Data Clusterng

P a g e | 1

[Type text]

Project Submitted By:

Name VIDYA NAND JHA

Stream IT, 3rd Year

Section B

Group II

Class Roll 083

University Roll 10900211092

University Reg. NO 11090110208

MOB 9748062585

P a g e | 2

ACKNOWLEDGEMENT

I would like to express my special thanks of

gratitude to Mr. CHANDAN BANERJEE, as well as

our mentor who gave me the golden opportunity to

do this wonderful seminar on the topic (Data

Clustering).I came to know about so many new

things. I am really thankful to them.

Secondly i would also like to thank my friends who

helped me a lot in finalizing this seminar within the

limited time frame.

.

P a g e | 3

Table of contents

ABSTRACT 04

INTRODUCTION 05

TYPES OF CLUSTERING 11

APPLICATION 30

CONCLUSION 31

REFERENCES 32

P a g e | 4

ABSTRACT

We know that fast retrieval of relevant

information from the database has been a

significant issue. Different techniques has been

developed for this purpose this one of them is

Data Clustering.

In this paper data clustering is discussed along

with different clustering method and analysis,

Like k-means, Hierarchical, Model-based and

Density-based clustering.

We also discussed application of data clustering

like Data Mining.

P a g e | 5

INTRODUCTION

Cluster: Cluster is just an ordered list of object

with similar characteristics. A cluster is

comprised of a number of similar objects

collected or grouped together. Everitt (1974)

documents some of the following definition of

cluster.

1. A cluster is a set of entities which are alike

and entities from different clusters are not

alike.

2. A cluster is an aggregation of point in the

test space such that the distance between two

points in the cluster is less than the distance

between point in the cluster and any point not

in it.

P a g e | 6

Data Clustering: The process of grouping a set

of physical or abstract objects into classes of

similar objects is called clustering.

We can also say that data clustering is method

in which we make cluster of similar object that

are similar in characteristics

Some example of clustering

1. Clustering images based on their perceptual

similarities.

2. Clustering webpage based on their content.

3. Clustering web search results.

4. Clustering user in social network site based

on their properties.

P a g e | 7

5. Image segmentation

Clustering pixel

Choice of similarities measure is very important

for clustering.Similarity is inversely related to

distance. Different way exits to measure

distances .

P a g e | 8

Clustering of objects

In the above figure we may calculate distance

through Euclidean method.

That is Euclidean distance :

P a g e | 9

Kernelized(non-linear) distance :

Collection of objects.

In above figure Kernelized(non-linear) distance

seems more reasonable.

P a g e | 10

WHAT IS GOOD CLUSTERING?

A good clustering is one that achieves

1) High within-cluster similarity

2) Low inter-cluster similarity

P a g e | 11

2. TYPES OF CLUSTERING METHODS

There are many clustering methods

available, and each of them may give a

different grouping of a dataset. The

choice of a particular method will

depend on the type of output desired.

The known performance of method with

particular types of data, the hardware

and software facilities available and the

size of the dataset. In general, clustering

methods may be divided into two

categories based on the cluster structure

which they produce. The non-

hierarchical methods divide a dataset of

N objects into M clusters, with or

without overlap.

P a g e | 12

2.1 PARTITIONING

What is K-Means Clustering?

Simply speaking it is an algorithm to classify or

to group your objects based on

attributes/features into K number of group. K is

positive integer number. The grouping is done

by minimizing the sum of squares of distances

between data and the corresponding cluster

centroid. Thus, the purpose of K-mean

clustering is to classify the data,

Example: Suppose we have 4 objects as your

training data point and each object have 2

attributes. Each attribute represents coordinate

of the object

.

P a g e | 13

Object Feature 1 (X): weight index

Feature 2 (Y): pH

Medicine A 1 1 Medicine B 2 1 Medicine C 4 3 Medicine D 5 4

Thus, we also know before hand that these

objects belong to two groups of medicine

(cluster 1 and cluster 2).

The problem now is to determine which

medicines belong to cluster 1 and which

medicines belong to the other cluster. Each

medicine represents one point with two

components coordinate.

P a g e | 14

Numerical Example (manual calculation)

The basic step of k-means clustering is simple.

In the beginning, we determine number of

cluster K and we assume the centroid or center

of these clusters. We can take any random

objects as the initial centroids or the first K

objects can also serve as the initial centroids.

Then the K means algorithm will do the three

steps below until convergence.

P a g e | 15

Suppose we have several objects (4 types of

medicines) and each object have two attributes

or features as

P a g e | 16

shown in table below. Our goal is to group

these objects into K=2 group of medicine based

on the two

features (pH and weight index).

Objects Feature 1 (X): weight index

Feature 2 (Y): pH

Medicine A 1 1

Medicine B 2 1

Medicine C 4 3

Medicine D 5 4

Each medicine represents one point with two

features (X, Y) that we can represent it as

coordinate in a feature space as shown in the

figure .

P a g e | 17

1.Initial value of centroids: Suppose we use

medicine A and medicine B as the first

centroids. Let 1 c and 2 c denote the coordinate

of the centroids, then c1 = (1,1) and 2 c = (2,1).

