Find Your Next Location

Five geospatial data modalities are acquired and harmonised into EPSG:27700 (British National Grid): population (LandScan), demographics (Census 2021), crime (police.uk 2021), transport (OSM stations + Overpass bus stops), and POIs (OSMnx).

Three Data Modalities

POI Categorisation

Each Point of Interest is classified into a business role relative to the target business type:

Competition Density (k=2 Ring)

For each business type, a competition density feature counts same-type businesses in a k=2 H3 ring (~18 neighboring hexagons, ~350m radius).

Census Merge

Three ONS Census 2021 CSVs (Economic Activity, Age Structure, Qualifications) are merged on geog_code (Output Area identifier), producing 846 OAs with 7 demographic columns. Missing values are imputed with the column median.

Exploratory Data Analysis

Fig. 1 — Feature missingness audit (left) and target class distribution (right).

Fig. 2 — Feature correlation matrix.

Fig. 3 — Feature distributions split by target class (cafe).

Uber's H3 library partitions Greater London into hierarchical hexagonal cells. Unlike square grids, hexagons have 6 equidistant neighbours — ideal for walking-distance analysis.

Why Resolution 9?

At Resolution 9, each hexagon covers roughly the area a person walks in 2 minutes — the micro-unit of the 15-minute city (Moreno et al., 2021).

Enrichment Pipeline

Census demographics are joined via sjoin_nearest with population-weighted mean aggregation. Hexes with no OA match receive the borough median (conservative imputation).

Street-level crime data from police.uk (Metropolitan Police + City of London Police, ~1.08M raw records across 2021) is cleaned, deduplicated, and aggregated to H3 hexagons.

Data Cleaning

The raw data contains significant quality issues that are resolved before feature engineering:

Post-cleaning: ~852,000 verified crime records across all 33 London boroughs.

Crime Type Grouping

14 raw crime types grouped into 3 retail-relevant categories:

Features (3 per Hexagon)

Each crime group is aggregated per hex, then log-transformed (log1p) to compress the right-skewed tail — hotspot hexes like Oxford Street and Stratford Westfield have thousands of incidents while most residential hexes have single digits. Hexes with no crime receive 0 (an observed zero, not imputed with borough median).

Transport connectivity features capture the accessibility gradient that drives retail footfall. Station data comes from the existing POI fetch (public_transport=station); bus stops are fetched separately via Overpass API (highway=bus_stop, ~19,000 across London).

Spatial Computation

All distance calculations use EPSG:27700 (British National Grid) for metric accuracy. A scipy.spatial.cKDTree indexes station locations for O(log n) nearest-neighbour and radius queries against ~16,000 hex centroids.

Features (3 per Hexagon)

Missing Values

Bus stops: 0 for hexes with no stops (observed zero). Station distance: always computed (no missing values). Station count: 0 when no stations within 800m.

The enriched H3 grid becomes a spatial graph where hexagons are nodes and edges connect adjacent hexes. From this graph we extract three layers of structural information.

Six Centrality Metrics

Louvain Community Detection

The Louvain algorithm partitions the H3 adjacency graph into communities, maximising modularity. Each hexagon receives a community_id capturing which spatial neighbourhood cluster it belongs to.

Node2Vec Graph Embeddings

Node2Vec learns a 3-dimensional vector representation for each hexagon by simulating biased random walks on the graph. Hexagons with similar graph neighbourhoods receive similar embeddings, even if geographically distant.

Heuristic Site Score

Where D_H = Level 4 qualification % / 100 (demand proxy), S = synergy count, A = anchor count, C = competitor count.

Problem Formulation

Binary classification: for each of 6 business types, predict whether a hexagon should contain that business. The commercially valuable output is the False Positives — locations predicted as suitable that have no current supply.

Feature Matrix (33 Features per Business Type)

Spatial Cross-Validation

Standard k-fold CV violates spatial independence. We group Resolution-9 hexes by their Resolution-7 parent cell (~0.74 km² blocks). All hexes sharing a parent are assigned to the same fold, preserving spatial integrity across 5 folds.

