STATS306B STATS306B. Clustering. Jonathan Taylor Department of Statistics Stanford University. June 3, 2010
|
|
|
- Marilynn Tate
- 6 years ago
- Views:
Transcription
1 STATS306B Jonathan Taylor Department of Statistics Stanford University June 3, 2010 Spring 2010
2 Outline K-means, K-medoids, EM algorithm choosing number of clusters: Gap test hierarchical clustering spectral clustering
3 K-means Figure: Simulated data in the plane, clustered into three classes (represented by red, blue and green) by the K-means clustering algorithm. From ESL.
4 K-means Algorithm 1. For each data point, the closest cluster center (in Euclidean distance) is identified; 2. Each cluster center is replaced by the coordinatewise average of all data points that are closest to it. 3. Steps 1. and 2. are alternated until convergence. Algorithm converges to a local minimum of the within-cluster sum of squares. 4. Typically one uses multiple runs from random starting guesses, and chooses the solution with lowest within cluster sum of squares.
5 K-means Figure: Successive iterations of the K-means clustering algorithm for the simulated data.
6 K-means Issues to consider Non-quantitative feature, e.g. categorical variables, are typically coded by dummy variables, and then treated as quantitative. How many centroids k do we use? As k increases, both training and test error decrease!
7 K-means Choosing K Ideally, the within cluster sum of squares flattens out quickly and we might choose the value of K at this elbow. We might also compare the observed within cluster sum of squares to a null model, like uniform on a box containing the data. This is the basis of the gap statistic see ESL.
8 K-means Figure: The Gap statistic ESL
9 K-medoid Algorithm Same as K-means, except that centroid is estimated not by the average, but by the observation having minimum pairwise distance with the other cluster members. Advantage: centroid is one of the observations useful, eg when features are 0 or 1. Also, one only needs pairwise distances for K-medoids rather than the raw observations.
10 K-medoid Example: Country Dissimilarities This example comes from a study in which political science students were asked to provide pairwise dissimilarity measures for 12 countries. BEL BRA CHI CUB EGY FRA IND ISR USA USS YUG BRA 5.58 CHI CUB EGY FRA IND ISR USA USS YUG ZAI
11 Figure: Left panel: dissimilarities reordered and blocked according to 3-medoid clustering. Heat map is coded from most similar (dark red) to least similar (bright red). Right panel: two-dimensional multidimensional scaling plot, with 3-medoid clusters indicated by different colors. STATS306B K-medoid
12 K-means Connection with EM algorithm Earlier, we saw EM algorithm for mixture of two Gaussians. The general case of K Gaussian components is based on the responsibilities γ (t+1) ij = π (t) j f (X i ; µ (t) j, Σ (t) ) K l=1 π(t) l f (X i ; µ (t) l, Σ (t) ) with f (x; µ, Σ) the multivariate Normal density. ˆl (t+1) By choosing labels i = argmax j γ (n+1) ij this yields a clustering algorithm that is almost K-means.
13 This approach produces a hierarchical clustering tree, or dendrogram. Usually a bottom-up (agglomerative); though top-down versions do exist. Starting with single observations as clusters, the closest pair of clusters are joined together and the distance matrix is updated. Different metrics can be used, yielding qualitatively different trees. Important advantage - the dendrogram can be cut at any level, yielding different clusterings of the data.
14 Hierarchical clustering Single linkage The pair of clusters ( C 1, C 2 ) to merge is chosen based on distance matrix D n n and the current clusters (C 1,..., C k ): ( C 1, C 2 ) = argmin (C i,c j ) min x C i,y C j D xy Finding the next cluster involves updating the minimum distances between the unmerged clusters and the new cluster ( C 1, C 2 ), an O(n 2 ) calculation. Tends to result in very few large clusters formed by adding one point at a time to a growing cluster.
15 Hierarchical clustering Complete linkage The pair of clusters ( C 1, C 2 ) to merge is chosen based on distance matrix D n n and the current clusters (C 1,..., C k ): ( C 1, C 2 ) = argmin (C i,c j ) max x C i,y C j D xy Finding the next cluster involves updating the maximum distances between the unmerged clusters and the new cluster ( C 1, C 2 ), an O(n 2 ) calculation. Resulting dendrogram typically has a wider range of interesting cut points than single linkage.
