zoning within the RQZM-2 framework, this study integrated indicators representing four major dimensions: built environment, accessibility, environmental conditions, and socio-economic characteristics. These indicators were derived from multiple spatial datasets to capture the multidimensional characteristics of regional transformation.

Built-environment characteristics were represented by building density (BD), measured as the number of buildings per square kilometer, and built-up fraction (BUF), expressed as the percentage of built-up land within each spatial unit. Accessibility conditions were quantified using an Accessibility to Arterial Roads (AAR) index, calculated as the inverse of the distance from each spatial unit to the nearest arterial road using OpenStreetMap (OSM) data. Environmental conditions were characterized using Normalized Difference Vegetation Index (NDVI). Socio-economic conditions were represented by several indicators, including the Human Development Index (HDI), population density (PD), open unemployment (OU), poor population (PP), and the farmers ratio (FAR), all expressed per 1000 population, along with the non-agricultural Gross Regional Domestic Product ratio (NAGRDP) to capture the relative importance of non-agricultural economic activities. In addition, a Regional Development Index (RDI) was constructed to represent spatial variation in regional service availability and development capacity across the study area. A summary of all variables and indicators is provided in

Table 1. Variables used in the study.

Variable		Unit	Year	Definition	Data Source
BD	Building Density	buildings/km2	2025	Density of building footprints aggregated at grid level.	Global Building Atlas
BUF	Built-up Fraction	%	2025	Percentage of built-up area within each raster cell.	LULC classification (30 m)
AAR	Accessibility to Arterial Roads	index	2025	Accessibility index based on inverse distance to arterial roads.	OpenStreetMap (OSM)
VC	Vegetation Cover	0–1	2025	Fraction of vegetation derived from NDVI satellite imagery.	Landsat 9
HDI	Human Development Index	index	2024	Composite indicator of education, health, and income dimensions	Indonesia Central Bureau of Statistics
PD	Population Density	persons/1000 population	2024	Spatial distribution of population based on gridded population data.	WorldPop and Indonesia Central Bureau of Statistics
OU	Open Unemployment	persons/1000 population	2024	Open unemployment rate per 1000 population.	Indonesia Central Bureau of Statistics
PP	Poor Population	persons/1000 population	2024	Poverty rate per 1000 population based on national criteria.	Indonesia Central Bureau of Statistics
FAR	Farmers Ratio	persons/1000 population	2023	Number of individuals primarily engaged in agriculture per 1000 population.	Agricultural Census—Indonesia Central Bureau of Statistics
NAGRDP	Non-agricultural GRDP Ratio	ratio	2024	Contribution of non-agricultural sectors to the regional economy.	Indonesia Central Bureau of Statistics
RDI	Regional Development Index	index	2024	Composite index representing availability and capacity of regional services.	Villages Potential—Indonesia Central Bureau of Statistics

.

Because the datasets originate from multiple official statistical sources with different publication cycles, the indicators used in this study come from slightly different years (2023–2025). To represent the most recent conditions of the JBMUR, the latest available datasets for each indicator were used. Most socio-economic indicators tend to change gradually over time; therefore, the minor temporal differences among datasets are unlikely to substantially affect the representation of the current spatial structure of the region.

2.3. Methods

2.3.1. Data Pre-Processing

To ensure transparency, detailed descriptions of indicator-specific data sources, transformation steps, and preprocessing procedures are provided in Appendix A. To maintain analytical consistency across multi-source datasets, a systematic data preprocessing procedure was applied to all variables prior to analysis. All preprocessing and spatial analyses were conducted using R (v4.5.1) and RStudio (v2025.09.2+418). Unlike conventional vector-based approaches, this study adopts a pixel-based analytical framework in which each pixel is treated as an independent spatial unit. All indicators were projected to a common coordinate reference system (WGS 84/UTM Zone 48S; EPSG:32748) and resampled to a uniform 30 m × 30 m raster grid, corresponding to the native resolution of the primary remote sensing-derived LULC dataset used in the analysis. This approach ensured spatial consistency across variables while preserving the spatial detail captured by the remote sensing inputs.

Built-environment, accessibility, and environmental indicators derived from remote sensing and spatial network data were transformed into continuous spatial surfaces representing density, proportion, and accessibility. Socio-economic indicators, originally compiled at administrative levels, were spatially disaggregated using population-based allocation, land-use weighting, or regression-based spatial downscaling using ridge regression [60], while preserving consistency with officially reported statistics. Although these downscaling procedures improve the spatial representation of socio-economic patterns, they may introduce uncertainties related to spatial allocation assumptions and the modifiable areal unit problem (MAUP) [61]. These limitations should therefore be considered when interpreting the resulting spatial classifications. To maintain unit comparability, all socio-economic indicators were expressed per 1000 population.

Because the indicators were derived from heterogeneous sources and measured in different units and magnitudes, direct comparison across variables could introduce scale bias in the analysis. To ensure comparability and prevent variables with larger numerical ranges from disproportionately influencing the results, all variables were standardized prior to clustering using z-score normalization. The z-score standardization is expressed as:

$$\begin{array}{cccc}& z_{k,i}={\displaystyle \frac{x_{k,i}-{\mu }_k}{{\sigma }_k}}& & \end{array}$$

(1)

where $x_{k,i}$ is the original value of variable k at spatial unit i, ${\mu }_k$ is the mean value of variable k, and ${\sigma }_k$ is the standard deviation of variable k. The spatial distributions of all preprocessed indicators are presented in Figure 2.

2.3.2. Rustiadi Quantitative Zoning Method (RQZM)

The Rustiadi Quantitative Zoning Method (RQZM) was introduced by Rustiadi and Kobayasi [47] to classify regions according to their degree of homogeneity. The method originates from the concept of homogeneous region (Figure 3), in which spatial units are grouped based on similarities in their functional and structural characteristics. In regional analysis, the concept of regions can be viewed from several perspectives, including homogeneous regions defined by similar attributes, functional or systems-based regions characterized by spatial interactions such as center–hinterland relationships, and planning regions shaped by administrative or policy considerations. As illustrated in Figure 3, these perspectives can be understood as simple systems (e.g., rural–urban or cultivation–protected relationships) or more complex systems involving economic, ecological, and socio-political interactions.