Model Comparison

Evaluation Figures

Fig. 4 — ROC curves (out-of-fold, spatial CV)

Fig. 5 — Confusion matrices (out-of-fold, all 6 types)

Fig. 6 — Top 10 features by business type (XGBoost gain)

Fig. 7 — Precision–Recall curves with F₁-optimal thresholds

Fig. 8 — Calibration curve

Fig. 9 — Failure mode analysis

Model Performance (33 Features, Spatial Block CV)

* Gym model has degraded AUC due to data sparsity (6.6% prevalence, only 1,014 positive hexes). Recommendations should be treated with lower confidence. See caveat below.

Feature Value-Add: Crime + Transport (30 → 33 Features)

Fig. 10 — Learning Curve (left) and Feature Ablation (right)

Statistical Significance

All 6 models are validated with bootstrap 95% confidence intervals (n=2000) and permutation tests (n=1000) at a strict p < 0.001 threshold. This high bar accounts for multiple comparisons (6 models tested simultaneously) and remains significant even after Bonferroni correction.

Fig. 11 — Permutation test: null distribution vs observed AUC (all 6 types)

Confidence Score Distributions

Histograms of out-of-fold predicted probabilities, split by actual label (positive vs negative), reveal whether the model achieves genuine score separation. A well-calibrated model produces bimodal distributions: negatives cluster near 0, positives near 1. Flat distributions indicate poor discrimination. Tier threshold lines show where Prime (≥0.95) and Strong (≥0.85) recommendations are carved from the probability space.

Fig. 14 — OOF predicted probability distributions: negative hexes (grey) vs positive hexes (red), with F₁ threshold (orange dashed) and tier thresholds (green dotted). Bimodal separation confirms genuine score discrimination.

Borough Holdout Cross-Validation (External Validity)

Standard spatial CV tests within-London generalisation. Borough holdout (leave-one-borough-out) tests a harder question: does the model generalise to administratively distinct areas it has never seen? Each of the 33 boroughs is used as a test set in turn (minimum 10 positives required to compute a valid AUC). The heatmap shows per-borough AUC; the boxplot shows the distribution across boroughs per type.

Fig. 15 — Borough holdout CV: AUC heatmap (boroughs × types, left) and per-type AUC distribution (right). Consistent AUC above 0.5 across boroughs confirms the model generalises beyond its training boroughs.

Gym Model Deep-Dive: Root Cause Analysis

The gym model (AUC 0.775) was subjected to three diagnostic tests: (1) removing crime+transport features to test whether the 6 new features cause the degradation, (2) doubling the class weight to test whether imbalance handling is insufficient, and (3) examining per-fold AUC variance to confirm the instability signature of data sparsity.

Fig. 16 — Gym deep-dive: class distribution (A), AUC comparison across configurations (B), precision-recall curve (C), and per-fold variance vs. Cafe (D).

5-Tier Recommendation System

Every recommendation comes with a per-location explanation powered by SHAP (SHapley Additive exPlanations) — a game-theoretic framework that decomposes each prediction into individual feature contributions.

Why SHAP, Not Feature Importance?

How It Works

For each hexagon, SHAP computes a signed contribution for every feature:

The top 3 SHAP drivers are stored per hexagon and displayed as “Why Here?” cards in the Site Finder tab, giving stakeholders transparent, actionable insight into each recommendation.

Fig. 12 — SHAP feature importance: mean |SHAP| value per feature across all 6 business types (top 8 features shown)

Contrastive SHAP: Why Did the Model Recommend Here but Not There?

Each hexagon is assigned to a confusion-matrix quadrant (TP, FP, FN, TN) based on out-of-fold predictions. The grouped bar chart compares mean absolute SHAP attribution for the top 10 features across TP (existing businesses the model confirms), FP (recommendations — gaps the model identifies), and FN (missed sites). Features where FP bars exceed FN bars indicate what separates an identified opportunity from a model blind spot.

Fig. 13 — Contrastive SHAP: mean absolute feature attribution for True Positives (red), False Positives / recommendations (green), and False Negatives / missed sites (orange) across all 6 business types.

Do Recommendations Systematically Exclude Deprived Areas?

