# Clustering UE 141 Spring 2013

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Clustering UE 141 Spring 013 Jing Gao SUNY Buffalo 1

2 Definition of Clustering Finding groups of obects such that the obects in a group will be similar (or related) to one another and different from (or unrelated to) the obects in other groups Intra-cluster similarity are maximized Inter-cluster similarity are minimized

3 K-means Partition {x 1,,x n } into K clusters K is predefined Initialization Specify the initial cluster centers (centroids) Iteration until no change For each obect x i Calculate the distances between x i and the K centroids (Re)assign x i to the cluster whose centroid is the closest to x i Update the cluster centroids based on current assignment 3

4 5 K-means: Initialization Initialization: Determine the three cluster centers 4 m 1 3 m m 3 4

5 K-means Clustering: Cluster Assignment Assign each obect to the cluster which has the closet distance from the centroid to the obect 5 4 m 1 3 m m 3 5

6 K-means Clustering: Update Cluster Centroid Compute cluster centroid as the center of the points in the cluster 5 4 m 1 3 m m 3 6

7 K-means Clustering: Update Cluster Centroid Compute cluster centroid as the center of the points in the cluster 5 4 m m m

8 K-means Clustering: Cluster Assignment Assign each obect to the cluster which has the closet distance from the centroid to the obect 5 4 m m m

9 K-means Clustering: Update Cluster Centroid Compute cluster centroid as the center of the points in the cluster 5 4 m m m

10 m m 3 K-means Clustering: Update Cluster Centroid Compute cluster centroid as the center of the points in the cluster 5 4 m

11 Sum of Squared Error (SSE) Suppose the centroid of cluster C is m For each obect x in C, compute the squared error between x and the centroid m Sum up the error of all the obects SSE = x C ( x - m ) m 1= 1.5 m = 4.5 SSE= (1-1.5) + ( -1.5) + (4-4.5) + (5-4.5) = 1 11

12 How to Minimize SSE min x C ( x - m Two sets of variables to minimize Each obect x belongs to which cluster? ) x C What s the cluster centroid? m Minimize the error wrt each set of variable alternatively Fix the cluster centroid find cluster assignment that minimizes the current error Fix the cluster assignment compute the cluster centroids that minimize the current error 1

13 Cluster Assignment Step min Cluster centroids (m ) are known For each obect x C ( x - m Choose C among all the clusters for x such that the distance between x and m is the minimum Choose another cluster will incur a bigger error Minimize error on each obect will minimize the SSE ) 13

14 Example Cluster Assignment Given m 1, m, which cluster each of the five points belongs to? Assign points to the closet centroid minimize SSE x 1, x, x C 3 1 x, x C 4 5 SSE= ( x - m 1 - m1 ) + ( x - m1 ) + ( x3 1) + ( x - m 4 - m) + ( x5 ) 14

15 Cluster Centroid Computation Step min For each cluster x C ( x - m Choose cluster centroid m as the center of the points x m = Minimize error on each cluster will minimize the SSE x C C ) 15

16 Example Cluster Centroid Computation Given the cluster assignment, compute the centers of the two clusters 16

17 Hierarchical Clustering Agglomerative approach a a b b a b c d e c c d e d d e e Initialization: Each obect is a cluster Iteration: Merge two clusters which are most similar to each other; Until all obects are merged into a single cluster Step 0 Step 1 Step Step 3 Step 4 bottom-up 17

18 Hierarchical Clustering Divisive Approaches a a b b a b c d e c c d e d d e e Initialization: All obects stay in one cluster Iteration: Select a cluster and split it into two sub clusters Until each leaf cluster contains only one obect Step 4 Step 3 Step Step 1 Step 0 Top-down 18

19 Dendrogram A tree that shows how clusters are merged/split hierarchically Each node on the tree is a cluster; each leaf node is a singleton cluster 19

20 Dendrogram A clustering of the data obects is obtained by cutting the dendrogram at the desired level, then each connected component forms a cluster 0

21 Agglomerative Clustering Algorithm More popular hierarchical clustering technique Basic algorithm is straightforward 1. Compute the distance matrix. Let each data point be a cluster 3. Repeat 4. Merge the two closest clusters 5. Update the distance matrix 6. Until only a single cluster remains Key operation is the computation of the distance between two clusters Different approaches to defining the distance between clusters distinguish the different algorithms 1