Within this conceptual framework, each resulting zone represents a distinct functional role within a broader spatial system. Spatial classification under the RQZM framework aims to identify regional zoning at micro or local scales by explicitly considering spatial proximity and spatial interaction among units, with smaller spatial units generally exhibiting stronger spatial interdependence. In the context of this study, quantitative zoning provides a systematic and data-driven approach for delineating spatial zones within JBMUR based on its current dynamics and observed characteristics. The zoning outcomes produced in this research classify the study area into urban, peri-urban, and rural zones, where urban areas function as activity centers, while peri-urban and rural zones serve complementary and supporting roles within the regional system [62].

RQZM comprises three spatial classification methods, Non-Contiguous (NC), Contiguous I (C), and Contiguous II (C″) which are grounded in two fundamental principles: spatial contiguity and spatial compactness. This study employs the Rustiadi Quantitative Zoning Method Contiguous II (C″) or Rustiadi Quantitative Zoning Method-2 (RQZM-2) that is designed to explicitly integrate attribute similarity and spatial location in order to identify areas with varying degrees of multifunctionality and to delineate zones requiring protection or intervention. The fundamental principle underlying RQZM-2 is spatial proximity, whereby adjacent spatial units exert mutual influence. As noted by Rustiadi and Kitamura [63], the attractiveness of a region is shaped by the spatial aggregation of related units. RQZM-2 refines each pixel value (zₖ,ᵢ″) by combining its own attribute (zₖ,ᵢ) with the mean values of its neighboring pixels (zₖ,ⱼ), weighted by their spatial relationships (Wᵢⱼ). The RQZM-2 is expressed by the following formula:

$$Z_{k,i}”=\sqrt{z_{k,i}.{\overline{z}}_{k,j}}= \sqrt{z_{k,i}.{\displaystyle \frac{\sum _j^m{W}_{i,j }{. z}_{k,j}}{\sum _j^m{W}_{i,j }}}}$$

(2)

where I is spatial unit, j is neighboring unit around unit I, zᵢ″ is pixel value of unit i for variable k after accounting for neighborhood effects, zₖ,ᵢ is attribute value of pixel i for variable k, ${\overline{z}}_{k,j}$ is mean value of neighboring pixels j for variable k, zⱼ is variable value of neighboring spatial unit j, Wᵢⱼ is spatial weight matrix between pixels i and j, and m is number of neighbors.

2.3.3. K-Means Clustering

K-Means is a widely used unsupervised clustering method that partitions observations into k clusters by minimizing the within-cluster sum of squared distances between observations and their corresponding cluster centroids [64,65]. The algorithm iteratively assigns each observation to the nearest centroid based on Euclidean distance and updates centroid positions until the clustering solution converges. Owing to its simplicity, computational efficiency, and scalability, K-Means has been extensively applied in urban studies, land-use classification, and regional zoning analysis [66,67]. In spatial applications, K-Means is particularly effective [41,48,49,68] when combined with spatial preprocessing techniques—such as neighborhood-based adjustment and spatial weighting—which help ensure spatial coherence in the resulting clusters, as implemented in this study.

In this research, K-Means clustering was evaluated using three different configurations—namely, k = 3, k = 4, and k = 5—to examine the sensitivity of spatial typologies to variations in cluster granularity. The selection of this range was guided by the conceptual structure of the rural–peri-urban–urban continuum commonly discussed in peri-urban studies. A three-cluster configuration represents a simplified differentiation between urban, peri-urban, and rural systems, while higher cluster numbers allow additional subdivision of transitional or heterogeneous landscapes. Similar clustering schemes employing a limited range of cluster numbers have been widely used in spatial and urban studies to represent differentiated spatial structures and transitional characteristics across urban and rural settings [28,41,69]. Evaluating k = 3–5 therefore enables the analysis to capture both the fundamental urban–rural gradient and potential sub-typologies while maintaining interpretability for regional spatial planning. The K-Means clustering objective function is defined as:

$$\underset{\left\{C_1,\dots ,C_k\right\}}{\mathrm{m}\mathrm{i}\mathrm{n}}\sum _{i=1}^k\sum _{x\in C_i}\parallel x-{\mu }_i{\parallel }^2$$

(3)

where $C_i$ denotes the $i$-th cluster, $x$ represents an observation assigned to cluster $C_i$, and ${\mu }_i$ is the centroid of cluster $i$.

2.3.4. Cluster Validation

Cluster validity was assessed using a combination of internal validation metrics, stability analysis, spatial coherence evaluation, and post-clustering diagnostic analysis. Similar multi-stage validation strategies have been widely applied in spatial clustering and regional zoning studies to improve the interpretability and reliability of cluster solutions [70,71,72]. Internal validation was first assessed using the Silhouette Index and the Davies–Bouldin Index (DBI), both of which evaluate cohesion and separation without reference to external labels [73,74]. The silhouette width measures how similar an observation is to its own cluster compared to other clusters and is defined as:

$$s(i)={\displaystyle \frac{b\left(i\right)-a\left(i\right)}{\mathrm{m}\mathrm{a}\mathrm{x}\left\{a\right(i),b(i\left)\right\}}}$$

(4)

where $a\left(i\right)$ is the average distance between observation i and all other observations within the same cluster, and $b\left(i\right)$ is the minimum average distance between observation i and observations in the nearest neighboring cluster. Silhouette values range from −1 to 1, with higher values indicating better cluster cohesion and separation [73].

