# 6. If there is no improvement of the categories after several steps, then choose new seeds using another criterion (e.g. the objects near the edge of

Save this PDF as:

Size: px
Start display at page:

Download "6. If there is no improvement of the categories after several steps, then choose new seeds using another criterion (e.g. the objects near the edge of"

## Transcription

1 Clustering Clustering is an unsupervised learning method: there is no target value (class label) to be predicted, the goal is finding common patterns or grouping similar examples. Differences between models/algorithms for clustering: Conceptual (model-based) vs. partitioning Exclusive vs. overlapping Deterministic vs. probabilistic Hierarchical vs. flat Incremental vs. batch learning Evaluating clustering quality: subjective approaches, objective functions (e.g. category utility, entropy). Major approaches: Cluster/2: flat, conceptual (model-based), batch learning, possibly overlapping, deterministic. Partitioning methods: flat, batch learning, exclusive, deterministic or probabilistic. Algorithms: k-means, probability-based clustering (EM) Hierarchical clustering Partitioning: agglomerative (bottom-up) or divisible (top-down). Conceptual: Cobweb, category utility function. 1

2 1 CLUSTER/2 One of the first conceptual clustering approaches [Michalski, 83]. Works as a meta-learning sheme - uses a learning algorithm in its inner loop to form categories. Has no practical value, but introduces important ideas and techniques, used in current appraoches to conceptual clustering. The CLUSTER/2 algorithm forms k categories by constructing individual objects grouped around k seed objects. It works as follows: 1. Select k objects (seeds) from the set of observed objects (randomly or using some selection function). 2. For each seed, using it as a positive example the all the other seeds as negative examples, find a maximally general description that covers all positive and none of the negative examples. 3. Classify all objects form the sample in categories according to these descriptions. Then replace each maximally general descriptions with a maximally specific one, that cover all objects in the category. (This possibly avoids category overlapping.) 4. If there are still overlapping categories, then using some metric (e.g. euclidean distance) find central objects in each category and repeat steps 1-3 using these objects as seeds. 5. Stop when some quality criterion for the category descriptions is satisfied. Such a criterion might be the complexity of the descriptions (e.g. the number of conjuncts) 2

3 6. If there is no improvement of the categories after several steps, then choose new seeds using another criterion (e.g. the objects near the edge of the category). 3

4 2 Partitioning methods k-means Iterative distance-based clustering. Used by statisticians for decades. Similarly to Cluster/2 uses k seeds (predefined k), but is based on a distance measure: 1. Select k instances (cluster centers) from the sample (usually at random). 2. Assign instances to clusters according to their distance to the cluster centers. 3. Find new cluster centers and go to step 2 until the process converges (i.e. the same instances are assigned to each cluster in two consecutive passes). The clustering depends greatly on the initial choice of cluster centers the algorithm may fall in a local minimum. Example of bad chioce of cluster centers: four instances at the vertices of a rectangle, two initial cluster centers midpoints of the long sides of the rectangle. This is a stable configuration, however not a good clustering. Solution to the local minimum problem: restart the algorithm with another set of cluster centers. Hierarchical k-means: apply k = 2 recursively to the resulting clusters. 4

5 3 Probabilty-based clustering Why probabilities? Restricted amount of evidence implies probabilistic reasoning. From a probabilistic perspective, we want to find the most likely clusters given the data. An instance only has certain probability of belonging to a particular cluster. 5

6 4 Probabilty-based clustering mixture models For a single attribute: three parameters - mean, standard deviation and sampling probability. Each cluster A is defined by a mean (µ A ) and a standard deviation (σ A ). Samples are taken from each cluster A with a specified probability of sampling P (A). Finite mixture problem: given a dataset, find the mean, standard deviation and the probability of sampling for each cluster. If we know the classification of each instance, then: mean (average), µ = 1 n1 n x i ; standard deviation, σ 2 = 1 n1 n 1 (x i µ) 2 ; probability of sampling for class A, P (A) = proportion of instances in it. If we know the three parameters, the probability that an instance x belongs to cluster A is: P (A x) = P (x A)P (A) P (x), (x µ A ) 2 where P (x A) is the density function for A, f(x; µ A, σ A ) = 1 2πσA e 2σ A 2. P (x) is not necessary as we calculate the numerators for all clusters and normalize them by dividing by their sum. In fact, this is exactly the Naive Bayes approach. For more attributes: naive Bayes assumption independence between attributes. The joint probabilities of an instance are calculated as a product of the probabilities of all attributes. 6