22 Starting Situation Start with clusters of individual points and a distance matrix p1 p p3 p4 p5... p1 p p3 p4 p5... Distance Matrix... p1 p p3 p4 p9 p10 p11 p1

23 Intermediate Situation After some merging steps, we have some clusters Choose two clusters that has the smallest distance (largest similarity) to merge C1 C1 C C3 C4 C5 C1 C3 C4 C C3 C4 C5 Distance Matrix C C5... p1 p p3 p4 p9 p10 p11 p1 3

24 Intermediate Situation We want to merge the two closest clusters (C and C5) and update the distance matrix. C1 C C3 C3 C4 C4 C5 C1 C1 C Distance Matrix C3 C4 C5 C C5... p1 p p3 p4 p9 p10 p11 p1 4

25 After Merging The question is How do we update the distance matrix? C1 C3 C4 C1 C U C5 C3 C4 C1 C U C5??????? C3 Distance Matrix C4 C U C5... p1 p p3 p4 p9 p10 p11 p1 5

26 How to Define Inter-Cluster Distance MIN MAX Group Average Distance? Distance Between Centroids p1 p p3 p4 p5... p1 p p3 p4 p5... Distance Matrix 6

27 Question Talk about big data What s the definition of big data? What applications generate big data? What are the challenges? What are the technologies for mining big data? 7

### Data Mining Cluster Analysis: Basic Concepts and Algorithms. Lecture Notes for Chapter 8. Introduction to Data Mining

Data Mining Cluster Analysis: Basic Concepts and Algorithms Lecture Notes for Chapter 8 Introduction to Data Mining by Tan, Steinbach, Kumar Tan,Steinbach, Kumar Introduction to Data Mining 4/8/2004 Hierarchical

### Data Mining Clustering (2) Sheets are based on the those provided by Tan, Steinbach, and Kumar. Introduction to Data Mining

Data Mining Clustering (2) Toon Calders Sheets are based on the those provided by Tan, Steinbach, and Kumar. Introduction to Data Mining Outline Partitional Clustering Distance-based K-means, K-medoids,

### DATA MINING CLUSTER ANALYSIS: BASIC CONCEPTS

DATA MINING CLUSTER ANALYSIS: BASIC CONCEPTS 1 AND ALGORITHMS Chiara Renso KDD-LAB ISTI- CNR, Pisa, Italy WHAT IS CLUSTER ANALYSIS? Finding groups of objects such that the objects in a group will be similar

### Clustering. Danilo Croce Web Mining & Retrieval a.a. 2015/201 16/03/2016

Clustering Danilo Croce Web Mining & Retrieval a.a. 2015/201 16/03/2016 1 Supervised learning vs. unsupervised learning Supervised learning: discover patterns in the data that relate data attributes with

### Clustering. Adrian Groza. Department of Computer Science Technical University of Cluj-Napoca

Clustering Adrian Groza Department of Computer Science Technical University of Cluj-Napoca Outline 1 Cluster Analysis What is Datamining? Cluster Analysis 2 K-means 3 Hierarchical Clustering What is Datamining?

### Data Mining Cluster Analysis: Basic Concepts and Algorithms. Lecture Notes for Chapter 8. Introduction to Data Mining

Data Mining Cluster Analsis: Basic Concepts and Algorithms Lecture Notes for Chapter 8 Introduction to Data Mining b Tan, Steinbach, Kumar Tan,Steinbach, Kumar Introduction to Data Mining /8/ What is Cluster

### Cluster Analysis. Isabel M. Rodrigues. Lisboa, 2014. Instituto Superior Técnico

Instituto Superior Técnico Lisboa, 2014 Introduction: Cluster analysis What is? Finding groups of objects such that the objects in a group will be similar (or related) to one another and different from

### Example: Document Clustering. Clustering: Definition. Notion of a Cluster can be Ambiguous. Types of Clusterings. Hierarchical Clustering

Overview Prognostic Models and Data Mining in Medicine, part I Cluster Analsis What is Cluster Analsis? K-Means Clustering Hierarchical Clustering Cluster Validit Eample: Microarra data analsis 6 Summar

### Data Mining Cluster Analysis: Basic Concepts and Algorithms. Clustering Algorithms. Lecture Notes for Chapter 8. Introduction to Data Mining

Data Mining Cluster Analsis: Basic Concepts and Algorithms Lecture Notes for Chapter 8 Introduction to Data Mining b Tan, Steinbach, Kumar Clustering Algorithms K-means and its variants Hierarchical clustering

