This document describes the K-means clustering algorithm. It begins by defining cluster analysis and its goal of grouping similar objects together. It then explains that K-means is a partitioning clustering method that assigns data points to K clusters based on minimizing distances between points and assigned cluster centroids. The document provides details on initializing centroids, assigning points, updating centroids, and determining convergence. It also discusses evaluating clusters and limitations of K-means. Finally, it provides examples of applying K-means to image segmentation and anomaly detection in wind turbine data.
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
Slides for Introductory session on K Means Clustering.
simple and good. ppt
Could be used for taking classes for MCA students on Clustering Algorithms for Data mining.
Prepared By K.T.Thomas HOD of Computer Science, Santhigiri College Vazhithala
New Approach for K-mean and K-medoids AlgorithmEditor IJCATR
K-means and K-medoids clustering algorithms are widely used for many practical applications. Original k
medoids algorithms select initial centroids and medoids randomly that affect the quality of the resulting clusters and sometimes it
generates unstable and empty clusters which are meaningless.
expensive and requires time proportional to the product of the number of data items, number of clusters and the number of iterations.
The new approach for the k mean algorithm eliminates the deficiency of exiting k mean. It first calculates the initial centro
requirements of users and then gives better, effective and stable cluster. It also takes less execution time because it eliminates
unnecessary distance computation by using previous iteration. The new approach for k
systematically based on initial centroids. It generates stable clusters to improve accuracy.
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
Slides for Introductory session on K Means Clustering.
simple and good. ppt
Could be used for taking classes for MCA students on Clustering Algorithms for Data mining.
Prepared By K.T.Thomas HOD of Computer Science, Santhigiri College Vazhithala
New Approach for K-mean and K-medoids AlgorithmEditor IJCATR
K-means and K-medoids clustering algorithms are widely used for many practical applications. Original k
medoids algorithms select initial centroids and medoids randomly that affect the quality of the resulting clusters and sometimes it
generates unstable and empty clusters which are meaningless.
expensive and requires time proportional to the product of the number of data items, number of clusters and the number of iterations.
The new approach for the k mean algorithm eliminates the deficiency of exiting k mean. It first calculates the initial centro
requirements of users and then gives better, effective and stable cluster. It also takes less execution time because it eliminates
unnecessary distance computation by using previous iteration. The new approach for k
systematically based on initial centroids. It generates stable clusters to improve accuracy.
Jiawei Han, Micheline Kamber and Jian Pei
Data Mining: Concepts and Techniques, 3rd ed.
The Morgan Kaufmann Series in Data Management Systems
Morgan Kaufmann Publishers, July 2011. ISBN 978-0123814791
Welcome to International Journal of Engineering Research and Development (IJERD)IJERD Editor
call for paper 2012, hard copy of journal, research paper publishing, where to publish research paper,
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals,
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IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
An improvement in k mean clustering algorithm using better time and accuracyijpla
Cluster
analysis
or
clustering
is the task of grouping a set of objects in such a way that objects in the same
group (called a
cluster
) are more similar (in some sense or another) to each other than to those in other
groups (clusters)
.
K
-
means
is
one of the simplest unsupervised learning algorithms that solve the well
known clustering problem.
The
process of k means algorithm data
is partiti
oned int
o K clusters and the
data are randomly choose
to the clusters resulti
ng in clusters that have
the sa
me number of data
set
.
This
paper is proposed a new K means clustering algorithm we calculate the initial
centroids
systemically
instead of random assigned due to which accuracy and time
improved.
K-Means clustering uses an iterative procedure which is very much sensitive and dependent upon the initial centroids. The initial centroids in the k-means clustering are chosen randomly, and hence the clustering also changes with respect to the initial centroids. This paper tries to overcome this problem of random selection of centroids and hence change of clusters with a premeditated selection of initial centroids. We have used the iris, abalone and wine data sets to demonstrate that the proposed method of finding the initial centroids and using the centroids in k-means algorithm improves the clustering performance. The clustering also remains the same in every run as the initial centroids are not randomly selected but through premeditated method.
Chapter 10. Cluster Analysis Basic Concepts and Methods.pptSubrata Kumer Paul
Jiawei Han, Micheline Kamber and Jian Pei
Data Mining: Concepts and Techniques, 3rd ed.