16 Hierarchical clustering Average linkage The pair of clusters ( C 1, C 2 ) to merge is chosen based on distance matrix D n n and the current clusters (C 1,..., C k ): ( C 1, C 2 ) = argmin (C i,c j ) 1 #C i #C j x C i,y C j D xy Finding the next cluster involves updating the mean distances between the unmerged clusters and the new cluster ( C 1, C 2 ). Resulting dendrogram is somewhat intermediate to single and complete linkage.
17 Hierarchical clustering Figure: applied to NCI human tumor data.
18 Hierarchical clustering Issues Allows one to see all numbers of clusters at once. Can use any distance matrix. Algorithm is greedy, clusters are not optimal in any sense Choice of features to use in clustering can make a big difference in the result. data
19 Spectral clustering Connection with EM algorithm In multidimensional scaling, we saw how a distance matrix, D n n leads to an embedding in m dimensions, i.e. a Euclidean matrix X n m. Given this Euclidean matrix, we can apply clustering methods that need Euclidean features, like K-means. If we chose the number of neighbours in such a way that the true clusters are disconnected in the graph and there are m + 1 connected components in the graph, then, in theory, m + 1-means will recover exactly these m + 1 connected components.
20 Spectral clustering Figure: Spectral clustering: 2-means clustering for embedding into 1 dimension, with two clusters disconnected.
21 Spectral clustering Figure: Spectral clustering: 2-means clustering for embedding into 1 dimension, with two clusters connected.
22 Spectral clustering Figure: Spectral clustering: 4-means clustering for embedding into 3 dimensions, with two clusters connected.
23 Spectral clustering Figure: Spectral clustering: 4-means clustering for embedding into 30 dimensions, with two clusters connected.
24 Spectral clustering Figure: Spectral clustering: 2-means clustering for embedding into 1 dimensions.
25 Spectral clustering Figure: Spectral clustering: 2-means clustering for embedding into 1 dimensions.
K-means clustering Based in part on slides from textbook, slides of Susan Holmes. December 2, Statistics 202: Data Mining.
K-means clustering Based in part on slides from textbook, slides of Susan Holmes December 2, 2012 1 / 1 K-means Outline K-means, K-medoids Choosing the number of clusters: Gap test, silhouette plot. Mixture
Statistics 202: Data Mining. c Jonathan Taylor. Week 8 Based in part on slides from textbook, slides of Susan Holmes. December 2, / 1
Week 8 Based in part on slides from textbook, slides of Susan Holmes December 2, 2012 1 / 1 Part I Clustering 2 / 1 Clustering Clustering Goal: Finding groups of objects such that the objects in a group
Machine Learning (BSMC-GA 4439) Wenke Liu
Machine Learning (BSMC-GA 4439) Wenke Liu 01-25-2018 Outline Background Defining proximity Clustering methods Determining number of clusters Other approaches Cluster analysis as unsupervised Learning Unsupervised
Machine Learning (BSMC-GA 4439) Wenke Liu
Machine Learning (BSMC-GA 4439) Wenke Liu 01-31-017 Outline Background Defining proximity Clustering methods Determining number of clusters Comparing two solutions Cluster analysis as unsupervised Learning
Clustering. Robert M. Haralick. Computer Science, Graduate Center City University of New York
Clustering Robert M. Haralick Computer Science, Graduate Center City University of New York Outline K-means 1 K-means 2 3 4 5 Clustering K-means The purpose of clustering is to determine the similarity
CSE 5243 INTRO. TO DATA MINING
CSE 5243 INTRO. TO DATA MINING Cluster Analysis: Basic Concepts and Methods Huan Sun, CSE@The Ohio State University Slides adapted from UIUC CS412, Fall 2017, by Prof. Jiawei Han 2 Chapter 10. Cluster
CS 1675 Introduction to Machine Learning Lecture 18. Clustering. Clustering. Groups together similar instances in the data sample
CS 1675 Introduction to Machine Learning Lecture 18 Clustering Milos Hauskrecht milos@cs.pitt.edu 539 Sennott Square Clustering Groups together similar instances in the data sample Basic clustering problem:
CS 2750 Machine Learning. Lecture 19. Clustering. CS 2750 Machine Learning. Clustering. Groups together similar instances in the data sample
Lecture 9 Clustering Milos Hauskrecht milos@cs.pitt.edu 539 Sennott Square Clustering Groups together similar instances in the data sample Basic clustering problem: distribute data into k different groups
Hierarchical Clustering
Hierarchical Clustering Hierarchical Clustering Produces a set of nested clusters organized as a hierarchical tree Can be visualized as a dendrogram A tree-like diagram that records the sequences of merges
SGN (4 cr) Chapter 11
SGN-41006 (4 cr) Chapter 11 Clustering Jussi Tohka & Jari Niemi Department of Signal Processing Tampere University of Technology February 25, 2014 J. Tohka & J. Niemi (TUT-SGN) SGN-41006 (4 cr) Chapter
DATA MINING LECTURE 7. Hierarchical Clustering, DBSCAN The EM Algorithm
DATA MINING LECTURE 7 Hierarchical Clustering, DBSCAN The EM Algorithm CLUSTERING What is a Clustering? In general a grouping of objects such that the objects in a group (cluster) are similar (or related)
Olmo S. Zavala Romero. Clustering Hierarchical Distance Group Dist. K-means. Center of Atmospheric Sciences, UNAM.
