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Project Presentation
Arpan Maheshwari
Y7082,CSE
[email protected]
Supervisor:
Prof. Amitav Mukerjee
Madan M Dabbeeru
Clustering:
 Organising a collection of k-dimensional vectors into
groups whose members share similar features in some
way.
 To reduce large amount of data by categorizing in
smaller set of similar items.
 Clustering is different from classification.
Elements of Clustering :
 Cluster : ordered list of objects sharing some
similarities.
 Distance Between Two Clusters : Implementation
Dependent;e.g. Minkowski Metric
 Similarity : function SIMILAR(Di , Dj ) ;
0 : no agreement
•
1 : perfect agreement
Threshold : lowest possible input value of similarity
required to join two objects in a cluster.
Clustering
Algorithms
Hierarchical
Non-Hierarchical
Partiti
Agglomerative
Divisive
oning(e.g.GNG,DBS
CAN,K-means)
Probabilistic(e.g.Mix
ture of Gaussians)
Clumping(e.g. Fuzzy
C-means)
Possible Applications:
 Marketing
 Biology & Medical Sciences
 Libraries
 Insurance
 City Planning
 WWW
Growing Neural Gas
 Proposed by Bernd Fritzke
 Parametres are constant in time
 Incremental
 Adaptive
 Competitive Hebbian Learning
Parametres in GNG:
 e_b : Learning rate of winner node
 e_n : Learning rate of neighbours
 lambda: when new node will be inserted
 alpha : error decrement of winner nodes upon
insertion of new node
 beta : error decrement of all nodes
Algorithm:
1)
2)
3)
Initialise a set A to contain two nodes randomly chosen according to probability
distribution p(ξ).
Generate an input signal ξ according to p(ξ).
Determine the winner node s1 and second nearest node s2 such that s1,s2 belong to A.
Create an edge between s1 & s2 (if not exist).Set its age to 0.
Increase error of s1 by distance between ξ & s1.
Move s1 and its neighbors towards input signal by e_w and e_n of difference between
the coordinates.
7)
Increment age of all edges emanating from s1.
8)
Delete all edges with age >= max_age .Delete nodes with no edges.
9)
If no. of input signals generated so far is a multiple of λ, insert
a new node ,r.
a)Find node with largest error ,q and neighbor of q with largest error ,f .
b)Assign r the mean position of q and f and
errorr = (errorq + errorf )/2
c)errorq -= α * errorq
&
errorf -= α* errorf
d)add r in A.
10) Decrease error of all nodes by β *errori.
4)
5)
6)
Demo of GNG
Reference:http://homepages.feis.herts.ac.uk/~nng
roup/software.php
DBSCAN : Density Based Spatial
Clustering of Application with
Noise
 Proposed by Martin Ester, Hans-Peter Kriegel, Jörg
Sander and Xiaovei Xui in 1996.
 Finds clusters starting from estimated density .
 Two parametres : epsilon(eps ) and minimum points
minPts.
 eps can be estimated.
Algorithm :
Reference:slides by
Francesco Satini
Phd Student
IMT
Comparing GNG & DBSCAN
 Time Complexity
 Capability of tackling high dimensional data
 Perfomance
 Number of initial parametres
 Perfomance with moving data
Data to be used
 Mainly design data
References:
 Jim Holmstrm :Master Thesis,Growing Neural Gas-Experiments





with GNG-GNG with Utility and Supervised GNG
M Ester, HP Kriegel, J Sander, X Xu : A Density-Based Algorithm
for Discovering Clusters in Large Spatial Databases with Noise Proc. 2nd Int. Conf. on Knowledge Discovery and Data Mining,
1996
Competitive
learning:http://homepages.feis.herts.ac.uk/~nngroup/software.p
hp
www.utdallas.edu/~lkhan/Spring2008G/DBSCAN.ppt
B. Fritzke. :A growing neural gas network learns topologies.
Jose Alfredo F. Costa and Ricardo S. Oliveira :Cluster Analysis
using Growing Neural Gas and Graph Partitioning