Density-based clustering divides spatially dense point distributions into clusters using specified algorithms. It provides three clustering methods: Density-Based Clustering, Hierarchical Clustering (HDBSCAN), and Ordering Clustering (OPTICS).

Definitions

• MinPts: Minimum number of points required to form a cluster.
• Clustering radius ε: Points within this radius that meet or exceed MinPts form a cluster.
• Core point: A point with at least MinPts neighboring points within ε.
• Boundary point: A point within ε of a core point but with fewer than MinPts neighbors.
• Noise point: Neither a core nor boundary point.
• Core distance: Distance from point X to its k-th nearest neighbor (k=MinPts), denoted as core_k(x). Example when k=5:

  

  

• Reachable distance: The maximum value between core distance and actual distance between two points.

  Example: With minPts=3 and ε=d(P,5), core distance of Point P is d(P,1). Reachable distances: Point 2 and 3 use core distance d(1,P); Point 4 uses actual distance d(4,P).

  

Principles

1. Density-Based Clustering (DBSCAN)

   Identifies clusters via spatial density, defining clusters as maximal sets of density-connected points. Robust to noise and detects arbitrary-shaped clusters.

   Algorithm: Finds core objects using Eps and MinPts, then expands clusters from these cores.

   

   Parameter adjustment: Increasing Eps merges clusters; decreasing splits clusters. Higher MinPts increases noise detection.

   Use case: Identifying accident-prone areas with explicit thresholds (e.g., 3 accidents within 2000m).

2. Hierarchical Clustering (HDBSCAN)

   Separates clusters from noise using variable density thresholds. Creates stable clusters through hierarchical merging.

   Algorithm: Improves DBSCAN by building minimum spanning trees with core/reachable distances. Splits clusters based on stability criteria.

   

   Cluster extraction conditions:

   1. Split clusters when 1/λ₁ + 1/λ₂ > 1/λ
   2. Stop splitting if subclusters have fewer than MinPts

   

3. Ordering Clustering (OPTICS): Reduces parameter sensitivity by considering density connectivity. Computationally intensive but flexible in detecting variable-density clusters.

Applications

• Site selection for chain stores using customer position data
• Emergency station planning for pipe burst clusters
• Identifying high-accident road sections
• Ecological population analysis
• Anomaly detection in data cleaning/security

Feature Entry

• Spatial Statistics Tab -> Cluster Distribution -> Density-Based Clustering
• Toolbox -> Spatial Statistics -> Cluster Distribution -> Density-Based Clustering

Parameters

Parameter requirements and output fields vary by method:

Method	DBSCAN	HDBSCAN	OPTICS
Parameters	Clustering radius MinPts	MinPts	Clustering radius MinPts Compactness
Output Fields	Source_ID Cluster_ID	Source_ID Cluster_ID Prob Outlier Exemplar Stability	Source_ID Cluster_ID ReachOrder ReachDist

• Source Dataset: Input point dataset for analysis.
• Clustering Method:
  1. DBSCAN: Requires clustering radius and MinPts.
  2. HDBSCAN: Requires MinPts only.
  3. OPTICS: Requires radius, MinPts, and compactness.
• Clustering Radius:
  • For DBSCAN: Defines neighborhood search range.
  • For OPTICS: Maximum reachable distance threshold.
• Unit: Measurement units (default: meters).
• MinPts: Minimum points to form cluster.
• Compactness: Clustering tightness (0-100). Higher values produce denser clusters.

Output Interpretation

Results vary by method but always include Cluster_ID rendering. Key fields:

• Source_ID: Original point ID.
• Cluster_ID: Cluster membership (-1=noise).
• Prob: Cluster membership probability (1=high).
• Outlier: 1 indicates potential outlier.
• Exemplar: 1 marks representative points.
• Stability: Cluster stability score.
• ReachOrder: Processing sequence.
• ReachDist: Reachability distance for density assessment.

Case Study

Using OPTICS to analyze restaurant customer distribution identified four clusters (grey=noise). New branches should prioritize high-density cluster areas:

Cluster 3 has the highest proportion, indicating maximum customer density:

Related Topics

Hot Spot Analysis (Getis-Ord Gi*)

Analyzing Patterns