Cluster compactness and separation were further evaluated using the DBI, expressed as:

$$DBI={\displaystyle \frac{1}{k}}\sum _{i=1}^k\underset{j\ne i}{\mathrm{m}\mathrm{a}\mathrm{x}}\left({\displaystyle \frac{S_i+S_j}{M_{ij}}}\right)$$

(5)

where $k$ is the number of clusters, $S_i$ and $S_j$ represent the average within-cluster distances for clusters i and j, respectively, and $M_{ij}$ is the distance between the centroids of clusters i and j. Lower DBI values indicate more compact and well-separated clusters [74].

Clustering robustness was evaluated through a subsampling-based stability analysis using the Adjusted Rand Index (ARI) [75,76,77]. For each clustering scenario, repeated random subsamples of a fixed proportion of observations were drawn, and the clustering algorithm was independently re-applied to each subsample. Pairwise agreement between clustering results derived from the same subsample was quantified using ARI, and stability was summarized as the mean ARI across repeated iterations:

$$\begin{array}{cccc}& \mathrm{Stability}={\displaystyle \frac{1}{R}}{\displaystyle \sum _{r=1}^R}\mathrm{ARI}\left(C_1^{\left(r\right)},C_2^{\left(r\right)}\right)& & \end{array}$$

(6)

where $R$ denotes the number of repetitions, and $C_1^{\left(r\right)}$ and $C_2^{\left(r\right)}$ represent two independently generated clustering solutions derived from the same subsample in repetition $r$. Higher mean ARI values indicate greater reproducibility and robustness of the clustering structure under sampling variation [77].

Beyond statistical robustness, spatial interpretability was evaluated through spatial coherence analysis, focusing on fragmentation. Spatial contiguity is a key consideration in spatial clustering, ensuring that similar spatial units form compact and connected geographic regions rather than scattered patches [78]. Fragmentation defined as the degree to which cluster memberships are spatially dispersed or disconnected provides a diagnostic measure of whether statistically distinct clusters also exhibit meaningful spatial structure [78,79]. Fragmentation was quantified using a patch-based diagnostic derived from the full-resolution clustered raster. For each clustering result, spatially contiguous grid cells sharing the same cluster label were identified using an eight-neighbor (queen) contiguity rule, and the total number of disconnected patches was computed as:

$$\begin{array}{cccc}& \mathrm{Fragmentation}=N_{\mathrm{patch}}& & \end{array}$$

(7)

where $N_{\mathrm{patch}}$ denotes the number of spatially disconnected patches within the clustering result. Higher values indicate greater spatial fragmentation, whereas lower values reflect stronger spatial contiguity and coherence. This metric was used comparatively across clustering configurations to assess the spatial implications of different clustering scenarios, rather than as a standalone indicator of clustering quality.

Post-clustering interpretation was supported by centroid profile analysis and diagnostic statistical testing [80,81]. Centroid profiles were derived from standardized variable means to characterize the functional attributes of each cluster and facilitate substantive interpretation in the context of regional zoning. To assess statistical differentiation among clusters, one-way analysis of variance (ANOVA) was applied as a preliminary screening step to identify variables exhibiting significant between-cluster differences. For variables meeting the significance threshold ($p<0.05$), Least Significant Difference (LSD) [82] tests were subsequently conducted to examine pairwise differences between cluster means. The LSD value was computed as:

$$LSD=t_{\alpha /2, N-k}\sqrt{M{S}_W\left({\displaystyle \frac{1}{n_i}}+{\displaystyle \frac{1}{n_j}}\right)}$$

(8)

where $t_{\alpha /2, N-k}$ is the critical value of the t-distribution at significance level $\alpha$ with $N-k$ degrees of freedom, $M{S}_W$ denotes the within-cluster mean square, and $n_i$ and $n_j$ represent the sample sizes of clusters $i$ and $j$, respectively. A pairwise difference between cluster means was considered statistically significant when:

$$\mid {\overline{\mathrm{x}}}_{\mathrm{i}}-{\overline{\mathrm{x}}}_{\mathrm{j}}\mid >\mathrm{L}\mathrm{S}\mathrm{D}$$

LSD results were used as a diagnostic tool to support interpretation of cluster differentiation rather than as a primary criterion for cluster validity, maintaining a clear distinction between validation and interpretative stages of the clustering analysis.

3. Results

3.1. Comparison Between Non-RQZM K-Means and RQZM-2 K-Means

Spatial clustering using Non-RQZM K-Means and RQZM-2 K-Means produced distinct spatial patterns across the JBMUR, reflecting differences in how attribute similarity and spatial context are incorporated into the clustering process. The results of the Non-RQZM K-Means analysis are presented through centroid profiles and spatial distribution maps for the three-, four-, and five-cluster configurations. The centroid profiles (Figure 4) illustrate inter-cluster differences in standardized variable means, while the corresponding maps (Figure 5) visualize the spatial distribution of cluster memberships across the study area.

Across the three Non-RQZM K-Means configurations (k = 3, 4, and 5), the centroid profiles and corresponding spatial maps jointly illustrate how attribute differentiation and spatial coherence evolve with increasing cluster granularity.

In the three-cluster solution, one cluster (Cluster 3) is characterized by high centroid values across built-environment indicators (BD, BUF), the accessibility indicator (AAR), and socio-economic indicators (HDI, PD, OU, PP, NAGRDP, RDI), while exhibiting lower values for the environmental indicator (VC) and the socio-economic indicator FAR. Spatially, this cluster forms a compact and contiguous core area. Another cluster (Cluster 2) displays centroid values close to the overall mean across built-environment, accessibility, environmental, and socio-economic indicators, resulting in a broadly distributed and spatially continuous pattern. The remaining cluster (Cluster 1) is characterized by lower values for socio-economic indicators (PD, OU, PP, NAGRDP) and higher values for VC and FAR, occupying more peripheral and less concentrated zones.

