1. DBSCAN Data Mining algorithm Dr Veljko Milutinović Milan Micić
Professor
Dr Veljko Milutinović
Student
Milan Micić
2011/3323
School of Electrical Engineering, University of Belgrade
Department of Computer Engineering

2. Content Introduction The DBSCAN basic idea Algorithm DBSCAN on R
Example
Advantages
Disadvantages
References
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3. 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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4. DBSCAN basic idea
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
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5. DBSCAN basic idea 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
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6. Algorithm Complexity with indexing structure: O(n*log(n))
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)
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))
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7. DBSCAN on R FPC - Flexible Procedures for Clustering
GNU General Public License 
Various methods for clustering and cluster validation
Interface functions for many methods implemented in language R
DBSCAN: O(n2)
dbscan(x,0.2,showplot=2)
dbscan Pts=600 MinPts=5 eps=0.2
seed
border
total
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8. Example 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
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9. 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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10. 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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11. Advantages 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
Has a notion of noise
Requires just two parameters
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12. References
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:
Wiki:
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13. Thank you for your attention!
Questions
Milan Micić
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