### Text Clustering. Clustering

Text Clustering 1 Clustering Partition unlabeled examples into disoint subsets of clusters, such that: Examples within a cluster are very similar Examples in different clusters are very different Discover

### CLASSIFICATION AND CLUSTERING. Anveshi Charuvaka

CLASSIFICATION AND CLUSTERING Anveshi Charuvaka Learning from Data Classification Regression Clustering Anomaly Detection Contrast Set Mining Classification: Definition Given a collection of records (training

### Clustering. 15-381 Artificial Intelligence Henry Lin. Organizing data into clusters such that there is

Clustering 15-381 Artificial Intelligence Henry Lin Modified from excellent slides of Eamonn Keogh, Ziv Bar-Joseph, and Andrew Moore What is Clustering? Organizing data into clusters such that there is

### Cluster Analysis: Basic Concepts and Algorithms

Cluster Analsis: Basic Concepts and Algorithms What does it mean clustering? Applications Tpes of clustering K-means Intuition Algorithm Choosing initial centroids Bisecting K-means Post-processing Strengths

### Data Mining Cluster Analysis: Basic Concepts and Algorithms. Lecture Notes for Chapter 8. Introduction to Data Mining

Data Mining Cluster Analysis: Basic Concepts and Algorithms Lecture Notes for Chapter 8 by Tan, Steinbach, Kumar 1 What is Cluster Analysis? Finding groups of objects such that the objects in a group will

### K-Means Cluster Analysis. Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 1

K-Means Cluster Analsis Chapter 3 PPDM Class Tan,Steinbach, Kumar Introduction to Data Mining 4/18/4 1 What is Cluster Analsis? Finding groups of objects such that the objects in a group will be similar

### Fig. 1 A typical Knowledge Discovery process [2]

Volume 4, Issue 7, July 2014 ISSN: 2277 128X International Journal of Advanced Research in Computer Science and Software Engineering Research Paper Available online at: www.ijarcsse.com A Review on Clustering

### Information Retrieval and Web Search Engines

Information Retrieval and Web Search Engines Lecture 7: Document Clustering December 10 th, 2013 Wolf-Tilo Balke and Kinda El Maarry Institut für Informationssysteme Technische Universität Braunschweig

### Data Mining. Cluster Analysis: Advanced Concepts and Algorithms

Data Mining Cluster Analysis: Advanced Concepts and Algorithms Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 1 More Clustering Methods Prototype-based clustering Density-based clustering Graph-based

### Clustering & Association

Clustering - Overview What is cluster analysis? Grouping data objects based only on information found in the data describing these objects and their relationships Maximize the similarity within objects

### Unsupervised learning: Clustering

Unsupervised learning: Clustering Salissou Moutari Centre for Statistical Science and Operational Research CenSSOR 17 th September 2013 Unsupervised learning: Clustering 1/52 Outline 1 Introduction What

### BIRCH: An Efficient Data Clustering Method For Very Large Databases

BIRCH: An Efficient Data Clustering Method For Very Large Databases Tian Zhang, Raghu Ramakrishnan, Miron Livny CPSC 504 Presenter: Discussion Leader: Sophia (Xueyao) Liang HelenJr, Birches. Online Image.

### Data Mining Cluster Analysis: Basic Concepts and Algorithms. Lecture Notes for Chapter 8. Introduction to Data Mining

Data Mining Cluster Analsis: Basic Concepts and Algorithms Lecture Notes for Chapter 8 Introduction to Data Mining b Tan, Steinbach, Kumar Tan,Steinbach, Kumar Introduction to Data Mining 4/8/4 What is

### Data Mining Clustering. Sheets are based on the those provided by Tan, Steinbach, and Kumar. Introduction to Data Mining

Data Mining Clustering Toon Calders Sheets are based on the those provided b Tan, Steinbach, and Kumar. Introduction to Data Mining What is Cluster Analsis? Finding groups of objects such that the objects

### SoSe 2014: M-TANI: Big Data Analytics

SoSe 2014: M-TANI: Big Data Analytics Lecture 4 21/05/2014 Sead Izberovic Dr. Nikolaos Korfiatis Agenda Recap from the previous session Clustering Introduction Distance mesures Hierarchical Clustering

### 10-810 /02-710 Computational Genomics. Clustering expression data

10-810 /02-710 Computational Genomics Clustering expression data What is Clustering? Organizing data into clusters such that there is high intra-cluster similarity low inter-cluster similarity Informally,

