Distances, Clustering, and Classification. Heatmaps

Save this PDF as:

Size: px
Start display at page:

Transcription

1 Distances, Clustering, and Classification Heatmaps 1

2 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 close? Once we know this, how do we define groups?

3 Distance We need a mathematical definition of distance between two points What are points? If each gene is a point, what is the mathematical definition of a point? Points Gene1= (E 11, E 1,, E 1N ) Gene= (E 1, E,, E N ) Sample1= (E 11, E 1,, E G1 ) Sample= (E 1, E,, E G ) E gi =expression gene g, sample i Most Famous Distance Euclidean distance Example distance between gene 1 and : Sqrt of Sum of (E 1i -E i ), i=1,,n When N is, this is distance as we know it: Baltimore Latitude Distance Longitud DC When N is 0,000 you have to think abstractly 3

4 Similarity Instead of distance, clustering can use similarity If we standardize points then Euclidean distance is equivalent to using absolute value of correlation as a similarity index Other examples: Spearman correlation Categorical measures 1 G The similarity/distance matrices 1 N 1 G 1 G DATA MATRIX GENE SIMILARITY MATRIX 1 G The similarity/distance matrices 1 N DATA MATRIX 1 N 1 N SAMPLE SIMILARITY MATRIX 4

5 K-means We start with some data Interpretation: We are showing expression for two samples for 14 genes We are showing expression for two genes for 14 samples This is simplifaction Iteration = 0 Choose K centroids These are starting values that the user picks There are some data driven ways to do it K-means Iteration = 0 Make first partition by finding the closest centroid for each point This is where distance is used K-means Iteration = 1 5

6 Now re-compute the centroids by taking the middle of each cluster K-means Iteration = Repeat until the centroids stop moving or until you get tired of waiting K-means Iteration = 3 A little different Centroid: The average of the samples within a cluster Medoid: The representative object within a cluster Initializing requires choosing medoids at random K-medoids 6

7 K-means Limitations Final results depend on starting values How do we chose K? There are methods but not much theory saying what is best Where are the pretty pictures? Hierarchical Divide all points into Then divide each group into Keep going until you have groups of 1 and can not divide further This is divisive or top-down hierarchical clustering There is also agglomerative clustering or bottom-up We can then make dendrograms showing divisions The y-axis represents the distance between the groups divided at that point Dendrograms Note: Left and right is assigned arbitrarily Look at the height of division to find out distance For example, S5 and S16 are very far 7

8 But how do we form actual clusters? We need to pick a height How to make a hierarchical clustering 1 Choose samples and genes to include in cluster analysis Choose similarity/distance metric 3 Choose clustering direction (top-down or bottom-up) 4 Choose linkage method (if bottom-up) 5 Calculate dendrogram 6 Choose height/number of clusters for interpretation 7 Assess cluster fit and stability 8 Interpret resulting cluster structure 8

9 1 Choose samples and genes to include Important step! Do you want housekeeping genes included? What to do about replicates from the same individual/tumor? Genes that contribute noise will affect your results Including all genes: dendrogram can t all be seen at the same time Perhaps screen the genes? Simulated Data with 4 clusters: 1-10, 11-0, 1-30, A: 450 relevant genes plus 450 noise genes B: 450 relevant genes Choose similarity/distance matrix Think hard about this step! Remember: garbage in garbage out The metric that you pick should be a valid measure of the distance/similarity of genes Examples: Applying correlation to highly skewed data will provide misleading results Applying Euclidean distance to data measured on categorical scale will be invalid Not just wrong, but which makes most sense 9

