Datasets:

Winternewt
/

cluster-distribution-simdata

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

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

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.