### Robotics 2 Clustering & EM. Giorgio Grisetti, Cyrill Stachniss, Kai Arras, Maren Bennewitz, Wolfram Burgard

Robotics 2 Clustering & EM Giorgio Grisetti, Cyrill Stachniss, Kai Arras, Maren Bennewitz, Wolfram Burgard 1 Clustering (1) Common technique for statistical data analysis to detect structure (machine learning,

### Clustering. Data Mining. Abraham Otero. Data Mining. Agenda

Clustering 1/46 Agenda Introduction Distance K-nearest neighbors Hierarchical clustering Quick reference 2/46 1 Introduction It seems logical that in a new situation we should act in a similar way as in

### Neural Networks Lesson 5 - Cluster Analysis

Neural Networks Lesson 5 - Cluster Analysis Prof. Michele Scarpiniti INFOCOM Dpt. - Sapienza University of Rome http://ispac.ing.uniroma1.it/scarpiniti/index.htm michele.scarpiniti@uniroma1.it Rome, 29

### Distance based clustering

// Distance based clustering Chapter ² ² Clustering Clustering is the art of finding groups in data (Kaufman and Rousseeuw, 99). What is a cluster? Group of objects separated from other clusters Means

### ROBERTO BATTITI, MAURO BRUNATO. The LION Way: Machine Learning plus Intelligent Optimization. LIONlab, University of Trento, Italy, Apr 2015

ROBERTO BATTITI, MAURO BRUNATO. The LION Way: Machine Learning plus Intelligent Optimization. LIONlab, University of Trento, Italy, Apr 2015 http://intelligentoptimization.org/lionbook Roberto Battiti

### Clustering and Data Mining in R

Clustering and Data Mining in R Workshop Supplement Thomas Girke December 10, 2011 Introduction Data Preprocessing Data Transformations Distance Methods Cluster Linkage Hierarchical Clustering Approaches

Cluster Analysis: Advanced Concepts and dalgorithms Dr. Hui Xiong Rutgers University Introduction to Data Mining 08/06/2006 1 Introduction to Data Mining 08/06/2006 1 Outline Prototype-based Fuzzy c-means

### Distances, Clustering, and Classification. Heatmaps

Distances, Clustering, and Classification Heatmaps 1 Distance Clustering organizes things that are close into groups What does it mean for two genes to be close? What does it mean for two samples to be

### Chapter 7. Cluster Analysis

Chapter 7. Cluster Analysis. What is Cluster Analysis?. A Categorization of Major Clustering Methods. Partitioning Methods. Hierarchical Methods 5. Density-Based Methods 6. Grid-Based Methods 7. Model-Based

### Cluster Analysis. Alison Merikangas Data Analysis Seminar 18 November 2009

Cluster Analysis Alison Merikangas Data Analysis Seminar 18 November 2009 Overview What is cluster analysis? Types of cluster Distance functions Clustering methods Agglomerative K-means Density-based Interpretation

### Data Mining Cluster Analysis: Advanced Concepts and Algorithms. Lecture Notes for Chapter 9. Introduction to Data Mining

Data Mining Cluster Analysis: Advanced Concepts and Algorithms Lecture Notes for Chapter 9 Introduction to Data Mining by Tan, Steinbach, Kumar Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004

### Constrained Clustering of Territories in the Context of Car Insurance

Constrained Clustering of Territories in the Context of Car Insurance Samuel Perreault Jean-Philippe Le Cavalier Laval University July 2014 Perreault & Le Cavalier (ULaval) Constrained Clustering July

### Machine Learning and Data Mining. Clustering. (adapted from) Prof. Alexander Ihler

Machine Learning and Data Mining Clustering (adapted from) Prof. Alexander Ihler Unsupervised learning Supervised learning Predict target value ( y ) given features ( x ) Unsupervised learning Understand

### Cluster Analysis using R

Cluster analysis or clustering is the task of assigning a set of objects into groups (called clusters) so that the objects in the same cluster are more similar (in some sense or another) to each other

### Cluster Analysis: Basic Concepts and Algorithms

8 Cluster Analysis: Basic Concepts and Algorithms Cluster analysis divides data into groups (clusters) that are meaningful, useful, or both. If meaningful groups are the goal, then the clusters should