10 Some correlations to choose from Pearson Correlation: s( x, x ) = 1 K " K " k = 1 ( x! x )( x! x ) 1k 1 k K " ( x! x ) ( x! x ) 1k 1 k = 1 k = 1 k Uncentered Correlation: Absolute Value of Correlation: s( x, x ) = 1 s( x, x ) = 1 k K! k = 1 K K! k " = 1 k = 1 K x " = 1 1k x x 1k k K! k = 1 x k ( x! x )( x! x ) 1k 1 k ( x! x ) ( x! x ) 1k 1 k K " = 1 k The difference is that, if you have two vectors X and Y with identical shape, but which are offset relative to each other by a fixed value, they will have a standard Pearson correlation (centered correlation) of 1 but will not have an uncentered correlation of 1 3 Choose clustering direction (top-down or bottom-up) Agglomerative clustering (bottom-up) Starts with as each gene in its own cluster Joins the two most similar clusters Then, joins next two most similar clusters Continues until all genes are in one cluster Divisive clustering (top-down) Starts with all genes in one cluster Choose split so that genes in the two clusters are most similar (maximize distance between clusters) Find next split in same manner Continue until all genes are in single gene clusters 10

11 Which to use? Both are only step-wise optimal: at each step the optimal split or merge is performed This does not imply that the final cluster structure is optimal! Agglomerative/Bottom-Up Computationally simpler, and more available More precision at bottom of tree When looking for small clusters and/or many clusters, use agglomerative Divisive/Top-Down More precision at top of tree When looking for large and/or few clusters, use divisive In gene expression applications, divisive makes more sense Results ARE sensitive to choice! 4 Choose linkage method (if bottom-up) Single Linkage: join clusters whose distance between closest genes is smallest (elliptical) Complete Linkage: join clusters whose distance between furthest genes is smallest (spherical) Average Linkage: join clusters whose average distance is the smallest 11

12 5 Calculate dendrogram 6 Choose height/number of clusters for interpretation In gene expression, we don t see rule-based approach to choosing cutoff very often Tend to look for what makes a good story There are more rigorous methods (more later) Homogeneity and Separation of clusters can be considered (Chen et al Statistica Sinica, 00) Other methods for assessing cluster fit can help determine a reasonable way to cut your tree 7 Assess cluster fit and stability PART OF THE MISUNDERSTOOD! Most often ignored Cluster structure is treated as reliable and precise BUT! Usually the structure is rather unstable, at least at the bottom Can be VERY sensitive to noise and to outliers Homogeneity and Separation Cluster Silhouettes and Silhouette coefficient: how similar genes within a cluster are to genes in other clusters (composite separation and homogeneity) (more later with K-medoids) (Rousseeuw Journal of Computation and Applied Mathematics, 1987) Assess cluster fit and stability (continued) WADP: Weighted Average Discrepant Pairs Bittner et al Nature, 000 Fit cluster analysis using a dataset Add random noise to the original dataset Fit cluster analysis to the noise-added dataset Repeat many times Compare the clusters across the noise-added datasets Consensus Trees Zhang and Zhao Functional and Integrative Genomics, 000 Use parametric bootstrap approach to sample new data using original dataset Proceed similarly to WADP Look for nodes that are in a majority of the bootstrapped trees More not mentioned 1

13 Careful though Some validation approaches are more suited to some clustering approaches than others Most of the methods require us to define number of clusters, even for hierarchical clustering Requires choosing a cut-point If true structure is hierarchical, a cut tree won t appear as good as it might truly be Final Thoughts The most overused statistical method in gene expression analysis Gives us pretty red-green picture with patterns But, pretty picture tends to be pretty unstable Many different ways to perform hierarchical clustering Tend to be sensitive to small changes in the data Provided with clusters of every size: where to cut the dendrogram is user-determined We should not use heatmaps to compare two Populations? 13

14 Prediction Common Types of Objectives Class Comparison Identify genes differentially expressed among predefined classes such as diagnostic or prognostic groups Class Prediction Develop multi-gene predictor of class for a sample using its gene expression profile Class Discovery Discover clusters among specimens or among genes What is the task Given the gene profile predict the class Mathematical representation: find function f that maps x to {1,,K} How do we do this? 14

