density-based clustering · main clustering approaches partitioning method →constructs partitions...

Density-Based ClusteringIzabela Moise, Evangelos Pournaras, Dirk Helbing

Izabela Moise, Evangelos Pournaras, Dirk Helbing 1

Reminder

Unsupervised data miningX Clustering→ k -Means


Main Clustering Approaches

• Partitioning method→ constructs partitions of data points→ evaluates the partitions by some criterion→ k -means, k -medoids

• Density-based method:→ based on connectivity and density functions→ DBSCAN, DJCluster


Density-Based Clustering




locates regions of high density that are separated from one anotherby regions of low density.


Main principles

• Two parameters:1. maximum radius of the neighbourhood→ Eps2. minimum number of points in an Eps neighbourhood of a point→ MinPts

• NEps(p) : {q ∈ D s.t . dist(p, q) ≤ Eps}• Key idea: the density of the neighbourhood has to exceed

some threshold.

• The shape of a neighbourhood depends on the dist function


Core, Border and Noise/Outlier

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1Jing Gao, SUNY BuffaloIzabela Moise, Evangelos Pournaras, Dirk Helbing 6

Directly Density-Reachable

Directly density-reachable:→ A point p is directly density-reachable from a point q wrt. Eps,MinPts if:

1. p ∈ NEps(q) and

2. |NEps(q)| ≥ MinPts


Density-Reachable

• Density-reachable:→ A point p is density-reachable from a point q wrt. Eps,MinPts if there is a chain of points p1, ..., pn, withp1 = q, pn = p, s.t .pi+1 is directly density reachable from pi

• transitive but not symmetric


Density-Connected

Density-connected:→ A point p is density-connected from a point q wrt. Eps, MinPts ifthere is a point o s.t. p and q are density-reachable from o wrt. Epsand MinPts


Density-Connected

Density-connected:→ A point p is density-connected from a point q wrt. Eps, MinPts ifthere is a point o s.t. p and q are density-reachable from o wrt. Epsand MinPts→ symmetric


DBSCAN - Density-Based Spatial Clustering of Applicationswith Noise


Main Principles

One of the most cited clustering algorithms

Main principle:

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

• Discovers clusters of arbitrary shapes (spherical, elongated,linear), and noise

• Works with spatial datasets:→ geomarketing, tomography, satellite images

• Requires only two parameters (no prior knowledge of thenumber of clusters)


Definition: Cluster

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2Erik Kropat, University of the Bundeswehr Munich


Definition: Noise

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The Algorithm

1. Randomly select a point p

2. Retrieve all points density-reachable from p wrt. Eps andMinPts

3. If p is a core point, a cluster is formed

4. If p is a border point, no points are density-reachable from p→visit the next data point

5. Continue the process until all points have been processed


Selecting Eps and MinPts

The two parameters can be determined by a heuristic

Observation:• For points in a cluster their k -th nearest neighbours are at

roughly the same distance.

• Noise points have the k -th nearest neighbour at fartherdistance.


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Pros and Cons

Pros:

X discovers clusters of arbitrary shapes

X handles noise

X needs density parameters as termination condition


Pros and Cons

Cons:

X cannot handle varying densities

X sensitive to parameters→ hard to determine the correct set ofparameters

X sampling affects density measures


density-based clustering · main clustering approaches partitioning method →constructs partitions...

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