Center of Atmospheric Sciences, UNAM November 16, 2016 Cluster Analisis Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster)
Machine learning - HT Clustering
Machine learning - HT 2016 10. Clustering Varun Kanade University of Oxford March 4, 2016 Announcements Practical Next Week - No submission Final Exam: Pick up on Monday Material covered next week is not
CSE 5243 INTRO. TO DATA MINING
CSE 5243 INTRO. TO DATA MINING Cluster Analysis: Basic Concepts and Methods Huan Sun, CSE@The Ohio State University 09/25/2017 Slides adapted from UIUC CS412, Fall 2017, by Prof. Jiawei Han 2 Chapter 10.
Network Traffic Measurements and Analysis
DEIB - Politecnico di Milano Fall, 2017 Introduction Often, we have only a set of features x = x 1, x 2,, x n, but no associated response y. Therefore we are not interested in prediction nor classification,
Supervised vs. Unsupervised Learning
Clustering Supervised vs. Unsupervised Learning So far we have assumed that the training samples used to design the classifier were labeled by their class membership (supervised learning) We assume now
Hard clustering. Each object is assigned to one and only one cluster. Hierarchical clustering is usually hard. Soft (fuzzy) clustering
An unsupervised machine learning problem Grouping a set of objects in such a way that objects in the same group (a cluster) are more similar (in some sense or another) to each other than to those in other
K-means and Hierarchical Clustering
K-means and Hierarchical Clustering Xiaohui Xie University of California, Irvine K-means and Hierarchical Clustering p.1/18 Clustering Given n data points X = {x 1, x 2,, x n }. Clustering is the partitioning
Clustering. CS294 Practical Machine Learning Junming Yin 10/09/06
Clustering CS294 Practical Machine Learning Junming Yin 10/09/06 Outline Introduction Unsupervised learning What is clustering? Application Dissimilarity (similarity) of objects Clustering algorithm K-means,
Clustering. CE-717: Machine Learning Sharif University of Technology Spring Soleymani
Clustering CE-717: Machine Learning Sharif University of Technology Spring 2016 Soleymani Outline Clustering Definition Clustering main approaches Partitional (flat) Hierarchical Clustering validation
Clustering CS 550: Machine Learning
Clustering CS 550: Machine Learning This slide set mainly uses the slides given in the following links: http://www-users.cs.umn.edu/~kumar/dmbook/ch8.pdf http://www-users.cs.umn.edu/~kumar/dmbook/dmslides/chap8_basic_cluster_analysis.pdf
An Introduction to Cluster Analysis. Zhaoxia Yu Department of Statistics Vice Chair of Undergraduate Affairs
An Introduction to Cluster Analysis Zhaoxia Yu Department of Statistics Vice Chair of Undergraduate Affairs zhaoxia@ics.uci.edu 1 What can you say about the figure? signal C 0.0 0.5 1.0 1500 subjects Two
Unsupervised Learning
Unsupervised Learning Learning without Class Labels (or correct outputs) Density Estimation Learn P(X) given training data for X Clustering Partition data into clusters Dimensionality Reduction Discover
MSA220 - Statistical Learning for Big Data
MSA220 - Statistical Learning for Big Data Lecture 13 Rebecka Jörnsten Mathematical Sciences University of Gothenburg and Chalmers University of Technology Clustering Explorative analysis - finding groups
Clustering algorithms
Clustering algorithms Machine Learning Hamid Beigy Sharif University of Technology Fall 1393 Hamid Beigy (Sharif University of Technology) Clustering algorithms Fall 1393 1 / 22 Table of contents 1 Supervised
Mixture Models and EM
