This document summarizes a group project report on clustering in data mining. It discusses different types of clustering algorithms including K-means clustering and agglomerative hierarchical clustering. For K-means clustering, it provides an example showing how clusters are formed by assigning objects to centroids and recalculating centroids over iterations. For hierarchical clustering, it shows how clusters are merged based on distances recorded in a distance matrix and represented through a dendrogram. The document contains examples and diagrams to illustrate key steps and concepts in clustering techniques.

1. Clustering in Data Mining
Lesson: Data Mining
Professor: Mrs M.Hosseini
Group Members: Mojtaba Derakhshandi,S.Mostafa Sayyedi,Mojtaba Sadeghi

2. Clustering in Data Mining
Our Group:
Mr. Mojtaba Derakhshandi:
*Introduction
*Example Usage of Clustering
*Two Dimensional Space
*Example
*Centroid
Mr. Mojtaba Sadeghi:
Mr. S.Mostafa Sayyedi:
*K-Means Clustering
*Example
*Finding the Best Set of Clusters
*Agglomerative Hierarchical Clustering
*Example
*Recording the Distance Between Clusters

3. Introduction
What is Clustering?
Clustering in Data Mining
Mojtaba Derakhshandi
Page: 1

4. Page 4
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Economics Application
We Might be Interested in Finding Countries
Whose Economies are Similar.
Financial Application
We Might Wish to Find Clusters of Companies
that Have Similar Financial Performance.
Marketing Application
We Might Wish to Find Clusters of Customers
With Similar Buying Behavior.
Medical Application
We Might Wish to Find Clusters of Patients With
Similar Symptoms.
Document Retrieval Application
We Might Wish to Find Clusters of Documents
With Related Content.
Crime Analysis Application
We Might Look for Clusters of High Volume Crimes Such
as Burglaries or Try to Cluster Together Much Rarer (But
Possibly Related) Crimes Such as Murders.
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Example Usage of Clustering
Clustering in Data Mining
Mojtaba Derakhshandi
Page: 2

5. Two Dimensional Space
Clustering in Data Mining
Mojtaba Derakhshandi
Object for Clustering Clustering of Objects (First Version)
Page: 3

6. Two Dimensional Space
Clustering in Data Mining
Mojtaba Derakhshandi
Clustering of Objects (Second Version)
Page: 4

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Centroid:
Clustering in Data Mining
Page: 5
‘Centre’ of a Cluster, Generally Called its Centroid.
So the Centroid of the Four Points (With 6 Attributes):
Would Be:
Mojtaba Derakhshandi

8. Page 8
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K-Means Clustering:
Clustering in Data Mining
The k-Means Clustering Algorithm
Page: 6
S.Mostafa Sayyedi

9. Page 9
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Example:
Clustering in Data Mining
S.Mostafa Sayyedi
Objects for Clustering (Attribute Values)
Page: 7

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Example:
Clustering in Data Mining
S.Mostafa Sayyedi
Objects for Clustering
Page: 8
Step1: Choose a value of k

11. Page 11
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Example:
Clustering in Data Mining
S.Mostafa Sayyedi
Initial Choice of Centroids
Page: 9
Step2: Select k Objects in an Arbitrary Fashion. Use These as the Initial Set of k Centroids

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Example:
Clustering in Data Mining
S.Mostafa Sayyedi
Objects for Clustering (Augmented)Page: 10
Step3: Assign Each of the Objects to the Cluster for Which it is Nearest to the Centroid

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Example:
Clustering in Data Mining
S.Mostafa Sayyedi
Initial Clusters
Page: 11
Step4: Recalculate the Centroids of the k Clusters

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Example:
Clustering in Data Mining
S.Mostafa Sayyedi
Centroids After First Iteration
Page: 12
Revised Clusters
Step 5: Repeat Steps 3 and 4 Until the Centroids no Longer Move

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Example:
Clustering in Data Mining
S.Mostafa Sayyedi
Centroids After First Two Iterations
Page: 13
Third Set of Clusters

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Finding the Best Set of Clusters:
Clustering in Data Mining
S.Mostafa Sayyedi
Value of Objective Function for Different Values of k
Page: 14

17. Page 17
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Clustering in Data Mining
Mojtaba Sadeghi
Agglomerative Hierarchical Clustering:
Agglomerative Hierarchical Clustering: Basic Algorithm
Page: 15

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Example
Clustering in Data Mining
Mojtaba Sadeghi
Page: 16

19. Clustering in Data Mining
Mojtaba Sadeghi
Original Data (11 Objects) Clusters After Two Passes
Page: 17

20. Clustering in Data Mining
Mojtaba Sadeghi
Without Knowing the Precise Distances Between Each Pair of Objects, a Plausible Sequence of Events is as Follows.
Page: 18

21. Clustering in Data Mining
Mojtaba Sadeghi
A Possible Dendrogram CorrespondingPage: 19

22. Clustering in Data Mining
Mojtaba Sadeghi
Example of a Distance Matrix
Page: 20
Recording the Distance Between Clusters:

23. Clustering in Data Mining
Mojtaba Sadeghi
Distance Matrix After First Merger (Incomplete)
Page: 21
Distance Matrix After First Merger
Recording the Distance Between Clusters:

24. Clustering in Data Mining
Mojtaba Sadeghi
Distance Matrix After Two Merger (Incomplete)
Page: 22
Recording the Distance Between Clusters:
Distance Matrix After Two Merger

25. Clustering in Data Mining
Mojtaba Sadeghi
Distance Matrix After Three Mergers (Incomplete)
Page: 23
Recording the Distance Between Clusters:
Distance Matrix After Three Mergers

26. Clustering in Data Mining
Mojtaba Sadeghi
Distance Matrix After Four Mergers (Incomplete)
Page: 24
Recording the Distance Between Clusters:
Distance Matrix After Four Mergers

27. Clustering in Data Mining
Mojtaba Sadeghi
Dendrogram Corresponding to Hierarchical Clustering Process
Page: 25

28. Any Question?

29. Resource
Principles of Data Mining
Third Edition
Prof. Max Bramer
School of Computing
University of Portsmouth
Portsmouth, Hampshire, UK
Publisher: Springer
29

30. THANK YOU