### Introduction to Clustering

Introduction to Clustering Yumi Kondo Student Seminar LSK301 Sep 25, 2010 Yumi Kondo (University of British Columbia) Introduction to Clustering Sep 25, 2010 1 / 36 Microarray Example N=65 P=1756 Yumi

### Clustering Hierarchical clustering and k-mean clustering

Clustering Hierarchical clustering and k-mean clustering Genome 373 Genomic Informatics Elhanan Borenstein The clustering problem: A quick review partition genes into distinct sets with high homogeneity

### An Enhanced Clustering Algorithm to Analyze Spatial Data

International Journal of Engineering and Technical Research (IJETR) ISSN: 2321-0869, Volume-2, Issue-7, July 2014 An Enhanced Clustering Algorithm to Analyze Spatial Data Dr. Mahesh Kumar, Mr. Sachin Yadav

### Hierarchical Cluster Analysis Some Basics and Algorithms

Hierarchical Cluster Analysis Some Basics and Algorithms Nethra Sambamoorthi CRMportals Inc., 11 Bartram Road, Englishtown, NJ 07726 (NOTE: Please use always the latest copy of the document. Click on this

### Data Mining Cluster Analysis: Advanced Concepts and Algorithms. Lecture Notes for Chapter 9. Introduction to Data Mining

Data Mining Cluster Analysis: Advanced Concepts and Algorithms Lecture Notes for Chapter 9 Introduction to Data Mining by Tan, Steinbach, Kumar Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004

### L15: statistical clustering

Similarity measures Criterion functions Cluster validity Flat clustering algorithms k-means ISODATA L15: statistical clustering Hierarchical clustering algorithms Divisive Agglomerative CSCE 666 Pattern

### SOME PRINCIPLES OF UNSUPERVISED LEARNING AND APPLICATION IN EDUCATION 1

SOME PRINCIPLES OF UNSUPERVISED LEARNING AND APPLICATION IN EDUCATION 1 In the beginning of the 90 s the idea of using data stored by computers to inform business really emerged under the name business

### Map-Reduce for Machine Learning on Multicore

Map-Reduce for Machine Learning on Multicore Chu, et al. Problem The world is going multicore New computers - dual core to 12+-core Shift to more concurrent programming paradigms and languages Erlang,

### A comparison of various clustering methods and algorithms in data mining

Volume :2, Issue :5, 32-36 May 2015 www.allsubjectjournal.com e-issn: 2349-4182 p-issn: 2349-5979 Impact Factor: 3.762 R.Tamilselvi B.Sivasakthi R.Kavitha Assistant Professor A comparison of various clustering

### Classifying Large Data Sets Using SVMs with Hierarchical Clusters. Presented by :Limou Wang

Classifying Large Data Sets Using SVMs with Hierarchical Clusters Presented by :Limou Wang Overview SVM Overview Motivation Hierarchical micro-clustering algorithm Clustering-Based SVM (CB-SVM) Experimental

### ARTIFICIAL INTELLIGENCE (CSCU9YE) LECTURE 6: MACHINE LEARNING 2: UNSUPERVISED LEARNING (CLUSTERING)

ARTIFICIAL INTELLIGENCE (CSCU9YE) LECTURE 6: MACHINE LEARNING 2: UNSUPERVISED LEARNING (CLUSTERING) Gabriela Ochoa http://www.cs.stir.ac.uk/~goc/ OUTLINE Preliminaries Classification and Clustering Applications

### There are a number of different methods that can be used to carry out a cluster analysis; these methods can be classified as follows:

Statistics: Rosie Cornish. 2007. 3.1 Cluster Analysis 1 Introduction This handout is designed to provide only a brief introduction to cluster analysis and how it is done. Books giving further details are

### Medical Information Management & Mining. You Chen Jan,15, 2013 You.chen@vanderbilt.edu

Medical Information Management & Mining You Chen Jan,15, 2013 You.chen@vanderbilt.edu 1 Trees Building Materials Trees cannot be used to build a house directly. How can we transform trees to building materials?

### Data Mining Project Report. Document Clustering. Meryem Uzun-Per

Data Mining Project Report Document Clustering Meryem Uzun-Per 504112506 Table of Content Table of Content... 2 1. Project Definition... 3 2. Literature Survey... 3 3. Methods... 4 3.1. K-means algorithm...