With four clusters, the centroid structure becomes more segmented. One cluster (Cluster 4) retains high values across BD, BUF, AAR, and key socio-economic indicators, and remains spatially concentrated, similar to the three-cluster solution. Another cluster (Cluster 3) shows centroid values near the overall mean across most built-environment, accessibility, and socio-economic indicators, while exhibiting relatively higher VC, and appears spatially extensive. An additional cluster (Cluster 2) is primarily distinguished by elevated FAR, whereas Cluster 1 continues to record lower values for PD, OU, and PP. Spatially, these clusters form more fragmented and interspersed patterns, particularly in transitional zones.

In the five-cluster configuration, centroid patterns largely mirror those of k = 3 and 4, with further subdivision of existing clusters. Cluster 3 consistently maintains high values across built-environment, accessibility, and socio-economic indicators and remains spatially concentrated, while Cluster 5 is mainly distinguished by high FAR. Cluster 1 continues to exhibit low values for PD, OU, PP, and NAGRDP, whereas the remaining clusters display near-mean or intermediate combinations of indicators. Spatially, clusters become increasingly scattered and discontinuous.

Overall, increasing the number of clusters in the Non-RQZM approach improves internal differentiation across built-environment, accessibility, environmental, and socio-economic indicators, but at the cost of increased spatial fragmentation. At higher values of k, clusters are defined primarily by marginal differences in a limited set of indicators, resulting in reduced spatial coherence.

When K-Means clustering is applied to spatially constrained variables using RQZM-2, the resulting centroid profiles (Figure 6) and spatial distribution maps (Figure 7) exhibit structural patterns that differ from those produced by the standard Non-RQZM approach. Across the three-, four-, and five-cluster configurations, the centroid profiles display inter-cluster variation across built-environment, socio-economic, and accessibility indicators. In parallel, the spatial maps depict differences in the spatial configuration of clusters, including variations in cluster extent, shape, and spatial dispersion across the study area. Together, these patterns reflect the influence of spatial constraints embedded within the RQZM-2 framework on both attribute-based differentiation and spatial configuration.

The three RQZM-2 K-Means configurations (k = 3, 4, and 5) show that the incorporation of spatially contextualized and constrained variables influences both attribute differentiation and spatial organization. While increasing the number of clusters mainly affects the degree of internal subdivision, the overall structural patterns remain clearly identifiable across configurations.

In the three-cluster solution, one cluster (Cluster 2) is characterized by higher values across built-environment (BD, BUF) and socio-economic indicators (HDI, PD, OU, PP, NAGRDP, RDI), together with relatively high VC, and occupies a spatially concentrated core area. Another cluster (Cluster 1) shows generally lower values across most indicators (BD, BUF, HDI, PD, OU, PP, NAGRDP, RDI) but records the highest FAR, while Cluster 3 is distinguished by relatively higher PD, OU, and PP, combined with lower VC. Spatially, the k = 3 configuration exhibits clearly differentiated cluster zones with limited intermixing, consistent with the distinct centroid profiles.

With four clusters, centroid patterns remain broadly consistent with k = 3 but show additional segmentation. Cluster 2 continues to exhibit elevated values across multiple development-related indicators, while Cluster 3 maintains higher PD, OU, and PP alongside lower VC. Cluster 1 remains distinguished by a pronounced peak in FAR, whereas Cluster 4 records lower values across most indicators, particularly PD, OU, PP, FAR, NAGRDP, and RDI. Spatially, these clusters form well-defined regions with limited overlap, reflecting differentiated centroid trajectories.

In the five-cluster configuration, centroid patterns largely extend those observed at k = 3 and 4, with further subdivision of existing clusters. One cluster (Cluster 5) remains clearly defined by a strong peak in FAR, while Cluster 4 retains high values across BD, BUF, AAR, VC, HDI, NAGRDP, and RDI. The remaining clusters exhibit intermediate or lower values across most indicators. Spatially, clusters occupy distinct portions of the study area, with limited interspersion and preserved regional structure.

Overall, the combined centroid and spatial analyses indicate that the RQZM-2 approach produces stable and structured differentiation across all configurations. Increasing k leads to finer internal subdivision while preserving recognizable spatial patterns, demonstrating how spatial context embedded in the RQZM-2 framework shapes both attribute-based variation and cluster spatial configuration.

Taken together, the results highlight systematic differences between Non-RQZM and RQZM-2 clustering outcomes. In the Non-RQZM configurations, higher k values primarily result in finer centroid subdivision accompanied by increased spatial intermixing. In contrast, the RQZM-2 results maintain identifiable centroid structures across k = 3, 4, and 5, with changes in cluster number mainly affecting internal partitioning rather than overall spatial organization. Spatially, RQZM-2 produces more structured and regionally differentiated cluster arrangements, indicating that incorporating spatially contextualized and constrained variables fundamentally alters both attribute differentiation and spatial configuration compared to the standard K-Means approach.

3.2. Validation of Clustering Results

The clustering results were evaluated using a comprehensive validation framework encompassing internal validation metrics, stability assessment, and spatial coherence analysis. Validation was conducted for three-, four-, and five-cluster configurations (k = 3, 4, and 5) under both the Non-RQZM and RQZM-2 approaches to assess clustering quality, robustness, and spatial interpretability prior to zoning interpretation.

Internal validation metrics reveal contrasting performance patterns between the two approaches as the number of clusters increases. Under the Non-RQZM framework, internal quality improves slightly from k = 3 (Silhouette = 0.299; DBI = 1.422) to k = 4, where the highest silhouette value (0.320) and lowest DBI (1.262) are achieved, indicating optimal separation at moderate cluster resolution. However, at k = 5, internal quality declines, as reflected by a lower silhouette value (0.256) and an increased DBI (1.336), suggesting reduced compactness and greater overlap at higher partitioning levels. In contrast, the RQZM-2 framework exhibits consistently strong internal performance across all cluster configurations. Silhouette values remain relatively high, peaking at k = 4 (0.337), while the DBI decreases monotonically from 1.454 (k = 3) to 1.226 (k = 5). This pattern indicates that spatial contextualization enhances cluster cohesion and separation, particularly as the number of clusters increases, even though marginal gains diminish beyond k = 4.