A model trained on commercial presence data risks learning historical inequity: businesses have historically avoided deprived areas, so the model may conclude deprived areas are unsuitable — a self-fulfilling prophecy. We audit this by computing recommendation rates across deprivation quintiles (using no_qualifications_perc as a deprivation proxy, as no IMD data is available).

Method

Hexagons are split into quintiles (Q1 = least deprived, Q5 = most deprived) and recommendation rate (False Positives / total hexes per quintile) is computed per business type. Spearman ρ tests whether recommendation rate monotonically increases or decreases with deprivation quintile. A positive ρ indicates the model over-recommends in deprived areas.

Fig. 17 — Recommendation rate by deprivation quintile across all 6 business types. Q1 = least deprived; Q5 = most deprived. Spearman ρ annotated per type.

Partial Dependence Plots (Cafe Model)

Partial Dependence Plots (PDPs) show the marginal effect of each feature on the predicted probability, holding all other features constant. Unlike SHAP (which explains individual predictions), PDPs reveal the global shape of each feature’s relationship: is it linear, threshold-based, or saturating? The top 6 features of the Cafe model are plotted below.

Fig. 18 — Partial Dependence Plots: top 6 features of the Cafe model, showing marginal effect on predicted probability. Rug plots indicate feature value density.

Spatial Autocorrelation of Residuals (Moran’s I)

If model residuals cluster spatially, the model is missing a spatially structured signal — a violation of the independence assumption that inflates confidence intervals. Moran’s I quantifies spatial autocorrelation using H3 k-ring adjacency as the spatial weight matrix. Values near 0 indicate spatial randomness; positive values indicate clustering; negative values indicate dispersion.

Fig. 19 — Moran’s I for model residuals: observed I (red line) vs permutation null distribution (grey histogram). Low I values confirm spatial CV effectively decorrelates residuals.

Feature Group Ablation Study

To quantify each feature category’s contribution, we perform a leave-one-group-out ablation: remove all features from one category (POI, Demographics, Crime, Transport, or Graph centrality), retrain the model, and measure AUC drop. Larger drops indicate higher dependency on that feature group.

Fig. 20 — Feature group ablation: AUC change when each feature group is removed. Negative values (red) indicate the model depends on that group; positive values (blue) indicate the features were adding noise.

Methodology Flowchart

End-to-end pipeline from raw data sources through H3 spatial indexing, feature engineering, spatial cross-validation, XGBoost classification, evaluation, and final recommendation output.

Fig. 21 — Pipeline architecture: data ingestion → H3 indexing → feature engineering → spatial CV → XGBoost → evaluation → tiered recommendations → interactive maps.

Why Does Crime Predict Retail Viability?

At first glance, property_crime_log1p appearing in 5/6 models’ top-5 features seems counterintuitive. The explanation lies in routine activity theory (Cohen & Felson, 1979): crime requires convergence of motivated offenders, suitable targets, and absent guardians. High-footfall commercial areas provide all three — more people, more targets, more opportunity. Crime is therefore a proxy for footfall intensity, not a causal driver of business viability.

Agglomeration Economics

POI co-occurrence dominates the feature importance rankings (e.g., n_restaurant at 38–42% for Cafe/Fast Food). This reflects Hotelling’s principle of minimum differentiation (1929): businesses cluster because proximity to competitors signals high demand density. The model captures this agglomeration effect, validating that retail location selection is fundamentally a clustering problem.

Fairness Implications of Training on Presence

A core limitation: the model is trained on existing business locations as positive labels. Areas that lack businesses (due to historical disinvestment, planning restrictions, or demographic change) are labelled as negatives. The model may therefore encode a self-fulfilling prophecy: “no businesses here → unsuitable location” even when genuine demand exists. The Fairness Audit (Fig. 17) quantifies this risk. Practitioners should supplement model recommendations with local market research in under-served areas.

Spatial CV Effectiveness

Borough-block spatial cross-validation prevents geographic data leakage by ensuring that no hexagons from the same borough appear in both train and test sets. The Moran’s I analysis (Fig. 19) validates this design: if residuals show no significant spatial clustering, the spatial CV folds are structured correctly and AUC estimates are unbiased. Borough holdout CV (Fig. 15) provides an even stronger test of external validity by holding out entire boroughs.