The Morgan Kaufmann Series in Data Management Systems
Morgan Kaufmann Publishers, July 2011. ISBN 978-0123814791
Our Business Analytics certification training course is designed by the industry experts, which is precisely tailored for the professionals who wants to pursue a career as a Data Scientist in job market.
ExcelR offers 160 hours classroom training on Business Analytics / Data Scientist / Data Analytics. We are considered as one of the best training institutes on Business Analytics in Hyderabad. “Faculty and vast course agenda is our differentiator”.
ExcelR offers 160 hours classroom training on Business Analytics / Data Scientist / Data Analytics. We are considered as one of the best training institutes on Business Analytics in Hyderabad. “Faculty and vast course agenda is our differentiator”.
Jiawei Han, Micheline Kamber and Jian Pei
Data Mining: Concepts and Techniques, 3rd ed.
The Morgan Kaufmann Series in Data Management Systems
Morgan Kaufmann Publishers, July 2011. ISBN 978-0123814791
Welcome to International Journal of Engineering Research and Development (IJERD)IJERD Editor
call for paper 2012, hard copy of journal, research paper publishing, where to publish research paper,
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals,
yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
An improvement in k mean clustering algorithm using better time and accuracyijpla
Cluster
analysis
or
clustering
is the task of grouping a set of objects in such a way that objects in the same
group (called a
cluster
) are more similar (in some sense or another) to each other than to those in other
groups (clusters)
.
K
-
means
is
one of the simplest unsupervised learning algorithms that solve the well
known clustering problem.
The
process of k means algorithm data
is partiti
oned int
o K clusters and the
data are randomly choose
to the clusters resulti
ng in clusters that have
the sa
me number of data
set
.
This
paper is proposed a new K means clustering algorithm we calculate the initial
centroids
systemically
instead of random assigned due to which accuracy and time
improved.
K-Means clustering uses an iterative procedure which is very much sensitive and dependent upon the initial centroids. The initial centroids in the k-means clustering are chosen randomly, and hence the clustering also changes with respect to the initial centroids. This paper tries to overcome this problem of random selection of centroids and hence change of clusters with a premeditated selection of initial centroids. We have used the iris, abalone and wine data sets to demonstrate that the proposed method of finding the initial centroids and using the centroids in k-means algorithm improves the clustering performance. The clustering also remains the same in every run as the initial centroids are not randomly selected but through premeditated method.
Chapter 10. Cluster Analysis Basic Concepts and Methods.pptSubrata Kumer Paul
Jiawei Han, Micheline Kamber and Jian Pei
Data Mining: Concepts and Techniques, 3rd ed.
The Morgan Kaufmann Series in Data Management Systems
Morgan Kaufmann Publishers, July 2011. ISBN 978-0123814791
Our Business Analytics certification training course is designed by the industry experts, which is precisely tailored for the professionals who wants to pursue a career as a Data Scientist in job market.
ExcelR offers 160 hours classroom training on Business Analytics / Data Scientist / Data Analytics. We are considered as one of the best training institutes on Business Analytics in Hyderabad. “Faculty and vast course agenda is our differentiator”.
ExcelR offers 160 hours classroom training on Business Analytics / Data Scientist / Data Analytics. We are considered as one of the best training institutes on Business Analytics in Hyderabad. “Faculty and vast course agenda is our differentiator”.
ExcelR offers 160 hours classroom training on Business Analytics / Data Scientist / Data Analytics. We are considered as one of the best training institutes on Business Analytics in Hyderabad. “Faculty and vast course agenda is our differentiator”.
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ExcelR offers 160+ Hours Classroom training to improve your skills on Business Analytics / Data Scientist / Data Analytics. The Leaders in Business Analytics
ExcelR offers 160+ Hours Classroom training to improve your skills on Business Analytics / Data Scientist / Data Analytics. The Leaders in Business Analytics
ExcelR offers 160+ Hours Classroom training to improve your skills on Business Analytics / Data Scientist / Data Analytics. The Leaders in Business Analytics
Our Business Analytics certification training course is designed by the industry experts, which is precisely tailored for the professionals who wants to pursue a career as a Data Scientist in job market.