Stability assessment based on subsampling robustness further highlights methodological differences. For Non-RQZM, clustering stability declines sharply with increasing k, as indicated by a substantial drop in mean ARI from 0.985 (k = 3) to 0.808 (k = 5). This pattern suggests growing sensitivity to sampling variability and reduced reproducibility at higher cluster numbers. Conversely, the RQZM-2 framework maintains consistently high stability across all configurations, with mean ARI values remaining above 0.98. Although a slight decline is observed as k increases, overall stability remains markedly higher than in the Non-RQZM scenario, indicating that spatial contextualization contributes to more robust and reproducible clustering outcomes.

Spatial coherence analysis shows that the number of spatial patches remains constant (69) across all clustering configurations. This consistency reflects the fixed spatial segmentation of the grid-based analytical framework rather than differences in clustering structure. Therefore, the patch-based metric is interpreted as a diagnostic indicator to ensure that clustering solutions do not introduce spatial fragmentation. A summary of the internal validation, stability, and spatial coherence metrics supporting these observations is presented in

Table 2. Summary of clustering validation results.

Validation Criterion	Non-RQZM			RQZM-2			Interpretation
	k = 3	k = 4	k = 5	k = 3	k = 4	k = 5
Mean Silhouette ↑ *	0.299	0.320	0.256	0.335	0.337	0.309	RQZM-2 (k = 4) provides the strongest overall cluster separation.
Davies–Bouldin Index ↓	1.422	1.262	1.336	1.454	1.321	1.226	RQZM-2 (k = 5) yields the most compact and well-separated clusters.
Mean ARI (Stability) ↑	0.985	0.982	0.808	0.989	0.987	0.981	RQZM-2 (k = 3) shows the highest clustering stability.
Spatial Patches ↓	69	69	69	69	69	69	Both methods (all k) exhibit identical spatial coherence.

* Arrow symbols (↑/↓) indicate the preferred direction of metric performance, where ↑ denotes higher values indicating better performance and ↓ denotes lower values indicating better performance.

.

Diagnostic statistical validation further clarifies these differences. The one-way ANOVA results confirm statistically significant differences among clusters for all input variables across all scenarios (p < 0.001), indicating that each clustering configuration successfully partitions the multivariate feature space. However, the LSD analysis reveals important contrasts in the clarity and consistency of inter-cluster differentiation between methods and k-values.

Under the Non-RQZM framework (Figure 8), the three-cluster solution (k = 3) already shows strong separation, with 10 of 11 variables strictly differentiated and a low mean ambiguity (0.061), indicating a stable clustering structure. Increasing the number of clusters to k = 4 slightly increases ambiguity, as strictly differentiated variables decline to nine and the mean ambiguity rises to 0.091, suggesting added complexity without improved separation. In contrast, the five-cluster configuration (k = 5) yields the lowest ambiguity (0.036), with 10 variables again strictly differentiated, indicating the most internally consistent solution. Overall, Non-RQZM exhibits a non-monotonic ambiguity pattern, with optimal separation achieved at k = 5 rather than through a linear increase in cluster number.

In contrast, the RQZM-2 framework (Figure 9) exhibits more persistent LSD overlaps than Non-RQZM, particularly for variables capturing transitional and economic characteristics, reflecting the constraining role of spatial zoning on centroid differentiation. At k = 3, RDI and NAGRDP show partial overlap, resulting in two ambiguous variables and a relatively high mean ambiguity (0.121), indicating reduced separability even at low cluster resolution. Increasing the number of clusters to k = 4 substantially improves differentiation, with only one ambiguous variable (AAR), 10 strictly differentiated indicators, and a marked decline in mean ambiguity (0.045), representing the most internally consistent RQZM-2 solution. However, at k = 5, ambiguity increases again as FAR, RDI, and NAGRDP exhibit overlap, raising the mean ambiguity to 0.109. Overall, RQZM-2 shows a non-monotonic ambiguity pattern, with optimal separation at k = 4, while the recurrence of overlap at higher k highlights how spatial reinforcement limits centroid extremity, leading to partial convergence in variables associated with gradual urban–rural and socio-economic transitions.

Overall, the validation outcomes indicate that clustering performance is jointly determined by the analytical framework employed and the number of clusters specified. While the Non-RQZM approach shows clear attribute separation at lower cluster numbers, increasing k yields limited improvements in robustness or interpretability. By contrast, the RQZM-2 framework responds positively to a moderate increase in cluster resolution. The four-cluster solution (k = 4) delivers the most balanced overall performance, achieving the highest mean silhouette value, which indicates superior internal separation, while LSD analysis reveals only a single overlapping variable, suggesting minimal and systematic ambiguity. In practical terms, this result indicates that the spatial units can be grouped into four relatively distinct territorial profiles characterized by different combinations of socio-economic conditions, built-environment structure, accessibility, and environmental characteristics. These clusters therefore represent meaningful spatial zoning that reflect heterogeneous development patterns across the study area, allowing the identification of areas with similar urbanization dynamics and structural conditions. Consequently, RQZM-2 with k = 4 is selected as the optimal configuration for subsequent spatial zoning analysis in this study.

3.3. R–P–U Zones in the Jakarta–Bandung Mega-Urban Region (JBMUR)

Based on the validated RQZM-2 four-cluster solution, the JBMUR is classified into one urban zone, one peri-urban zone, and two rural sub-zones (Rural I and Rural II). Zoning interpretation is grounded in observed spatial patterns of built-up intensity, accessibility, environmental conditions, and socio-economic structure, ensuring that the resulting zoning reflects consistent empirical characteristics rather than a priori definitions.