### Validity Measure of Cluster Based On the Intra-Cluster and Inter-Cluster Distance

International Journal of Electronics and Computer Science Engineering 2486 Available Online at www.ijecse.org ISSN- 2277-1956 Validity Measure of Cluster Based On the Intra-Cluster and Inter-Cluster Distance

### Clustering and Cluster Evaluation. Josh Stuart Tuesday, Feb 24, 2004 Read chap 4 in Causton

Clustering and Cluster Evaluation Josh Stuart Tuesday, Feb 24, 2004 Read chap 4 in Causton Clustering Methods Agglomerative Start with all separate, end with some connected Partitioning / Divisive Start

### Summary Data Mining & Process Mining (1BM46) Content. Made by S.P.T. Ariesen

Summary Data Mining & Process Mining (1BM46) Made by S.P.T. Ariesen Content Data Mining part... 2 Lecture 1... 2 Lecture 2:... 4 Lecture 3... 7 Lecture 4... 9 Process mining part... 13 Lecture 5... 13

### Lecture 20: Clustering

Lecture 20: Clustering Wrap-up of neural nets (from last lecture Introduction to unsupervised learning K-means clustering COMP-424, Lecture 20 - April 3, 2013 1 Unsupervised learning In supervised learning,

### Unsupervised Learning and Data Mining. Unsupervised Learning and Data Mining. Clustering. Supervised Learning. Supervised Learning

Unsupervised Learning and Data Mining Unsupervised Learning and Data Mining Clustering Decision trees Artificial neural nets K-nearest neighbor Support vectors Linear regression Logistic regression...

### Statistical Databases and Registers with some datamining

Unsupervised learning - Statistical Databases and Registers with some datamining a course in Survey Methodology and O cial Statistics Pages in the book: 501-528 Department of Statistics Stockholm University

### Clustering in Machine Learning. By: Ibrar Hussain Student ID:

Clustering in Machine Learning By: Ibrar Hussain Student ID: 11021083 Presentation An Overview Introduction Definition Types of Learning Clustering in Machine Learning K-means Clustering Example of k-means

### A Survey of Clustering Techniques

A Survey of Clustering Techniques Pradeep Rai Asst. Prof., CSE Department, Kanpur Institute of Technology, Kanpur-0800 (India) Shubha Singh Asst. Prof., MCA Department, Kanpur Institute of Technology,

### KNIME TUTORIAL. Anna Monreale KDD-Lab, University of Pisa Email: annam@di.unipi.it

KNIME TUTORIAL Anna Monreale KDD-Lab, University of Pisa Email: annam@di.unipi.it Outline Introduction on KNIME KNIME components Exercise: Market Basket Analysis Exercise: Customer Segmentation Exercise:

### Comparison and Analysis of Various Clustering Methods in Data mining On Education data set Using the weak tool

Comparison and Analysis of Various Clustering Metho in Data mining On Education data set Using the weak tool Abstract:- Data mining is used to find the hidden information pattern and relationship between

### Machine Learning using MapReduce

Machine Learning using MapReduce What is Machine Learning Machine learning is a subfield of artificial intelligence concerned with techniques that allow computers to improve their outputs based on previous

### Evolutionary Clustering. Presenter: Lei Tang

Evolutionary Clustering Presenter: Lei Tang Evolutionary Clustering Processing time stamped data to produce a sequence of clustering. Each clustering should be similar to the history, while accurate to

### SPECIAL PERTURBATIONS UNCORRELATED TRACK PROCESSING

AAS 07-228 SPECIAL PERTURBATIONS UNCORRELATED TRACK PROCESSING INTRODUCTION James G. Miller * Two historical uncorrelated track (UCT) processing approaches have been employed using general perturbations

### COC131 Data Mining - Clustering

COC131 Data Mining - Clustering Martin D. Sykora m.d.sykora@lboro.ac.uk Tutorial 05, Friday 20th March 2009 1. Fire up Weka (Waikako Environment for Knowledge Analysis) software, launch the explorer window

### Visualizing non-hierarchical and hierarchical cluster analyses with clustergrams

Visualizing non-hierarchical and hierarchical cluster analyses with clustergrams Matthias Schonlau RAND 7 Main Street Santa Monica, CA 947 USA Summary In hierarchical cluster analysis dendrogram graphs

### International Journal of Advance Research in Computer Science and Management Studies

Volume 2, Issue 12, December 2014 ISSN: 2321 7782 (Online) International Journal of Advance Research in Computer Science and Management Studies Research Article / Survey Paper / Case Study Available online