Table of Content Chapter 9 Mixture Models and EM -means Clustering Gaussian Mixture Models (GMM) Expectation Maximiation (EM) for Mixture Parameter Estimation Introduction Mixture models allows Complex
Clustering Algorithms. Margareta Ackerman
Clustering Algorithms Margareta Ackerman A sea of algorithms As we discussed last class, there are MANY clustering algorithms, and new ones are proposed all the time. They are very different from each
Hierarchical clustering
Hierarchical clustering Based in part on slides from textbook, slides of Susan Holmes December 2, 2012 1 / 1 Description Produces a set of nested clusters organized as a hierarchical tree. Can be visualized
Cluster Analysis. Ying Shen, SSE, Tongji University
Cluster Analysis Ying Shen, SSE, Tongji University Cluster analysis Cluster analysis groups data objects based only on the attributes in the data. The main objective is that The objects within a group
MultiDimensional Signal Processing Master Degree in Ingegneria delle Telecomunicazioni A.A
MultiDimensional Signal Processing Master Degree in Ingegneria delle Telecomunicazioni A.A. 205-206 Pietro Guccione, PhD DEI - DIPARTIMENTO DI INGEGNERIA ELETTRICA E DELL INFORMAZIONE POLITECNICO DI BARI
Machine Learning for OR & FE
Machine Learning for OR & FE Unsupervised Learning: Clustering Martin Haugh Department of Industrial Engineering and Operations Research Columbia University Email: martin.b.haugh@gmail.com (Some material
Cluster Analysis. Summer School on Geocomputation. 27 June July 2011 Vysoké Pole
Cluster Analysis Summer School on Geocomputation 27 June 2011 2 July 2011 Vysoké Pole Lecture delivered by: doc. Mgr. Radoslav Harman, PhD. Faculty of Mathematics, Physics and Informatics Comenius University,
Clustering Part 3. Hierarchical Clustering
Clustering Part Dr Sanjay Ranka Professor Computer and Information Science and Engineering University of Florida, Gainesville Hierarchical Clustering Two main types: Agglomerative Start with the points
Note Set 4: Finite Mixture Models and the EM Algorithm
Note Set 4: Finite Mixture Models and the EM Algorithm Padhraic Smyth, Department of Computer Science University of California, Irvine Finite Mixture Models A finite mixture model with K components, for
Working with Unlabeled Data Clustering Analysis. Hsiao-Lung Chan Dept Electrical Engineering Chang Gung University, Taiwan
Working with Unlabeled Data Clustering Analysis Hsiao-Lung Chan Dept Electrical Engineering Chang Gung University, Taiwan chanhl@mail.cgu.edu.tw Unsupervised learning Finding centers of similarity using
Clustering Lecture 5: Mixture Model
Clustering Lecture 5: Mixture Model Jing Gao SUNY Buffalo 1 Outline Basics Motivation, definition, evaluation Methods Partitional Hierarchical Density-based Mixture model Spectral methods Advanced topics
Hierarchical Clustering
Hierarchical Clustering Produces a set of nested clusters organized as a hierarchical tree Can be visualized as a dendrogram A tree like diagram that records the sequences of merges or splits 0 0 0 00
Understanding Clustering Supervising the unsupervised
Understanding Clustering Supervising the unsupervised Janu Verma IBM T.J. Watson Research Center, New York http://jverma.github.io/ jverma@us.ibm.com @januverma Clustering Grouping together similar data
Cluster Analysis. Angela Montanari and Laura Anderlucci
Cluster Analysis Angela Montanari and Laura Anderlucci 1 Introduction Clustering a set of n objects into k groups is usually moved by the aim of identifying internally homogenous groups according to a
Distances, Clustering! Rafael Irizarry!
