Density-based Clustering: DBSCAN Algorithm and Parameter Selection, Exams of Data Mining

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Clustering

Lecture 4: Density-based Methods

Jing Gao

SUNY Buffalo

Outline

• Basics
  • Motivation, definition, evaluation
• Methods
  • Partitional
  • Hierarchical
  • Density-based
  • Mixture model
  • Spectral methods
• Advanced topics
  • Clustering ensemble
  • Clustering in MapReduce
  • Semi-supervised clustering, subspace clustering, co-clustering, etc.

Density Definition

• -Neighborhood – Objects within a radius of  from

an object.

• “High density” - ε-Neighborhood of an object contains

at least MinPts of objects.

q p^

ε ε

ε-Neighborhood of p ε-Neighborhood of q Density of p is “high” (MinPts = 4) Density of q is “low” (MinPts = 4)

N  ( p ):{ q | d ( p , q )  }

Core, Border & Outlier

Given  and MinPts ,

categorize the objects into three exclusive groups.

 = 1unit, MinPts = 5

Core

Border

Outlier

A point is a core point if it has more than a specified number of points (MinPts) within Eps—These are points that are at the interior of a cluster. A border point has fewer than MinPts within Eps, but is in the neighborhood of a core point. A noise point is any point that is not a core point nor a border point.

Density-reachability

• Directly density-reachable
  • An object q is directly density-reachable from object p if p is a core object and q is in p’s -neighborhood.

q p^

ε ε

• q is directly density-reachable from p
• p is not directly density-reachable from q
• Density-reachability is asymmetric

MinPts = 4

Density-reachability

• Density-Reachable (directly and indirectly):
  • A point p is directly density-reachable from p 2
  • p 2 is directly density-reachable from p 1
  • p 1 is directly density-reachable from q
  • p  p 2  p 1  q form a chain

p

q

p 2

• p is (indirectly) density-reachable from q p (^1) • q is not density-reachable from p

MinPts = 7

DBSCAN Algorithm: Example

• Parameter
  •  = 2 cm
  • MinPts = 3

for each o  D do if o is not yet classified then if o is a core-object then collect all objects density-reachable from o and assign them to a new cluster. else assign o to NOISE

DBSCAN Algorithm: Example

• Parameter
  •  = 2 cm
  • MinPts = 3

for each o  D do if o is not yet classified then if o is a core-object then collect all objects density-reachable from o and assign them to a new cluster. else assign o to NOISE

DBSCAN: Determining EPS and MinPts

• Idea is that for points in a cluster, their kth^ nearest neighbors are at roughly the same distance
• Noise points have the kth^ nearest neighbor at farther distance
• So, plot sorted distance of every point to its kth^ nearest neighbor

When DBSCAN Works Well

Original Points (^) Clusters

• Resistant to Noise
• Can handle clusters of different shapes and sizes

Take-away Message

• The basic idea of density-based clustering
• The two important parameters and the definitions of

neighborhood and density in DBSCAN

• Core, border and outlier points
• DBSCAN algorithm
• DBSCAN’s pros and cons