2. Objects-Centroids distance: we calculate the

distance between cluster centroid to each

object. Let ususe Euclidean distance, then we

have distance matrix at iteration 0 is

P a g e | 18

c1= (1, 1), group-1 c2= (1,

1), group-2

Each column in the distance matrix symbolizes

the object. The first row of the distance matrix

Corresponds to the distance of each object to the

first centroid and the second row is the distance

of

each object to the second centroid. For example,

distance from medicine C = (4, 3) to the first

centroid 1 c 1 = (1, 1) is =3.61, and its

distance to the second centroid c 2= (2, 1) is

=2.83 etc.

3. Objects clustering: We assign each object

based on the minimum distance. Thus, medicine

A is

P a g e | 19

assigned to group 1, medicine B to group 2,

medicine C to group 2 and medicine D to group

2. The element of Group matrix below is 1 if

and only if the object is assigned to that group

4. Iteration-1, determine centroids: Knowing the

members of each group, now we compute the

new centroid of each group based on these new

memberships. Group 1 only has one member

thus the centroid remains in c1 = (1, 1).

Group 2 now has three members, thus the

centroid is the average

Co-ordinate among the

three members:

P a g e | 20

.

This is figure shows that c1 = (1, 1) and

P a g e | 21

5.Iteration-1, Objects-Centroids distances: The

next step is to compute the distance of all

objects to

the new centroids. Similar to step 2, we have

distance matrix at iteration 1 is

6. Iteration-1, Objects clustering: Similar to step

3, we assign each object based on the minimum

P a g e | 22

distance. Based on the new distance matrix, we

move the medicine B to Group 1 while all the

other objects remain.The Group matrix is show

7. Iteration 2, determine centroids: Now we

repeat step 4 to calculate the new centroids

coordinate based on the clustering of previous

iteration. Group1 and group 2 both has two

members, thus the new centroids are

.

P a g e | 23

8. Iteration-2, Objects-Centroids distances:

Repeat step 2 again, we have new distance

matrix at

iteration 2 as

P a g e | 24

9. Iteration-2, Objects clustering: Again, we

assign each object based on the minimum

distance

We obtain result thatG2 = G1 . Comparing the

grouping of last iteration and this iteration

reveals that the objects does not move group

anymore. Thus, the computation of the k-mean

clustering has reached its stability and no more

P a g e | 25

iteration is needed. We get the final grouping

as the results

Object Feature 1 (X): weight

index

Feature2(y) PH

Group result

Medicine A 1 1 1 Medicine B 2 1 1 Medicine C 4 3 2 Medicine D 5 4 2 If the number of data is less than the number of

cluster then we assign each data as the

centroid of the cluster. Each centroid will have

a cluster number.

2.2HIERARCHICAL :

Hierarchical clustering is an agglomerative (top

down) clustering method. As its name suggests,

the idea of this method is to build a hierarchy

P a g e | 26

of clusters, showing relations between the

individual members and merging clusters of

data based on similarity.

In the first step of clustering, the algorithm will

look for the two most similar data points and

merge them to create a new "pseudo-

datapoint", which represents the average of the

two merged datapoints. Each iterative step

takes the next two closest datapoints (or

pseduo-datapoints) and merges them. This

proces is generally continued until there is one

large cluster containing all the original

datapoints.

An example of agglomerative clustering using

colours.

The example below demonstrates the

agglomerative clustering using colours. In the

P a g e | 27

first stages, the red and orange are combined

to make reddish-orange. Green and blue are

similar to each other and are merged to form

aqua. Next, the reddish-orange and yellow are

the closest colours, and create a light orange.

Now we have three remaining colours: light

orange, the original purple and aqua. The

hierarchical clustering algorithm is only

interested in finding the closest relationship at

each stage regardless of the degree of

similarity. So in this case, the light orange and

purple are more similar than the any other

combination.

We are now left with the orange-purple

mixture and aqua. They are now the most

similar samples left and

P a g e | 28

so form a final cluster. The resulting tree shows

the overall similarity of the original samples .

.

P a g e | 29

3. APPLICATION

Data clustering has immense number of

applications in every field of life. One has to

cluster a lot of thing on the basis of similarity

either consciously or unconsciously. So the

history of data clustering is old as the history of

mankind.

In computer field also, use of data clustering

has its own value. Specially in the field of

information retrieval data clustering plays an

important role. Some of the applications are

listed below.

P a g e | 30

4. CONCLUSION

This paper, we try to give the basic concept of

clustering by first providing the definition and

clustering and then the definition of some

related terms. We give some examples to

elaborate the concept. Then we give different

approaches to data clustering and also

discussed some algorithms to implement that

approaches. The partitioning method and

hierarchical method of clustering were

explained. The applications of clustering are

also discussed with the examples of medical

images database, data mining using data

clustering and finally the case study of windows

NT. So we try to prove the importance of

clustering in every area of computer science.

We also try to prove that clustering is not

something really typical to databases but it has

its applications in the fields like networking.

P a g e | 31

5. REFERENCES

http://members.tripod.com/asim_saeed/paper

.htm

http://www-

users.cs.umn.edu/~kumar/dmbook/dmslides/c

hap8_basic_cluster_analysis.pdf.

http://people.revoledu.com/kardi/tutorial/kMe

an/index.html

P a g e | 32