• The urban zone (Cluster 2) is characterized by very high values of BD and BUF, indicating intensive built-up development, combined with relatively high VC and slightly elevated PD, OU, and PP, reflecting concentrated population and moderate social pressure. NAGRDP and RDI consistently exhibit high values, indicating a diversified non-agricultural economic structure and advanced regional development. In contrast, FAR shows relatively low values, confirming the limited role of agricultural activities within urban areas. Accessibility (AAR) is generally higher than in rural typologies, supporting dense urban functions, although it partially overlaps with peri-urban areas.
• The peri-urban zone (Cluster 3) represents a transitional system with moderate values of BD and BUF and relatively good accessibility (AAR). This typology exhibits the highest values of PD, OU, and PP among all clusters, indicating intense population pressure and heightened social vulnerability associated with ongoing rural–urban transition. Environmental indicators show relatively low values, reflecting increasing land conversion and reduced vegetation cover. NAGRDP and RDI remain at moderate levels and are unexpectedly lower than those observed in Rural I, highlighting areas undergoing structural transformation rather than fully established urban economic systems.
• The rural zones (Cluster 4 and 1) display consistently low built-up intensity (BD and BUF) and weaker socio-economic performance. Rural I shows relatively balanced but low values across PD, OU, PP, NAGRDP, and RDI, combined with low VC and moderate FAR, indicating stable agricultural-based systems with limited diversification and gradual land-use change. Accessibility (AAR) remains low to moderate, reinforcing the predominantly rural character of these areas. Rural II exhibits a highly distinctive profile characterized by extremely high FAR, indicating strong agricultural dominance, alongside very low HDI, reflecting limited human development outcomes. Built-up indicators (BD and BUF) are slightly higher than in Rural I, but accessibility (AAR) remains consistently low, while VC is relatively higher than in both rural and peri-urban zones. This zone represents agrarian-dominated yet structurally isolated rural areas, predominantly located in peripheral and weakly integrated into the regional urban system.

The proportional distribution of the four R–P–U zones was calculated based on the classified grid cells (

Table 3. Proportional distribution of R–P–U zonings in the JBMUR.

Zone	Area (km2)	Percentage of Total Area (%)	Spatial Characteristics
Urban (Cluster 2)	2697.68	16.28	Compact urban cores with intensive built-up development and strong non-agricultural economic activities
Peri-urban/Desakota (Cluster 3)	2497.43	15.07	Transitional belts with mixed land-use and the highest population and social pressure
Rural I (Cluster 4)	10,301.02	62.17	Dominant rural landscapes with stable agricultural activities and moderate connectivity
Rural II (Cluster 1)	1074.08	6.48	Spatially isolated rural areas with strong agricultural dominance and limited accessibility
Total	16,570.21	100.00	—

). The urban typology covers 2697.68 km² (16.28% of the total area) and is concentrated within compact urban cores and contiguous built-up zones, as illustrated in Figure 10, which presents a new interpretation of mega urban zoning in the JBMUR. The peri-urban zone accounts for 2497.43 km² (15.07%) and forms broad transitional belts surrounding urban areas, highlighting zones of active interaction between urban and rural systems. Rural I dominates the study area, covering 10,301.02 km² (62.17%), and is widely distributed across both interior and peripheral regions, reflecting the prevailing rural structure of the JBMUR. Meanwhile, Rural II occupies the smallest proportion, totaling 1074.08 km² (6.48%), and is primarily located in spatially isolated peripheral areas with minimal urban influence. Overall, this spatial configuration, as depicted in Figure 10, underscores a new interpretation of mega urban zoning in which urban and peri-urban systems exert strong functional influence, while the spatial structure of the region remains predominantly rural with varying degrees of accessibility and development intensity.

4. Discussion

4.1. Functional R–P–U Structure of the JBMUR

The RQZM-2-based zoning reveals that the JBMUR is structured as a functionally asymmetric and spatially heterogeneous regional system rather than a simple urban–rural dichotomy. Instead, the region exhibits a continuum of urban influence expressed through differentiated urban, peri-urban, and rural sub-systems, each performing distinct functional roles. Although urban areas occupy a relatively limited proportion of total land area, they concentrate high levels of development intensity, accessibility, and non-agricultural economic activity. This confirms their role as dominant functional nodes whose influence extends beyond administrative boundaries and shapes broader regional dynamics. Such dynamics are particularly evident along the Jakarta–Bandung corridor, where urban cores drive economic polarization and uneven development through the concentration of industrial and service activities [56]. This observation aligns with studies on mega-urbanization in Indonesia, which highlight how continuous urban expansion from Jakarta to Bandung has produced a conurbation over agricultural lands, thereby exacerbating functional and spatial imbalances across the region [59].

The peri-urban zone emerges as a critical intermediary within this structure. Rather than functioning as a marginal extension of urban areas, peri-urban zones form extensive transitional belts that mediate interactions between urban systems and surrounding rural landscapes. Their spatial extent and socio-economic characteristics suggest that a substantial share of regional transformation in the JBMUR occurs within these zones, where population pressure, social vulnerability, and land-use change intensify simultaneously. This finding aligns with empirical evidence from rapidly urbanizing regions in Southeast Asia and other parts of the Global South, where peri-urban areas function as dynamic interfaces shaped by industrial decentralization, infrastructure expansion, and informal development processes [83]. For instance, in the greater Ho Chi Minh City metropolitan area, peri-urbanization has been monitored through similar spatial analyses, revealing heightened vulnerabilities to environmental changes and governance gaps [84]. Such zones often exhibit heightened governance challenges, as rapid transformation outpaces institutional capacity and spatial planning frameworks [85].