7 5 EM (expectation maximization) Similarly to k-means, first select the cluster parameters (µ A, σ A and P (A)) or guess the classes of the instances, then iterate. Adjustment needed: we know cluster probabilities, not actual clusters for each instance. So, we use these probabilities as weights. For cluster A: µ A = n 1 w ix i n 1 w i, where w i is the probability that x i belongs to cluster A; σ 2 A = n 1 w i(x i µ) 2 n 1 w. i When to stop iteration - maximizing overall likelihood that the data come form the dataset with the given parameters ( goodness of clustering): Log-likelihood = i log( A P (A)P (x i A) ) Stop when the difference between two successive iteration becomes negligible (i.e. there is no improvement of clustering quality). 7

8 6 Criterion functions for clustering 1. Distance-based functions. Sum of squared error: m A = 1 n J = A x A x A x x m A 2 Optimal clustering minilizes J: minimal variance clustering. 2. Probability (entropy) based functions. Probability of instance P (x i ) = A P (A)P (x i A) Probability of sample x 1,..., x n : Π n i ( A P (A)P (x i A) ) Log-likelihood: 3. Category utility (Cobweb): n i log( A P (A)P (x i A) ) CU = 1 n C P (C) A v [P (A = v C) 2 P (A = v) 2 ] 4. Error-based evaluation: evaluate clusters with respect to classes using preclassified examples (Classes to clusters evaluation mode in Weka). 8

9 7 Hierarchical partitioning methods Bottom-up (agglomerative): at each step merge the two closest clusters. Top-down (divisible): split the current set into two clusters and proceed recursively with the subsets. Distance function between instances (e.g. Euclidean distance). Distance function between clusters (e.g. distance between centers, minimal distance, average distance). Criteria for stopping merging or splitting: desired number of clusters; distance between the closest clusters is above (top-down) or below (bottom-up) a threshold. Algorithms: Nearest neighbor (single-linkage) agglomerative clustering: cluster distance = minimal distance between elements. Merging stops when distance > threshold. In fact, this is an algorithm for generating a minimal spanning tree. Farthest neighbor (complete-linkage) agglomerative clustering: cluster distance = maximal distance between elements. Merging stops when distance > threshold. The algorithm computes the complete subgraph for every cluster. Problems: greedy algorithm (local minimum), once created a subtree cannot be restructured. 9

10 8 Example of agglomerative hierarchical clustering 8.1 Data Day Outlook Temperature Humidity Wind Play 1 sunny hot high weak no 2 sunny hot high strong no 3 overcast hot high weak yes 4 rain mild high weak yes 5 rain cool normal weak yes 6 rain cool normal strong no 7 overcast cool normal strong yes 8 sunny mild high weak no 9 sunny cool normal weak yes 10 rain mild normal weak yes 11 sunny mild normal strong yes 12 overcast mild high strong yes 13 overcast hot normal weak yes 14 rain mild high strong no 10

11 8.2 Farthest neighbor (complete-linkage) agglomerative clustering, threshold = yes 8 - no 12 - yes 14 - no 1 - no 2 - no 3 - yes 13 - yes 5 - yes 10 - yes 9 - yes 11 - yes 6 - no 7 - yes Classes to clusters evaluation for the three top level classes: {4, 8, 12, 14, 1, 2} majority class=no, 2 incorrectly classified instances. {3, 13, 5, 10} majority class=yes, 0 incorrectly classified instances. {9, 11, 6, 7} majority class=yes, 1 incorrectly classified instance. Total number of incorrectly classified instances = 3, Error = 3/14 11

12 9 Hierarchical conceptual clustering: Cobweb Incremental clustering algorithm, which builds a taxonomy of clusters without having a predefined number of clusters. The clusters are represented probabilistically by conditional probability P (A = v C) with which attribute A has value v, given that the instance belongs to class C. The algorithm starts with an empty root node. Instances are added one by one. For each instance the following options (operators) are considered: classifying the instance into an existing class; creating a new class and placing the instance into it; combining two classes into a single class (merging) and placing the new instance in the resulting hierarchy; dividing a class into two classes (splitting) and placing the new instance in the resulting hierarchy. The algorithm searches the space of possible hierarchies by applying the above operators and an evaluation function based on the category utility. 12