15 Possibilities Have expert tell us what genes to look for being over/under expressed? Then we do not really need microarrrays Use clustering algorithms? Not appropriate for this taks Clustering is not a good tool Simulated Data with 4 clusters: 1-10, 11-0, 1-30, A: 450 relevant genes plus 450 noise genes B: 450 relevant genes 15

16 Problem with clustering Noisy genes will ruin it for the rest How do we know which genes to use We are ignoring useful information in our prototype data: We know the classes! Train an algorithm A powerful approach is to train a classification algorithm on the data we collected and propose the use of it in the future This has successfully worked in many areas: zip code reading, voice recognition, etc Using multiple genes How do we combine information from various genes to help us form our discriminant function f? There are many methods out there three examples are LDA, knn, SVM Weighted gene voting and PAM were developed for microarrays (but they can be thought of as versions of DLDA) 16

17 Weighted Gene Voting is DLDA With equal priors, DLDA is: " k (x) = G % g=1 (x g # µ kg ) \$ g With two classes we select class 1 if This can be written as with! a g = (x 1g " x g ) # ˆ g! G (x 1g " x g )% ( \$ x # ˆ g " x + x 1g g) ( ' g=1 g & * + 0 ) ( b g = x 1g + x g )! G " a g x g # b g g=1 ( ) \$ 0 Weighted Gene Voting simply uses!! Notice the units and scale fore sum are wrong!! a g = (x 1g " x g ) # ˆ 1g + ˆ # g KNN Another simple and useful method is K nearest neighbors It is very simple Example 17

18 Too many genes A problem with most existing approaches: They were not developed for p>>n A simple way around this is to filter genes first: Pick genes that, marginally, appear to have good predictive power Beware of over-fitting With p>>n you can always find a prediction algorithm that predicts perfectly on the training set Also, many algorithm can be made to me too flexible An example is KNN with K=1 Example 18

19 Split-Sample Evaluation Training-set Used to select features, select model type, determine parameters and cut-off thresholds Test-set Withheld until a single model is fully specified using the training-set Fully specified model is applied to the expression profiles in the test-set to predict class labels Number of errors is counted Note: Also called cross-validation Important You have apply the entire algorithm, from scratch, on the train set This includes the choice of feature gene, and in some cases normalization! Example Cross-validation: none (resubstitution method) Cross-validation: after gene selection Cross-validation: prior to gene selection Proportion of simulated data sets Number of misclassifications 19

20 CV Keeping yourself honest Try out algorithm on reshuffled data Try it out on completely random data Conclusions Clustering algorithms not appropriate Do not reinvent the wheel! Many methods available but need feature selection (PAM does it all in one step!) Use cross validation to assess Be suspicious of new complicated methods: Simple methods are already too complicated 0

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

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 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

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

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

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

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

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

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,

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

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

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...

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?

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

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.,

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

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 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

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

Text Analytics. Text Clustering. Ulf Leser

Text Analytics Text Clustering Ulf Leser Content of this Lecture (Text) clustering Cluster quality Clustering algorithms Application Ulf Leser: Text Analytics, Winter Semester 2010/2011 2 Clustering Clustering

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 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. 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

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

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

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

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

CPSC 340: Machine Learning and Data Mining. K-Means Clustering Fall 2015

CPSC 340: Machine Learning and Data Mining K-Means Clustering Fall 2015 Admin Assignment 1 solutions posted after class. Tutorials for Assignment 2 on Monday. Random Forests Random forests are one of the

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

Chapter 7. Hierarchical cluster analysis. Contents 7-1

7-1 Chapter 7 Hierarchical cluster analysis In Part 2 (Chapters 4 to 6) we defined several different ways of measuring distance (or dissimilarity as the case may be) between the rows or between the columns

