Add dataset card

README.md

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+---
+license: cc-by-4.0
+task_categories:
+- other
+language:
+- en
+tags:
+- spatial-statistics
+- DBSCAN
+- point-process
+- cluster-detection
+- Monte-Carlo
+pretty_name: DBSCAN Cluster Density Ratios on CSR Point Fields
+size_categories:
+- 1B<n<10B
+---
+
+# DBSCAN Cluster Density Ratios — CSR Simulation Data
+
+Monte-Carlo simulation of DBSCAN clustering applied to complete-spatial-randomness (CSR)
+point fields. Used to characterize the null distribution of detected cluster density ratios
+and calibrate anomaly detection p-values (look-elsewhere correction).
+
+## Simulation parameters
+
+| Parameter | Value |
+|---|---|
+| N (points per field) | 10,000 |
+| Domain | Disk, radius R=100 |
+| Domain area S₀ | π·100² ≈ 31,415.93 |
+| Background intensity λ₀ | N/S₀ = 1/π ≈ 0.31831 |
+| DBSCAN min_samples | 10 |
+| Post-filter min_cluster_size | 10 |
+| Post-filter min_area | 0.5 |
+| eps sweep | 0.80 → 2.86 (step 0.01, 207 values) |
+| Iterations per eps | ~12,000 – 1,000,000 |
+
+**Total compute**: ~60 h on a single workstation (16-process parallel).
+
+## Schema
+
+Each parquet file corresponds to one `eps` value (filename: `data/eps_X.XX.parquet`).
+
+| Column | Type | Description |
+|---|---|---|
+| `S_prime` | float64 | Convex-hull area of detected cluster. **-1.0 = no cluster found** (placeholder row) |
+| `N_prime` | int64 | Point count of detected cluster. **-1 = no cluster found** |
+| `iteration` | int64 | Field index (1-based). Multiple clusters per iteration are all recorded. |
+
+**Always filter** `S_prime != -1` before analysis. Placeholder rows mark iterations with no
+valid DBSCAN cluster (common at low eps where clustering is rare).
+
+## Key derived quantities
+
+```python
+lambda0 = 10000 / (np.pi * 100**2)   # ≈ 0.31831
+R = (df.N_prime / df.S_prime) / lambda0   # density ratio (main statistic)
+R_tilde = R * eps**2                       # eps-collapsed statistic (eps-invariant master)
+```
+
+The density ratio `R` follows a heavy-tailed distribution (tail index α≈7). After
+rescaling to `R̃ = R·eps²`, the distribution collapses to a single master inverse-gamma
+(shape≈20.5) across all eps — the central empirical finding of this dataset.
+
+## Usage
+
+```python
+import pandas as pd
+import numpy as np
+
+# Load one eps slice
+eps = 1.20
+df = pd.read_parquet(f"hf://datasets/Winternewt/cluster-distribution-simdata/data/eps_{eps:.2f}.parquet")
+df = df[df.S_prime != -1]   # drop placeholder rows
+
+lambda0 = 10000 / (np.pi * 100**2)
+df['R'] = (df.N_prime / df.S_prime) / lambda0
+df['R_tilde'] = df['R'] * eps**2
+print(df.R_tilde.describe())
+```
+
+## Repository
+
+Source code and analysis: https://github.com/winternewt/cluster_distribution
+Analytic findings: see `docs/analytic_findings.md` in the source repo.