13 10 Measuring quality of clustering Category utility (CU) function CU attempts to maximize both the probability that two instances in the same category have attribute values in common and the probability that instances from different categories have different attribute values. CU = C A v P (A = v)p (A = v C)P (C A = v) P (A = v C) is the probability that an instance has value v for its attribute A, given that it belongs to category C. The higher this probability, the more likely two instances in a category share the same attribute values. P (C A = v) is the probability that an instance belongs to category C, given that it has value v for its attribute A. The greater this probability, the less likely instances from different categories will have attribute values in common. P (A = v) is a weight, assuring that frequently occurring attribute values will have stronger influence on the evaluation. 13

14 11 Category utility After applying Bayes rule we get A CU = C A v P (C)P (A = v C) 2 v P (A = v C) 2 is the expected number of attribute values that one can correctly guess for an arbitrary member of class C. This expectation assumes a probability matching strategy, in which one guesses an attribute value with a probability equal to its probability of occurring. Without knowing the cluster structure the above term is A v) 2. v P (A = The final CU is defined as the increase in the expected number of attribute values that can be correctly guessed, given a set of n categories, over the expected number of correct guesses without such knowledge. That is: CU = 1 n C P (C) A v [P (A = v C) 2 P (A = v) 2 ] The above expression is divided by n to allow comparing different size clusterings. Handling numeric attributes (Classit): assuming normal distribution and using probability density function (based on mean and standard deviation). 14

15 12 Control parameters Acuity: a single instance in a cluster results in a zero variance, which in turn produces infinite value for CU. The acuity parameter is the minimum value for the variance (can be interpreted as a measurement error). Cutoff: the minimum increase of CU to add a new node to the hierarchy, otherwise the new node is cut off. 15

16 13 Example color nuclei tails white 1 1 white 2 2 black 2 2 black

17 14 Cobweb s clustering hierarchy C 2 P (C 2 ) = 0.25 attr val P tails color white 1.0 black 0.0 nuclei C 5 P (C 5 ) = 0.25 attr val P tails color white 1.0 black 0.0 nuclei C 1 P (C 1 ) = 1.0 attr val P tails color white 0.5 black 0.5 nuclei C 3 P (C 3 ) = 0.5 attr val P tails color white 0.5 black 0.5 nuclei C 6 P (C 6 ) = 0.25 attr val P tails color white 0.0 black 1.0 nuclei C 4 P (C 1 ) = 0.25 attr val P tails color white 0.0 black 1.0 nuclei

18 15 Cobweb algorithm cobweb(n ode,instance) begin end If Node is a leaf then begin Create two children of Node - L 1 and L 2 ; Set the probabilities of L 1 to those of Node; Set the probabilities of L 2 to those of Insnatce; Add Instance to N ode, updating N ode s probabilities. end else begin Add Instance to Node, updating Node s probabilities; For each child C of Node, compute the category utility of clustering achieved by placing Instance in C; Calculate: S 1 = the score for the best categorization (Instance is placed in C 1 ); S 2 = the score for the second best categorization (Instance is placed in C 2 ); S 3 = the score for placing Instance in a new category; S 4 = the score for merging C 1 and C 2 into one category; S 5 = the score for splitting C 1 (replacing it with its child categories. end If S 1 is the best score then call cobweb(c 1, Instance). If S 3 is the best score then set the new category s probabilities to those of Instance. If S 4 is the best score then call cobweb(c m, Instance), where C m is the result of merging C 1 and C 2. If S 5 is the best score then split C 1 and call cobweb(node, Instance). 18

### 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

### More Data Mining with Weka

More Data Mining with Weka Class 3 Lesson 1 Decision trees and rules Ian H. Witten Department of Computer Science University of Waikato New Zealand weka.waikato.ac.nz Lesson 3.1: Decision trees and rules

### 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 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

### 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,

### Clustering UE 141 Spring 2013

Clustering UE 141 Spring 013 Jing Gao SUNY Buffalo 1 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

### 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

### 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,

### 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

### Flat Clustering K-Means Algorithm

Flat Clustering K-Means Algorithm 1. Purpose. Clustering algorithms group a set of documents into subsets or clusters. The cluster algorithms goal is to create clusters that are coherent internally, but