Data Warehousing and Data Mining

Data Warehousing and Data Mining Lecture Clustering Methods CITS CITS Wei Liu School of Computer Science and Software Engineering Faculty of Engineering, Computing and Mathematics Acknowledgement: The

A K-means-like Algorithm for K-medoids Clustering and Its Performance

A K-means-like Algorithm for K-medoids Clustering and Its Performance Hae-Sang Park*, Jong-Seok Lee and Chi-Hyuck Jun Department of Industrial and Management Engineering, POSTECH San 31 Hyoja-dong, Pohang

Agglomerative Hierarchical Clustering

Student name, Data Mining (H6016), Assignment Paper 2. Dec 2010. 1. Abstract Agglomerative Hierarchical Clustering In this paper agglomerative hierarchical clustering (AHC) is described. The algorithms

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

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

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

Data Mining Techniques Chapter 11: Automatic Cluster Detection

Data Mining Techniques Chapter 11: Automatic Cluster Detection Clustering............................................................. 2 k-means Clustering......................................................

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

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

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

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

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

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

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

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

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

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

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

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

Trees and Random Forests

Trees and Random Forests Adele Cutler Professor, Mathematics and Statistics Utah State University This research is partially supported by NIH 1R15AG037392-01 Cache Valley, Utah Utah State University Leo

CLUSTERING (Segmentation)

CLUSTERING (Segmentation) Dr. Saed Sayad University of Toronto 2010 saed.sayad@utoronto.ca http://chem-eng.utoronto.ca/~datamining/ 1 What is Clustering? Given a set of records, organize the records into

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

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 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

Reference Books. Data Mining. Supervised vs. Unsupervised Learning. Classification: Definition. Classification k-nearest neighbors

Classification k-nearest neighbors Data Mining Dr. Engin YILDIZTEPE Reference Books Han, J., Kamber, M., Pei, J., (2011). Data Mining: Concepts and Techniques. Third edition. San Francisco: Morgan Kaufmann

Data Mining Cluster Analysis: Advanced Concepts and Algorithms. ref. Chapter 9. Introduction to Data Mining

Data Mining Cluster Analysis: Advanced Concepts and Algorithms ref. Chapter 9 Introduction to Data Mining by Tan, Steinbach, Kumar 1 Outline Prototype-based Fuzzy c-means Mixture Model Clustering Density-based

HQJHQH70 *XLGHG7RXU This document contains a Guided Tour through the HQJHQH platform and it was created for training purposes with respect to the system options and analysis possibilities. It is not intended

Data Mining for Model Creation. Presentation by Paul Below, EDS 2500 NE Plunkett Lane Poulsbo, WA USA 98370 paul.below@eds.

Sept 03-23-05 22 2005 Data Mining for Model Creation Presentation by Paul Below, EDS 2500 NE Plunkett Lane Poulsbo, WA USA 98370 paul.below@eds.com page 1 Agenda Data Mining and Estimating Model Creation

Multivariate Analysis of Ecological Data

Multivariate Analysis of Ecological Data MICHAEL GREENACRE Professor of Statistics at the Pompeu Fabra University in Barcelona, Spain RAUL PRIMICERIO Associate Professor of Ecology, Evolutionary Biology

Decision Support System Methodology Using a Visual Approach for Cluster Analysis Problems

Decision Support System Methodology Using a Visual Approach for Cluster Analysis Problems Ran M. Bittmann School of Business Administration Ph.D. Thesis Submitted to the Senate of Bar-Ilan University Ramat-Gan,

Introduction to machine learning and pattern recognition Lecture 1 Coryn Bailer-Jones

Introduction to machine learning and pattern recognition Lecture 1 Coryn Bailer-Jones http://www.mpia.de/homes/calj/mlpr_mpia2008.html 1 1 What is machine learning? Data description and interpretation

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

Classification Techniques (1)

10 10 Overview Classification Techniques (1) Today Classification Problem Classification based on Regression Distance-based Classification (KNN) Net Lecture Decision Trees Classification using Rules Quality