Our Business Analytics certification training course is designed by the industry experts, which is precisely tailored for the professionals who wants to pursue a career as a Data Scientist in job market.
Our Business Analytics certification training course is designed by the industry experts, which is precisely tailored for the professionals who wants to pursue a career as a Data Scientist in job market.
ExcelR offers 160+ Hours Classroom training to improve your skills on Business Analytics / Data Scientist / Data Analytics. The Leaders in Business Analytics
ExcelR offers 160+ Hours Classroom training to improve your skills on Business Analytics / Data Scientist / Data Analytics. The Leaders in Business Analytics
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ExcelR offers 160+ Hours Classroom training to improve your skills on Business Analytics / Data Scientist / Data Analytics. The Leaders in Business Analytics
ExcelR offers 160+ Hours Classroom training to improve your skills on Business Analytics / Data Scientist / Data Analytics. The Leaders in Business Analytics
ExcelR offers 160+ Hours Classroom training to improve your skills on Business Analytics / Data Scientist / Data Analytics. The Leaders in Business Analytics
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
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Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
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An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
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Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
1. 3/22/2012
1
K-means Algorithmg
Cluster Analysis in Data Mining
Presented by Zijun Zhang
Algorithm Description
What is Cluster Analysis?
Cluster analysis groups data objects based only on
information found in data that describes the objects and their
relationships.
Goal of Cluster Analysis
The objects within a group be similar to one another andj g p
different from the objects in other groups
2. 3/22/2012
2
Algorithm Description
Types of Clustering
Partitioning and Hierarchical Clustering
Hierarchical Clustering
- A set of nested clusters organized as a hierarchical tree
Partitioning Clusteringg g
- A division data objects into non-overlapping subsets
(clusters) such that each data object is in exactly one subset
Algorithm Description
p4
p1
p3
p2
A Partitional Clustering Hierarchical Clustering
3. 3/22/2012
3
Algorithm Description
What is K-means?
1. Partitional clustering approach
2. Each cluster is associated with a centroid (center point)
3. Each point is assigned to the cluster with the closest centroid
4 Number of clusters K must be specified4. Number of clusters, K, must be specified
Algorithm Statement
Basic Algorithm of K-means
4. 3/22/2012
4
Algorithm Statement
Details of K-means
1 Initial centroids are often chosen randomly1. Initial centroids are often chosen randomly.
- Clusters produced vary from one run to another
2. The centroid is (typically) the mean of the points in the cluster.
3.‘Closeness’ is measured by Euclidean distance, cosine similarity, correlation,
etc.
4. K-means will converge for common similarity measures mentioned above.
5. Most of the convergence happens in the first few iterations.5. Most of the convergence happens in the first few iterations.
- Often the stopping condition is changed to ‘Until relatively few points
change clusters’
Algorithm Statement
Euclidean Distance
A simple example: Find the distance between two points, the original
and the point (3,4)
5. 3/22/2012
5
Algorithm Statement
Update Centroid
We use the following equation to calculate the n dimensionalWe use the following equation to calculate the n dimensional
centroid point amid k n-dimensional points
Example: Find the centroid of 3 2D points, (2,4), (5,2)
and (8,9)and (8,9)
Example of K-means
Select three initial centroids
1
1.5
2
2.5
3
y
Iteration 1
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0
0.5
x
6. 3/22/2012
6
Example of K-means
Assigning the points to nearest K clusters and re-compute the
centroids
1
1.5
2
2.5
3
y
Iteration 3
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0
0.5
x
Example of K-means
K-means terminates since the centroids converge to certain points
and do not change.
1
1.5
2
2.5
3
y
Iteration 6
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0
0.5
x
7. 3/22/2012
7
Example of K-means
2
2.5
3
Iteration 1
2
2.5
3
Iteration 2
2
2.5
3
Iteration 3
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0
0.5
1
1.5
x
y
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0
0.5
1
1.5
x
y
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0
0.5
1
1.5
x
y
3
Iteration 4
3
Iteration 5
3
Iteration 6
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0
0.5
1
1.5
2
2.5
x
y
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0
0.5
1
1.5
2
2.5
x
y
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0
0.5
1
1.5
2
2.5
x
y
Example of K-means
Demo of K-means
8. 3/22/2012
8
Evaluating K-means Clusters
Most common measure is Sum of Squared Error (SSE)
For each point, the error is the distance to the nearest cluster
To get SSE we square these errors and sum them To get SSE, we square these errors and sum them.
