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ClusteringLecture 4: Density-based Methods

Jing GaoSUNY Buffalo

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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.

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Density-based Clustering

Basic idea Clusters are dense regions in the data space,

separated by regions of lower object density

A cluster is defined as a maximal set of density-connected points

Discovers clusters of arbitrary shape

Method

DBSCAN

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Density Definition

-NeighborhoodObjects within a radius of

froman object.

High density - -Neighborhood of an object contains

at least MinPtsof objects.

q p

-Neighborhood ofp

-Neighborhood of q

Density of p is high (MinPts = 4)

Density of qis low (MinPts = 4)

}),(|{:)(

qpdqpN

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Core, Border & Outlier

Given and MinPts,categorize the objects into

three exclusive groups.

= 1unit, MinPts = 5

Core

Border

Outlier

A point is a core pointif it has more than a

specified number of points (MinPts) within

EpsThese are points that are at the

interior of a cluster.

A border pointhas fewer than MinPts

within Eps, but is in the neighborhoodof a core point.

A noise pointis any point that is not a

core point nor a border point.

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Example

Original Points Point types: core,

borderand outliers

= 10, MinPts = 4

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Density-reachability

Directly density-reachable

An object qis directly density-reachable from objectp

ifpis a core object and qis in ps -neighborhood.

q p

qis directly density-reachable fromp

pis not directly density-reachable from

q

Density-reachability is asymmetric

MinPts = 4

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DBSCAN Algorithm: Example

Parameter

= 2 cm

MinPts= 3

foreach o Ddo

ifois not yet classified thenifois a core-object then

collect all objects density-reachable from o

and assign them to a new cluster.

else

assign oto NOISE

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DBSCAN Algorithm: Example

Parameter

= 2 cm

MinPts= 3

foreach o Ddo

ifois not yet classified thenifois a core-object then

collect all objects density-reachable from o

and assign them to a new cluster.

else

assign oto NOISE

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DBSCAN Algorithm: Example

Parameter

= 2 cm

MinPts= 3

foreach o Ddo

ifois not yet classified then

ifois a core-object thencollect all objects density-reachable from o

and assign them to a new cluster.

else

assign oto NOISE

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DBSCAN: Sensitive to Parameters

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DBSCAN: Determining EPS and MinPts

Idea is that for points in a cluster, their kthnearest

neighbors are at roughly the same distance

Noise points have the kthnearest neighbor at fartherdistance

So, plot sorted distance of every point to its kthnearest

neighbor

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When DBSCAN Works Well

Original Points Clusters

Resistant to Noise

Can handle clusters of different shapes and sizes

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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

DBSCANs pros and cons

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