### Learning a Metric during Hierarchical Clustering based on Constraints

Learning a Metric during Hierarchical Clustering based on Constraints Korinna Bade and Andreas Nürnberger Otto-von-Guericke-University Magdeburg, Faculty of Computer Science, D-39106, Magdeburg, Germany

### Data Clustering. Dec 2nd, 2013 Kyrylo Bessonov

Data Clustering Dec 2nd, 2013 Kyrylo Bessonov Talk outline Introduction to clustering Types of clustering Supervised Unsupervised Similarity measures Main clustering algorithms k-means Hierarchical Main

### DATA CLUSTERING USING MAPREDUCE

DATA CLUSTERING USING MAPREDUCE by Makho Ngazimbi A project submitted in partial fulfillment of the requirements for the degree of Master of Science in Computer Science Boise State University March 2009

### Chapter ML:XI (continued)

Chapter ML:XI (continued) XI. Cluster Analysis Data Mining Overview Cluster Analysis Basics Hierarchical Cluster Analysis Iterative Cluster Analysis Density-Based Cluster Analysis Cluster Evaluation Constrained

### ANALYSIS & PREDICTION OF SALES DATA IN SAP- ERP SYSTEM USING CLUSTERING ALGORITHMS

ANALYSIS & PREDICTION OF SALES DATA IN SAP- ERP SYSTEM USING CLUSTERING ALGORITHMS S.HanumanthSastry and Prof.M.S.PrasadaBabu Department of Computer Science & Systems Engineering, Andhra University, Visakhapatnam,

### K-Means Clustering Tutorial

K-Means Clustering Tutorial By Kardi Teknomo,PhD Preferable reference for this tutorial is Teknomo, Kardi. K-Means Clustering Tutorials. http:\\people.revoledu.com\kardi\ tutorial\kmean\ Last Update: July

### K-Means Clustering. Clustering and Classification Lecture 8

K-Means Clustering Clustering and Lecture 8 Today s Class K-means clustering: What it is How it works What it assumes Pitfalls of the method (locally optimal results) 2 From Last Time If you recall the

### A Comparative Study of clustering algorithms Using weka tools

A Comparative Study of clustering algorithms Using weka tools Bharat Chaudhari 1, Manan Parikh 2 1,2 MECSE, KITRC KALOL ABSTRACT Data clustering is a process of putting similar data into groups. A clustering

### Clustering Techniques: A Brief Survey of Different Clustering Algorithms

Clustering Techniques: A Brief Survey of Different Clustering Algorithms Deepti Sisodia Technocrates Institute of Technology, Bhopal, India Lokesh Singh Technocrates Institute of Technology, Bhopal, India

### Cluster Analysis: Basic Concepts and Methods

10 Cluster Analysis: Basic Concepts and Methods Imagine that you are the Director of Customer Relationships at AllElectronics, and you have five managers working for you. You would like to organize all

### Degeneracy on K-means clustering

on K-means clustering Abdulrahman Alguwaizani Assistant Professor Math Department College of Science King Faisal University Kingdom of Saudi Arabia Office # 0096635899717 Mobile # 00966505920703 E-mail:

### Social Media Mining. Data Mining Essentials

Introduction Data production rate has been increased dramatically (Big Data) and we are able store much more data than before E.g., purchase data, social media data, mobile phone data Businesses and customers

### Machine Learning for NLP

Natural Language Processing SoSe 2015 Machine Learning for NLP Dr. Mariana Neves May 4th, 2015 (based on the slides of Dr. Saeedeh Momtazi) Introduction Field of study that gives computers the ability

### DISTRIBUTED ANOMALY DETECTION IN WIRELESS SENSOR NETWORKS

DISTRIBUTED ANOMALY DETECTION IN WIRELESS SENSOR NETWORKS Sutharshan Rajasegarar 1, Christopher Leckie 2, Marimuthu Palaniswami 1 ARC Special Research Center for Ultra-Broadband Information Networks 1

### Echidna: Efficient Clustering of Hierarchical Data for Network Traffic Analysis

Echidna: Efficient Clustering of Hierarchical Data for Network Traffic Analysis Abdun Mahmood, Christopher Leckie, Parampalli Udaya Department of Computer Science and Software Engineering University of

### ! Two Fundamental Methods in Machine Learning! Supervised Learning ( learn from my example )

Supervised vs. Unsupervised Learning Basic Machine Learning: Clustering CS 315 Web Search and Data Mining! Two Fundamental Methods in Machine Learning! Supervised Learning ( learn from my example ) n Goal:

