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Spatial-Morphological Modeling for Multi-Attribute Imputation of Urban Blocks

Vasilii Starikov, Ruslan Kozliak, Georgii Kontsevik, Sergey Mityagin

TL;DR

This work addresses missing built-form indicators at the urban-block level by introducing the Spatial-Morphological (SM) imputer, which combines data-driven morphological clustering in the joint $(FSI,GSI)$ space with local spatial information. The method predicts the probability of a block belonging to morphological clusters via a CatBoost classifier trained on land-use shares and site area, and imputes $FSI$ and $GSI$ as probability-weighted cluster medians, yielding globally coherent priors. Experimental results on Saint Petersburg blocks show that SM alone captures meaningful morphology, while hybrids of SM with inverse distance weighting ($IDW$) or spatial $k$-nearest neighbors ($sKNN$) achieve the best accuracy, outperforming existing baselines such as SMV-NMF. The findings demonstrate the practical value of integrating city-scale morphological patterns with local spatial context for robust, context-aware urban data reconstruction, with implications for planning and digital-twin pipelines across cities.

Abstract

Accurate reconstruction of missing morphological indicators of a city is crucial for urban planning and data-driven analysis. This study presents the spatial-morphological (SM) imputer tool, which combines data-driven morphological clustering with neighborhood-based methods to reconstruct missing values of the floor space index (FSI) and ground space index (GSI) at the city block level, inspired by the SpaceMatrix framework. This approach combines city-scale morphological patterns as global priors with local spatial information for context-dependent interpolation. The evaluation shows that while SM alone captures meaningful morphological structure, its combination with inverse distance weighting (IDW) or spatial k-nearest neighbor (sKNN) methods provides superior performance compared to existing SOTA models. Composite methods demonstrate the complementary advantages of combining morphological and spatial approaches.

Spatial-Morphological Modeling for Multi-Attribute Imputation of Urban Blocks

TL;DR

This work addresses missing built-form indicators at the urban-block level by introducing the Spatial-Morphological (SM) imputer, which combines data-driven morphological clustering in the joint space with local spatial information. The method predicts the probability of a block belonging to morphological clusters via a CatBoost classifier trained on land-use shares and site area, and imputes and as probability-weighted cluster medians, yielding globally coherent priors. Experimental results on Saint Petersburg blocks show that SM alone captures meaningful morphology, while hybrids of SM with inverse distance weighting () or spatial -nearest neighbors () achieve the best accuracy, outperforming existing baselines such as SMV-NMF. The findings demonstrate the practical value of integrating city-scale morphological patterns with local spatial context for robust, context-aware urban data reconstruction, with implications for planning and digital-twin pipelines across cities.

Abstract

Accurate reconstruction of missing morphological indicators of a city is crucial for urban planning and data-driven analysis. This study presents the spatial-morphological (SM) imputer tool, which combines data-driven morphological clustering with neighborhood-based methods to reconstruct missing values of the floor space index (FSI) and ground space index (GSI) at the city block level, inspired by the SpaceMatrix framework. This approach combines city-scale morphological patterns as global priors with local spatial information for context-dependent interpolation. The evaluation shows that while SM alone captures meaningful morphological structure, its combination with inverse distance weighting (IDW) or spatial k-nearest neighbor (sKNN) methods provides superior performance compared to existing SOTA models. Composite methods demonstrate the complementary advantages of combining morphological and spatial approaches.
Paper Structure (26 sections, 5 equations, 2 figures, 2 tables)

This paper contains 26 sections, 5 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. The problem of incomplete and uneven urban data
  4. Image-based methods
  5. Methods based on mobile and behavioral data
  6. The role of land use and causal approaches
  7. Data-driven approaches and digital twins; the role of OSM
  8. Digital twins of cities
  9. Graph Neural Networks (GNN) for Urban Tasks
  10. Multi-view imputation of urban data
  11. Comparison of levels: building vs neighborhood; multi-attribute imputation
  12. Morphological Clustering and SpaceMatrix
  13. Conclusion
  14. Problem Formulation
  15. Empirical motivation.
  16. ...and 11 more sections

Figures (2)

  • Figure 1: Workflow of the Spatial-morphological (SM) imputation model. The model derives morphological clusters from observed data and predicts missing built-form indicators based on land-use composition and site area.
  • Figure 2: Performance of SM, baseline methods, and composite imputers across missing rates for each reconstructed feature. Composite methods (SM + IDW, SM + sKNN) achieve the best results.