DBSCAN

School of Electrical Engineering, University of Belgrade

Department of Computer Engineering

Data Mining algorithm

Professor

Dr Veljko MilutinovićStudent

Milan Micić2011/3323

milan.z.micic@gmail.com

Content

• Introduction• The DBSCAN basic idea• Algorithm• DBSCAN on R• Example• Advantages• Disadvantages• References

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Introduction

• Data clustering algorithms• Using in machine learning, pattern recognition, image analyses,

information retrieval, and bioinformatics• Hierarchical, centroid-based, distribution-based, density-based, etc

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DBSCAN basic idea

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• Density-Based Spatial Clustering of Applications with Noise• Munich,1996• Derived from a human natural

clustering approach

• Input parameters• The size of epsilon neighborhood – ε• Minimum points in cluster – MinPts

• Neighborhood of a given radius ε has to contain at least a minimum number of points MinPts

DBSCAN basic idea

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• Directly density-reachable, p1 from p2

• p1 belongs to the ε neighborhood of p2

• p2's neighborhood size is greater than a given parameter MinPts

• Density-reachable, p0 from pn

• Exists a chain of points p1,..., pn-1, where pi+1 is directly density-reachable from pi

• Core, border and noise point

Algorithm

DBSCAN(D, eps, MinPts)

C = 0

for each unvisited point P in dataset D

mark P as visited

N = regionQuery(P, eps)

if sizeof(N) < MinPts

mark P as NOISE

else

C = next cluster

expandCluster(P, N, C, eps, MinPts)

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expandCluster(P,N,C,eps,MinPts)

add P to cluster C

for each point P' in N

if P' is not visited

mark P' as visited

N' = regionQuery(P', eps)

if sizeof(N') >= MinPts

N = N joined with N'

if P' is not yet member of any cluster

add P' to cluster C

• Complexity with indexing structure: O(n*log(n))

DBSCAN on R

• GNU General Public License • Various methods for clustering

and cluster validation• Interface functions for many methods

implemented in language R• DBSCAN: O(n2)

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• dbscan(x,0.2,showplot=2)• dbscan Pts=600 MinPts=5 eps=0.2

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• FPC - Flexible Procedures for Clustering

Example

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• Astronomy task• Identifying celestial objects by capturing the radiation they emit

• Captured noise (by sensors, diffuse emission from atmosphere and space itself)

• Eliminating method – to constrain the relevant intensity by a known threshold

• In this case – only pixels whose intensity are less than 50 (and consequently darker) are being considered

Example

• DBSCAN algorithm applied on individual pixels • Linking together a complete emission area

• Each of the generated cluster will define a celestial entity• ε = 5, MinPts = 5, 64 clusters and 224 outliers found

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Disadvantages

• Appropriate parameters ε and MinPts• Numerous experiments indicates best MinPts = 4

• Clustering datasets with large difference in densities• “Curse of dimensionality”

• In every algorithm based on the Euclidean distance for high-dimensional data sets

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Advantages

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• Has a notion of noise• Requires just two parameters

• Does not require number of clusters in the data a priori• Can find arbitrarily shaped clusters

• Even clusters completely surrounded by a different cluster

• Mostly insensitive to the ordering of the points in the database

• Only border points might swap cluster membership

References

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• Martin Ester, Hans-Peter Kriegel, Joerg Sander, Xiaowei Xu: “A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise”, Institute for Computer Science, University of Munich,1996;

• Mehmed Kantardzic: “Data Mining: Concepts, Models, Methods, and Algorithms”, 2011;

• Wikibooks: http://en.wikibooks.org/wiki/Data_Mining_Algorithms_In_R/Clustering/Density-Based_Clustering;

• Wiki: http://en.wikipedia.org/wiki/DBSCAN

Thank you for your attention!

Questions

Milan Micić

milan.z.micic@gmail.com13/13