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### Decision-Tree Learning

Decision-Tree Learning Introduction ID3 Attribute selection Entropy, Information, Information Gain Gain Ratio C4.5 Decision Trees TDIDT: Top-Down Induction of Decision Trees Numeric Values Missing Values

### 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

### 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

### Data Mining: Foundation, Techniques and Applications

Data Mining: Foundation, Techniques and Applications Lesson 1b :A Quick Overview of Data Mining Li Cuiping( 李 翠 平 ) School of Information Renmin University of China Anthony Tung( 鄧 锦 浩 ) School of Computing

### 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

### 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

### Data Mining Classification: Basic Concepts, Decision Trees, and Model Evaluation. Lecture Notes for Chapter 4. Introduction to Data Mining

Data Mining Classification: Basic Concepts, Decision Trees, and Model Evaluation Lecture Notes for Chapter 4 Introduction to Data Mining by Tan, Steinbach, Kumar Tan,Steinbach, Kumar Introduction to Data

### 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,

### Knowledge Discovery and Data Mining

Knowledge Discovery and Data Mining Unit # 6 Sajjad Haider Fall 2014 1 Evaluating the Accuracy of a Classifier Holdout, random subsampling, crossvalidation, and the bootstrap are common techniques for

### Monday Morning Data Mining

Monday Morning Data Mining Tim Ruhe Statistische Methoden der Datenanalyse Outline: - data mining - IceCube - Data mining in IceCube Computer Scientists are different... Fakultät Physik Fakultät Physik

### 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

### 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

### 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

### 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

### 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,

### Introduction to Machine Learning Connectionist and Statistical Language Processing

Introduction to Machine Learning Connectionist and Statistical Language Processing Frank Keller keller@coli.uni-sb.de Computerlinguistik Universität des Saarlandes Introduction to Machine Learning p.1/22

### 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.,

### 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

### 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

### 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

### The SPSS TwoStep Cluster Component

White paper technical report The SPSS TwoStep Cluster Component A scalable component enabling more efficient customer segmentation Introduction The SPSS TwoStep Clustering Component is a scalable cluster

### A Gentle Introduction to Machine Learning

A Gentle Introduction to Machine Learning Second Lecture Part I Olov Andersson, AIICS Linköpings Universitet Outline of Machine Learning Lectures First we will talk about Supervised Learning Definition

### Professor Anita Wasilewska. Classification Lecture Notes

Professor Anita Wasilewska Classification Lecture Notes Classification (Data Mining Book Chapters 5 and 7) PART ONE: Supervised learning and Classification Data format: training and test data Concept,

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

### PERFORMANCE ANALYSIS OF CLUSTERING ALGORITHMS IN DATA MINING IN WEKA

PERFORMANCE ANALYSIS OF CLUSTERING ALGORITHMS IN DATA MINING IN WEKA Prakash Singh 1, Aarohi Surya 2 1 Department of Finance, IIM Lucknow, Lucknow, India 2 Department of Computer Science, LNMIIT, Jaipur,

### 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

### Université de Montpellier 2 Hugo Alatrista-Salas : hugo.alatrista-salas@teledetection.fr

Université de Montpellier 2 Hugo Alatrista-Salas : hugo.alatrista-salas@teledetection.fr WEKA Gallirallus Zeland) australis : Endemic bird (New Characteristics Waikato university Weka is a collection

### Big Data: The Science of Patterns. Dr. Lutz Hamel Dept. of Computer Science and Statistics hamel@cs.uri.edu

Big Data: The Science of Patterns Dr. Lutz Hamel Dept. of Computer Science and Statistics hamel@cs.uri.edu The Blessing and the Curse: Lots of Data Outlook Temp Humidity Wind Play Sunny Hot High Weak No

### Data Mining Classification: Decision Trees

Data Mining Classification: Decision Trees Classification Decision Trees: what they are and how they work Hunt s (TDIDT) algorithm How to select the best split How to handle Inconsistent data Continuous

### 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

### 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...

### 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

### 152 International Journal of Computer Science and Technology. Paavai Engineering College, India

IJCST Vol. 2, Issue 3, September 2011 Improving the Performance of Data Mining Algorithms in Health Care Data 1 P. Santhi, 2 V. Murali Bhaskaran, 1,2 Paavai Engineering College, India ISSN : 2229-4333(Print)