Despite the functional prominence of urban and peri-urban systems, rural areas remain the dominant typology in terms of spatial coverage within the JBMUR. However, the differentiation between Rural I and Rural II indicates that rural spaces in the region are far from homogeneous. Rural I corresponds to relatively stable rural landscapes that continue to perform agricultural functions while retaining residual connectivity to urban systems. In contrast, Rural II denotes more isolated and structurally constrained rural areas, characterized by strong agricultural dominance but limited accessibility and socio-economic development. This internal differentiation underscores that rural persistence within mega-urban regions does not equate to uniform resilience; rather, it reflects uneven capacities to adapt to urban influence and broader processes of regional restructuring. Evidence from the wider literature on peri-urbanization in populous Asian countries such as Indonesia, China, and India corroborates these dynamics, demonstrating how varying degrees of urban–rural connectivity shape disparities in livelihoods, resource access, and developmental outcomes [86].

Overall, the identified zones reveal a regional configuration in which urban influence is articulated through a continuous and non-linear spatial gradient rather than discrete territorial boundaries. Peri-urban zones function as pivotal intermediaries linking urban dynamics with rural systems, while the differentiation of rural typologies reflects simultaneous processes of integration and marginalization. This configuration is consistent with broader peri-urbanization processes observed across the Global South, where territorial, functional, and experiential dimensions intersect to produce complex urban–rural transitions [56,87]. The functional asymmetry identified in this study has important implications for sustainable development, particularly in addressing spatial inequality, strengthening adaptive capacity in transitional zones, and mitigating ecological degradation under sustained mega-urban expansion.

From a spatial planning perspective, the RQZM-2-based zoning provides an operationally relevant framework within Indonesia’s planning system. The identified functional zones can be aligned with existing instruments such as RTRW (Rencana Tata Ruang Wilayah) at the provincial and district levels and RDTR (Rencana Detail Tata Ruang) in rapidly transforming areas. This is particularly important in the JBMUR, where the mega-urban system spans multiple administrative jurisdictions resulting in fragmented planning authority and uneven policy implementation. Such fragmentation is especially evident along the Jakarta–Bandung corridor, where rapid development often exceeds the regulatory and monitoring capacity of local governments [59,88].

In peri-urban zones, which experience the highest levels of land-use pressure and governance challenges, planning interventions should prioritize stricter control of land-use permits, integrated infrastructure provision, and strengthened environmental regulation. However, given the uneven governance capacity across jurisdictions within the JBMUR, these interventions need to be differentiated. Areas with higher institutional capacity may directly integrate zoning outputs into formal planning revisions, while areas with more limited capacity may require incremental approaches, such as simplified zoning enforcement and community-based monitoring mechanisms [89]. For rural areas, differentiated strategies are likewise necessary. Rural I areas can be supported through improved agro-logistics, enhanced market access, and sustainable agricultural intensification, whereas Rural II areas require more fundamental interventions, including accessibility improvement and basic service provision, to reduce structural disparities. These distinctions underscore the need for stronger multi-level and inter-jurisdictional coordination across the JBMUR, particularly in addressing overlapping authorities and ensuring policy coherence.

While the RQZM-2 framework provides a robust analytical basis for identifying functional zones, its practical implementation depends on its alignment with institutional realities and governance capacity. Therefore, the zoning outputs should be interpreted as decision support tools rather than prescriptive spatial directives, highlighting the broader challenge of translating data-driven spatial models into effective policy within complex and uneven governance contexts.

4.2. Peri-Urban Transformation and Empirical Representation of Classical Concepts

The peri-urban typology identified in this study aligns closely with classical perspectives on rural–urban transformation, particularly the desakota concept, which conceptualizes peri-urban spaces as expansive, hybrid zones characterized by intertwined rural and urban functions rather than as marginal transitional fringes. Originating from observations in Southeast Asia, desakota—derived from the Indonesian terms desa (village) and kota (city)—describes regions of high population density where agricultural and non-agricultural activities coexist amid intense socio-economic interaction and infrastructure-led growth [19]. This framework conceptualizes peri-urbanization as a spatially heterogeneous and non-linear process shaped by overlapping trajectories such as industrial decentralization, labor mobility, and uneven institutional development, rather than as a linear progression toward full urbanization.

Building on these conceptual foundations, the RQZM-2 classification (Figure 11) provides an empirical operationalization of desakota within the JBMUR by delineating peri-urban zones as broad transition belts characterized by mixed land-use systems, heightened demographic pressures, and ongoing socio-economic restructuring. By explicitly incorporating spatial contextualization into the clustering algorithm, the model captures desakota as continuous and measurable spatial patterns, transcending rigid administrative boundaries or distance-based thresholds. This approach resonates with recent methodological advancements in peri-urban research that emphasize data-driven typologies to map hybrid landscapes across Asian mega-regions [90].

The peri-urban typology identified in the JBMUR exhibits key attributes consistent with the desakota framework as documented in earlier studies of Indonesian mega-urban regions [54,91]. High population densities combined with moderate built-up intensity and diversified economic activities indicate zones of demographic concentration and livelihood mixing, where agricultural practices persist alongside expanding non-agricultural employment. These areas also exhibit elevated levels of unemployment and poverty, underscoring structural vulnerabilities associated with incomplete socio-economic transformation and inadequate governance—conditions frequently described as hallmarks of desakota’s “incomplete urbanization.” Comparable patterns are evident in Jabodetabek’s peri-urban agriculture, where rapid urban expansion has sustained mixed farming systems while intensifying land competition, thereby posing risks to food security and environmental sustainability [92].

Spatially, peri-urban zones in the JBMUR manifest as fragmented and elongated belts aligned with major transportation corridors, particularly along the Jakarta–Bandung axis. This infrastructure-oriented morphology reflects desakota’s characteristic ribbon-like development, facilitating commuting flows, industrial spillover, and land-use intermixing without producing a cohesive urban form. Similar corridor-driven patterns have been documented in other Southeast Asian contexts [3,19]. In Vietnam’s Hanoi region, for example, peri-urbanization emerges through corridor expansion driven by state-led infrastructure projects that integrate rural settlements into urban networks, fostering hybrid economies while exacerbating social inequalities [93]. Likewise, Malaysia’s emerging mega-regions display desakota-like traits, with dispersed settlements and mixed economic activities shaped by global economic integration [94].