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,

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

Knowledge Discovery and Data Mining. Bootstrap review. Bagging Important Concepts. Notes. Lecture 19 - Bagging. Tom Kelsey. Notes

Knowledge Discovery and Data Mining Lecture 19 - Bagging Tom Kelsey School of Computer Science University of St Andrews http://tom.host.cs.st-andrews.ac.uk twk@st-andrews.ac.uk Tom Kelsey ID5059-19-B &

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

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 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

Knowledge Discovery and Data Mining

Knowledge Discovery and Data Mining Unit # 11 Sajjad Haider Fall 2013 1 Supervised Learning Process Data Collection/Preparation Data Cleaning Discretization Supervised/Unuspervised Identification of right

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,

Introduction to Statistical Machine Learning

CHAPTER Introduction to Statistical Machine Learning We start with a gentle introduction to statistical machine learning. Readers familiar with machine learning may wish to skip directly to Section 2,

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

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

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

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

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

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

Data Mining - Evaluation of Classifiers

Data Mining - Evaluation of Classifiers Lecturer: JERZY STEFANOWSKI Institute of Computing Sciences Poznan University of Technology Poznan, Poland Lecture 4 SE Master Course 2008/2009 revised for 2010

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

MODULE 15 Clustering Large Datasets LESSON 34

MODULE 15 Clustering Large Datasets LESSON 34 Incremental Clustering Keywords: Single Database Scan, Leader, BIRCH, Tree 1 Clustering Large Datasets Pattern matrix It is convenient to view the input data

Cluster analysis Cosmin Lazar. COMO Lab VUB

Cluster analysis Cosmin Lazar COMO Lab VUB Introduction Cluster analysis foundations rely on one of the most fundamental, simple and very often unnoticed ways (or methods) of understanding and learning,

An Introduction to Cluster Analysis for Data Mining

An Introduction to Cluster Analysis for Data Mining 10/02/2000 11:42 AM 1. INTRODUCTION... 4 1.1. Scope of This Paper... 4 1.2. What Cluster Analysis Is... 4 1.3. What Cluster Analysis Is Not... 5 2. OVERVIEW...

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

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...

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

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

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,

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

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

Content-Based Recommendation

Content-Based Recommendation Content-based? Item descriptions to identify items that are of particular interest to the user Example Example Comparing with Noncontent based Items User-based CF Searches

Computational Complexity between K-Means and K-Medoids Clustering Algorithms for Normal and Uniform Distributions of Data Points

Journal of Computer Science 6 (3): 363-368, 2010 ISSN 1549-3636 2010 Science Publications Computational Complexity between K-Means and K-Medoids Clustering Algorithms for Normal and Uniform Distributions

Introduction to Predictive Models Book Chapters 1, 2 and 5. Carlos M. Carvalho The University of Texas McCombs School of Business

Introduction to Predictive Models Book Chapters 1, 2 and 5. Carlos M. Carvalho The University of Texas McCombs School of Business 1 1. Introduction 2. Measuring Accuracy 3. Out-of Sample Predictions 4.

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

An Introduction to Data Mining. Big Data World. Related Fields and Disciplines. What is Data Mining? 2/12/2015

An Introduction to Data Mining for Wind Power Management Spring 2015 Big Data World Every minute: Google receives over 4 million search queries Facebook users share almost 2.5 million pieces of content

Important Characteristics of Cluster Analysis Techniques

Cluster Analysis Can we organize sampling entities into discrete classes, such that within-group similarity is maximized and amonggroup similarity is minimized according to some objective criterion? Sites

Steven M. Ho!and. Department of Geology, University of Georgia, Athens, GA 30602-2501

CLUSTER ANALYSIS Steven M. Ho!and Department of Geology, University of Georgia, Athens, GA 30602-2501 January 2006 Introduction Cluster analysis includes a broad suite of techniques designed to find groups