### 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

### Data Mining for Knowledge Management. Classification

1 Data Mining for Knowledge Management Classification Themis Palpanas University of Trento http://disi.unitn.eu/~themis Data Mining for Knowledge Management 1 Thanks for slides to: Jiawei Han Eamonn Keogh

### 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?

### Overview. Introduction to Machine Learning. Definition of Learning. A Sample Data Set. Connectionist and Statistical Language Processing

Overview Introduction to Machine Learning Connectionist and Statistical Language Processing Frank Keller keller@coli.uni-sb.de Computerlinguistik Universität des Saarlandes definition of learning sample

### Entropy based Graph Clustering: Application to Biological and Social Networks

Entropy based Graph Clustering: Application to Biological and Social Networks Edward C Kenley Young-Rae Cho Department of Computer Science Baylor University Complex Systems Definition Dynamically evolving

### 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

### 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...

### 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?

### Classification and Prediction

Classification and Prediction Slides for Data Mining: Concepts and Techniques Chapter 7 Jiawei Han and Micheline Kamber Intelligent Database Systems Research Lab School of Computing Science Simon Fraser

### Data Mining Practical Machine Learning Tools and Techniques

Some Core Learning Representations Data Mining Practical Machine Learning Tools and Techniques Slides for Chapter of Data Mining by I. H. Witten and E. Frank Decision trees Learning Rules Association rules

### Why the Normal Distribution?

Why the Normal Distribution? Raul Rojas Freie Universität Berlin Februar 2010 Abstract This short note explains in simple terms why the normal distribution is so ubiquitous in pattern recognition applications.

### Guido Sciavicco. 11 Novembre 2015

classical and new techniques Università degli Studi di Ferrara 11 Novembre 2015 in collaboration with dr. Enrico Marzano, CIO Gap srl Active Contact System Project 1/27 Contents What is? Embedded Wrapper

### 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

### Learning Example. Machine learning and our focus. Another Example. An example: data (loan application) The data and the goal

Learning Example Chapter 18: Learning from Examples 22c:145 An emergency room in a hospital measures 17 variables (e.g., blood pressure, age, etc) of newly admitted patients. A decision is needed: whether

### 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,

### Data Mining Essentials

This chapter is from Social Media Mining: An Introduction. By Reza Zafarani, Mohammad Ali Abbasi, and Huan Liu. Cambridge University Press, 2014. Draft version: April 20, 2014. Complete Draft and Slides

### Decision Trees. Andrew W. Moore Professor School of Computer Science Carnegie Mellon University. www.cs.cmu.edu/~awm awm@cs.cmu.

Decision Trees Andrew W. Moore Professor School of Computer Science Carnegie Mellon University www.cs.cmu.edu/~awm awm@cs.cmu.edu 42-268-7599 Copyright Andrew W. Moore Slide Decision Trees Decision trees

### Foundations of Artificial Intelligence. Introduction to Data Mining

Foundations of Artificial Intelligence Introduction to Data Mining Objectives Data Mining Introduce a range of data mining techniques used in AI systems including : Neural networks Decision trees Present

### IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 20, NO. 7, JULY 2009 1181

IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 20, NO. 7, JULY 2009 1181 The Global Kernel k-means Algorithm for Clustering in Feature Space Grigorios F. Tzortzis and Aristidis C. Likas, Senior Member, IEEE

### Comparative Analysis of EM Clustering Algorithm and Density Based Clustering Algorithm Using WEKA tool.

International Journal of Engineering Research and Development e-issn: 2278-067X, p-issn: 2278-800X, www.ijerd.com Volume 9, Issue 8 (January 2014), PP. 19-24 Comparative Analysis of EM Clustering Algorithm

### Chapter 4: Non-Parametric Classification

Chapter 4: Non-Parametric Classification Introduction Density Estimation Parzen Windows Kn-Nearest Neighbor Density Estimation K-Nearest Neighbor (KNN) Decision Rule Gaussian Mixture Model A weighted combination

### Clustering Via Decision Tree Construction

Clustering Via Decision Tree Construction Bing Liu 1, Yiyuan Xia 2, and Philip S. Yu 3 1 Department of Computer Science, University of Illinois at Chicago, 851 S. Morgan Street, Chicago, IL 60607-7053.