### Clustering. Chapter 7. 7.1 Introduction to Clustering Techniques. 7.1.1 Points, Spaces, and Distances

240 Chapter 7 Clustering Clustering is the process of examining a collection of points, and grouping the points into clusters according to some distance measure. The goal is that points in the same cluster

### Clustering: Techniques & Applications. Nguyen Sinh Hoa, Nguyen Hung Son. 15 lutego 2006 Clustering 1

Clustering: Techniques & Applications Nguyen Sinh Hoa, Nguyen Hung Son 15 lutego 2006 Clustering 1 Agenda Introduction Clustering Methods Applications: Outlier Analysis Gene clustering Summary and Conclusions

### EM Clustering Approach for Multi-Dimensional Analysis of Big Data Set

EM Clustering Approach for Multi-Dimensional Analysis of Big Data Set Amhmed A. Bhih School of Electrical and Electronic Engineering Princy Johnson School of Electrical and Electronic Engineering Martin

### STATISTICA. Clustering Techniques. Case Study: Defining Clusters of Shopping Center Patrons. and

Clustering Techniques and STATISTICA Case Study: Defining Clusters of Shopping Center Patrons STATISTICA Solutions for Business Intelligence, Data Mining, Quality Control, and Web-based Analytics Table

### Vector Quantization and Clustering

Vector Quantization and Clustering Introduction K-means clustering Clustering issues Hierarchical clustering Divisive (top-down) clustering Agglomerative (bottom-up) clustering Applications to speech recognition

### PCA, Clustering and Classification. By H. Bjørn Nielsen strongly inspired by Agnieszka S. Juncker

PCA, Clustering and Classification By H. Bjørn Nielsen strongly inspired by Agnieszka S. Juncker Motivation: Multidimensional data Pat1 Pat2 Pat3 Pat4 Pat5 Pat6 Pat7 Pat8 Pat9 209619_at 7758 4705 5342

### Distributed Aggregation in Cloud Databases. By: Aparna Tiwari tiwaria@umail.iu.edu

Distributed Aggregation in Cloud Databases By: Aparna Tiwari tiwaria@umail.iu.edu ABSTRACT Data intensive applications rely heavily on aggregation functions for extraction of data according to user requirements.

### Lecture 10: Regression Trees

Lecture 10: Regression Trees 36-350: Data Mining October 11, 2006 Reading: Textbook, sections 5.2 and 10.5. The next three lectures are going to be about a particular kind of nonlinear predictive model,

### Data visualization and clustering. Genomics is to no small extend a data science

Data visualization and clustering Genomics is to no small extend a data science [www.data2discovery.org] Data visualization and clustering Genomics is to no small extend a data science [Andersson et al.,

### UNSUPERVISED MACHINE LEARNING TECHNIQUES IN GENOMICS

UNSUPERVISED MACHINE LEARNING TECHNIQUES IN GENOMICS Dwijesh C. Mishra I.A.S.R.I., Library Avenue, New Delhi-110 012 dcmishra@iasri.res.in What is Learning? "Learning denotes changes in a system that enable

### Branch-and-Price Approach to the Vehicle Routing Problem with Time Windows

TECHNISCHE UNIVERSITEIT EINDHOVEN Branch-and-Price Approach to the Vehicle Routing Problem with Time Windows Lloyd A. Fasting May 2014 Supervisors: dr. M. Firat dr.ir. M.A.A. Boon J. van Twist MSc. Contents

### CLUSTERING FOR FORENSIC ANALYSIS

IMPACT: International Journal of Research in Engineering & Technology (IMPACT: IJRET) ISSN(E): 2321-8843; ISSN(P): 2347-4599 Vol. 2, Issue 4, Apr 2014, 129-136 Impact Journals CLUSTERING FOR FORENSIC ANALYSIS

### SPSS Tutorial. AEB 37 / AE 802 Marketing Research Methods Week 7

SPSS Tutorial AEB 37 / AE 802 Marketing Research Methods Week 7 Cluster analysis Lecture / Tutorial outline Cluster analysis Example of cluster analysis Work on the assignment Cluster Analysis It is a

### Machine Learning Big Data using Map Reduce

Machine Learning Big Data using Map Reduce By Michael Bowles, PhD Where Does Big Data Come From? -Web data (web logs, click histories) -e-commerce applications (purchase histories) -Retail purchase histories