x is a data point in cluster Ci and mi is the representative point for cluster
Ci
can show that mi corresponds to the center (mean) of the cluster
Given two clusters we can choose the one with the smallest error
K
i Cx
i
i
xmdistSSE
1
2
),(
Given two clusters, we can choose the one with the smallest error
One easy way to reduce SSE is to increase K, the number of clusters
A good clustering with smaller K can have a lower SSE than a poor
clustering with higher K
Problem about K
How to choose K?
1. Use another clustering method, like EM.
2. Run algorithm on data with several different values of K.
3. Use the prior knowledge about the characteristics of the problem.
9. 3/22/2012
9
Problem about initialize centers
How to initialize centers?
- Random Points in Feature Space
- Random Points From Data Set
- Look For Dense Regions of Space
- Space them uniformly around the feature space
Cluster Quality
10. 3/22/2012
10
Cluster Quality
Limitation of K-means
K-means has problems when clusters are of
differingg
Sizes
Densities
Non-globular shapes
K h bl h h d i K-means has problems when the data contains
outliers.
11. 3/22/2012
11
Limitation of K-means
Original Points K-means (3 Clusters)
Application of K-means
Image Segmentation
The k-means clustering algorithm is commonly used in
computer vision as a form of image segmentation. The
results of the segmentation are used to aid border detection
and object recognition.
12. 3/22/2012
12
K-means in Wind Energy
Clustering can be applied to detect
b lit i i d d t ( b labnormality in wind data (abnormal
vibration)
Monitor Wind Turbine Conditions
Beneficial to preventative maintenance
K means can be more powerful and K-means can be more powerful and
applicable after appropriate modifications
K-means in Wind Energy
Modified K-means
13. 3/22/2012
13
K-means in Wind Energy
Clustering cost function
2
1
1
( , , )
j i
k
j i
i C
d k
n
x
x c x c
1
k
i
i
n m
21 k
1
1
1
( , , )
j i
j ik
i C
i
i
d k
m
x
x c x c
K-means in Wind Energy
Determination of k value
0 02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
Costofclustering
0
0.01
0.02
2 3 4 5 6 7 8 9 10 11 12 13
Numberof clusters
14. 3/22/2012
14
K-means in Wind Energy
Summary of clustering result
No. of Cluster c1 (Drive train acc.) c2 (Wind speed) Number of points Percentage (%)
1 71.9612 9.97514 313 8.75524
2 65.8387 9.42031 295 8.25175
3 233.9184 9.57990 96 2.68531
4 17.4187 7.13375 240 6.71329
5 3.3706 8.99211 437 12.22378
6 0.3741 0.40378 217 6.06993
7 18.1361 8.09900 410 11.46853
8 0.7684 10.56663 419 11.72028
9 62.0493 8.81445 283 7.91608
10 81.7522 10.67867 181 5.06294
11 83.8067 8.10663 101 2.82517
12 0.9283 9.78571 583 16.30769
K-means in Wind Energy
Visualization of monitoring result
15. 3/22/2012
15
K-means in Wind Energy
Visualization of vibration under normal condition
14
4
6
8
10
12
14
Windspeed(m/s)
0
2
0 20 40 60 80 100 120 140
Drive train acceleration
Reference
1. Introduction to Data Mining, P.N. Tan, M. Steinbach, V. Kumar, Addison Wesley
2. An efficient k-means clustering algorithm: Analysis and implementation, T. Kanungo, D. M.
Mount, N. Netanyahu, C. Piatko, R. Silverman, and A. Y. Wu, IEEE Trans. PatternAnalysis
and Machine Intelligence, 24 (2002), 881-892
3. http://www.cs.cmu.edu/~cga/ai-course/kmeans.pdf
4. http://www.cse.msstate.edu/~url/teaching/CSE6633Fall08/lec16%20k-means.pdf
16. 3/22/2012
16
Appendix One
Original Points K-means (2 Clusters)
Appendix Two
Original Points K-means Clusters
One solution is to use many clusters.
Find parts of clusters, but need to put together.