### Cluster analysis with SPSS: K-Means Cluster Analysis

analysis with SPSS: K-Means Analysis analysis is a type of data classification carried out by separating the data into groups. The aim of cluster analysis is to categorize n objects in k (k>1) groups,

### Classification algorithm in Data mining: An Overview

Classification algorithm in Data mining: An Overview S.Neelamegam #1, Dr.E.Ramaraj *2 #1 M.phil Scholar, Department of Computer Science and Engineering, Alagappa University, Karaikudi. *2 Professor, Department

### 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

### 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

### Probability Theory. Elementary rules of probability Sum rule. Product rule. p. 23

Probability Theory Uncertainty is key concept in machine learning. Probability provides consistent framework for the quantification and manipulation of uncertainty. Probability of an event is the fraction

### Unsupervised Data Mining (Clustering)

Unsupervised Data Mining (Clustering) Javier Béjar KEMLG December 01 Javier Béjar (KEMLG) Unsupervised Data Mining (Clustering) December 01 1 / 51 Introduction Clustering in KDD One of the main tasks in

### Hadoop SNS. renren.com. Saturday, December 3, 11

Hadoop SNS renren.com Saturday, December 3, 11 2.2 190 40 Saturday, December 3, 11 Saturday, December 3, 11 Saturday, December 3, 11 Saturday, December 3, 11 Saturday, December 3, 11 Saturday, December

### 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

### 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

### 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

### Data Mining Practical Machine Learning Tools and Techniques

Ensemble learning Data Mining Practical Machine Learning Tools and Techniques Slides for Chapter 8 of Data Mining by I. H. Witten, E. Frank and M. A. Hall Combining multiple models Bagging The basic idea

### Analysis of kiva.com Microlending Service! Hoda Eydgahi Julia Ma Andy Bardagjy December 9, 2010 MAS.622j

Analysis of kiva.com Microlending Service! Hoda Eydgahi Julia Ma Andy Bardagjy December 9, 2010 MAS.622j What is Kiva? An organization that allows people to lend small amounts of money via the Internet

### 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

### Class #6: Non-linear classification. ML4Bio 2012 February 17 th, 2012 Quaid Morris

Class #6: Non-linear classification ML4Bio 2012 February 17 th, 2012 Quaid Morris 1 Module #: Title of Module 2 Review Overview Linear separability Non-linear classification Linear Support Vector Machines

### Environmental Remote Sensing GEOG 2021

Environmental Remote Sensing GEOG 2021 Lecture 4 Image classification 2 Purpose categorising data data abstraction / simplification data interpretation mapping for land cover mapping use land cover class

### Using multiple models: Bagging, Boosting, Ensembles, Forests

Using multiple models: Bagging, Boosting, Ensembles, Forests Bagging Combining predictions from multiple models Different models obtained from bootstrap samples of training data Average predictions or

### COMP3420: Advanced Databases and Data Mining. Classification and prediction: Introduction and Decision Tree Induction

COMP3420: Advanced Databases and Data Mining Classification and prediction: Introduction and Decision Tree Induction Lecture outline Classification versus prediction Classification A two step process Supervised

### 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.

### Big Data Analytics CSCI 4030

High dim. data Graph data Infinite data Machine learning Apps Locality sensitive hashing PageRank, SimRank Filtering data streams SVM Recommen der systems Clustering Community Detection Web advertising

### 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

### Data Mining with R. Decision Trees and Random Forests. Hugh Murrell

Data Mining with R Decision Trees and Random Forests Hugh Murrell reference books These slides are based on a book by Graham Williams: Data Mining with Rattle and R, The Art of Excavating Data for Knowledge

### 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

### Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 1 Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 2. Tid Refund Marital Status

Data Mining Classification: Basic Concepts, Decision Trees, and Evaluation Lecture tes for Chapter 4 Introduction to Data Mining by Tan, Steinbach, Kumar Classification: Definition Given a collection of

### Data Mining. Practical Machine Learning Tools and Techniques. Classification, association, clustering, numeric prediction

Data Mining Practical Machine Learning Tools and Techniques Slides for Chapter 2 of Data Mining by I. H. Witten and E. Frank Input: Concepts, instances, attributes Terminology What s a concept? Classification,