Beyond Southeast Asia, the applicability of the desakota framework to other Asian contexts further reinforces its relevance to the JBMUR findings. In Shenzhen, peri-urban regions exhibit hybrid land-use dynamics linking urban cores through in situ population transformations rather than large-scale rural–urban migration [95]. Shanghai’s peri-urban expansion similarly combines state-led urbanization with bottom-up adaptations, producing mixed zones that challenge formal planning regimes and heighten sprawl-related risks [96]. These cases illustrate the evolution of desakota as a “worlding” hybrid space within global urbanization processes, where local conditions and transnational forces jointly reproduce persistent rural–urban interfaces [97]. Importantly, the JBMUR’s peri-urban typology challenges linear models of urban transition by portraying desakota as a relatively stable and enduring spatial configuration rather than a temporary stage of urbanization. Persistent mixed land-uses and moderate non-agricultural intensities suggest long-term hybridity shaped by land fragmentation, informal markets, and uneven governance capacities. This interpretation is consistent with broader Global South experiences, where desakota regions often resist complete urban transformation due to structural and institutional constraints [87].

Finally, the clustering results interrogate conventional urban–rural dichotomies by revealing early signals of desakota expansion within ostensibly rural zones, such as reduced vegetation cover associated with mega-project development. In regions like Jabodetabek, such processes threaten ecosystem services and underscore the environmental vulnerabilities inherent in desakota landscapes [98]. Methodologically, while the RQZM-2 outcomes remain sensitive to grid resolution and neighborhood specifications, their strong conceptual alignment with desakota theory supports the robustness of the approach for mega-urban analysis. By empirically grounding a classical qualitative concept in spatially explicit data, this study bridges conceptual and quantitative traditions, contributing to the advancement of peri-urban research and sustainability-oriented planning in hybrid MURs.

5. Conclusions

This study demonstrates that incorporating spatial constraints into clustering analysis substantially improves the empirical delineation of R–P–U zones within rapidly transforming MURs. By applying the RQZM-2 to JBMUR, the analysis moves beyond conventional non-spatial clustering approaches and produces a spatially coherent and statistically robust representation of settlement structures across the region.

The results show that spatially constrained clustering enhances the quality and interpretability of cluster solutions compared with conventional non-spatial approaches. Relative to standard Non-RQZM K-Means, the RQZM-2 method improves internal cluster cohesion and separation, maintains strong stability across different cluster configurations, and preserves spatial contiguity without increasing fragmentation. The incorporation of neighborhood effects ensures that clusters correspond to geographically continuous regions rather than isolated statistical groupings. As the number of clusters increases, the RQZM-2 framework allows finer internal differentiation while maintaining recognizable regional structures, indicating its ability to balance analytical detail with spatial coherence.

Empirically, the validated four-cluster solution reveals that the JBMUR is structured as a spatial continuum rather than a simple urban–rural dichotomy. Urban areas emerge as compact cores characterized by high development intensity and diversified economic activity, while peri-urban areas form extensive transitional belts experiencing strong population pressure and socio-economic vulnerability. The identification of two rural sub-types further highlights the internal heterogeneity of rural spaces within mega-urban regions, distinguishing relatively connected agricultural landscapes from more structurally isolated agrarian systems. This typology provides a spatially explicit operationalization of classical peri-urban concepts, particularly the desakota phenomenon, by translating long-standing qualitative interpretations into measurable spatial patterns.

Beyond the empirical case of JBMUR, the findings highlight the broader methodological value of integrating spatial contextualization into clustering analysis. The combination of grid-based spatial representation and spatially constrained clustering provides a replicable framework for identifying functional settlement zones that better capture the continuous and transitional nature of peri-urban systems. Such an approach may be particularly relevant for rapidly urbanizing regions in the Global South, where conventional administrative classifications often fail to reflect the spatial dynamics of urban expansion.

Several limitations should be acknowledged in relation to the methodological design of this study. First, the analysis relies on a static, cross-sectional representation of spatial conditions, which constrains the ability to capture temporal dynamics and evolutionary trajectories of peri-urban transformation within the JBMUR. As a result, the identified functional zones should be interpreted as a snapshot of ongoing processes rather than stable or persistent spatial structures. Second, while the grid-based framework enhances spatial comparability and reduces administrative bias, the results remain sensitive to key modeling choices, including grid resolution, neighborhood configuration, and the weighting scheme applied in the contextualization process. Variations in these parameters may lead to different delineations of functional zones, particularly in transitional peri-urban areas where spatial characteristics are highly heterogeneous. Third, the integration of socio-economic indicators through spatial downscaling introduces additional uncertainty, especially in areas where underlying administrative data are sparse, aggregated, or internally heterogeneous. This may affect the accuracy of localized representations of socio-economic conditions and, consequently, the classification of functional zones. Fourth, the use of K-Means as the core clustering algorithm entails structural assumptions that may not fully capture the complexity and non-linearity of spatial relationships in MURs. These limitations highlight that the RQZM-2 framework should be understood as a simplified representation of complex spatial systems, and its outputs should be interpreted as exploratory and decision-supporting in nature rather than definitive classifications.

Future research should extend the RQZM-2 framework along several directions. First, incorporating longitudinal analysis using multi-temporal remote sensing and socio-economic datasets would enable the explicit examination of peri-urban dynamics and transition pathways over time. Second, methodological development could explore alternative or hybrid clustering approaches, such as density-based or graph-based methods, that relax the assumptions of K-Means while preserving spatial dependency structures. Third, systematic sensitivity analysis focusing on grid resolution, neighborhood definition, and spatial weighting schemes is necessary to assess the robustness and reproducibility of zoning outcomes. Finally, integrating governance capacity, institutional arrangements, and environmental risk indicators into the analytical framework would enhance its explanatory power and improve its applicability for sustainability-oriented spatial planning and policy evaluation in mega-urban regions such as the JBMUR.