Distances, Clustering! Rafael Irizarry! Heatmaps! 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
BBS654 Data Mining. Pinar Duygulu. Slides are adapted from Nazli Ikizler
BBS654 Data Mining Pinar Duygulu Slides are adapted from Nazli Ikizler 1 Classification Classification systems: Supervised learning Make a rational prediction given evidence There are several methods for
Part I. Hierarchical clustering. Hierarchical Clustering. Hierarchical clustering. Produces a set of nested clusters organized as a
Week 9 Based in part on slides from textbook, slides of Susan Holmes Part I December 2, 2012 Hierarchical Clustering 1 / 1 Produces a set of nested clusters organized as a Hierarchical hierarchical clustering
CS Introduction to Data Mining Instructor: Abdullah Mueen
CS 591.03 Introduction to Data Mining Instructor: Abdullah Mueen LECTURE 8: ADVANCED CLUSTERING (FUZZY AND CO -CLUSTERING) Review: Basic Cluster Analysis Methods (Chap. 10) Cluster Analysis: Basic Concepts
Clustering Lecture 3: Hierarchical Methods
Clustering Lecture 3: Hierarchical Methods Jing Gao SUNY Buffalo 1 Outline Basics Motivation, definition, evaluation Methods Partitional Hierarchical Density-based Mixture model Spectral methods Advanced
Clustering. Chapter 10 in Introduction to statistical learning
Clustering Chapter 10 in Introduction to statistical learning 16 14 12 10 8 6 4 2 0 2 4 6 8 10 12 14 1 Clustering ² Clustering is the art of finding groups in data (Kaufman and Rousseeuw, 1990). ² What
University of Florida CISE department Gator Engineering. Clustering Part 2
Clustering Part 2 Dr. Sanjay Ranka Professor Computer and Information Science and Engineering University of Florida, Gainesville Partitional Clustering Original Points A Partitional Clustering Hierarchical
Data Exploration with PCA and Unsupervised Learning with Clustering Paul Rodriguez, PhD PACE SDSC
Data Exploration with PCA and Unsupervised Learning with Clustering Paul Rodriguez, PhD PACE SDSC Clustering Idea Given a set of data can we find a natural grouping? Essential R commands: D =rnorm(12,0,1)
Cluster Analysis. Jia Li Department of Statistics Penn State University. Summer School in Statistics for Astronomers IV June 9-14, 2008
Cluster Analysis Jia Li Department of Statistics Penn State University Summer School in Statistics for Astronomers IV June 9-1, 8 1 Clustering A basic tool in data mining/pattern recognition: Divide a
Chapter 6 Continued: Partitioning Methods
Chapter 6 Continued: Partitioning Methods Partitioning methods fix the number of clusters k and seek the best possible partition for that k. The goal is to choose the partition which gives the optimal
Cluster Analysis for Microarray Data
Cluster Analysis for Microarray Data Seventh International Long Oligonucleotide Microarray Workshop Tucson, Arizona January 7-12, 2007 Dan Nettleton IOWA STATE UNIVERSITY 1 Clustering Group objects that
Machine Learning. Unsupervised Learning. Manfred Huber
Machine Learning Unsupervised Learning Manfred Huber 2015 1 Unsupervised Learning In supervised learning the training data provides desired target output for learning In unsupervised learning the training
Clustering. Supervised vs. Unsupervised Learning
Clustering Supervised vs. Unsupervised Learning So far we have assumed that the training samples used to design the classifier were labeled by their class membership (supervised learning) We assume now
Data Mining Cluster Analysis: Basic Concepts and Algorithms. Slides From Lecture Notes for Chapter 8. Introduction to Data Mining
Data Mining Cluster Analysis: Basic Concepts and Algorithms Slides From Lecture Notes for Chapter 8 Introduction to Data Mining by Tan, Steinbach, Kumar Tan,Steinbach, Kumar Introduction to Data Mining
5/15/16. Computational Methods for Data Analysis. Massimo Poesio UNSUPERVISED LEARNING. Clustering. Unsupervised learning introduction
Computational Methods for Data Analysis Massimo Poesio UNSUPERVISED LEARNING Clustering Unsupervised learning introduction 1 Supervised learning Training set: Unsupervised learning Training set: 2 Clustering
Today s lecture. Clustering and unsupervised learning. Hierarchical clustering. K-means, K-medoids, VQ
Clustering CS498 Today s lecture Clustering and unsupervised learning Hierarchical clustering K-means, K-medoids, VQ Unsupervised learning Supervised learning Use labeled data to do something smart What
Market basket analysis
Market basket analysis Find joint values of the variables X = (X 1,..., X p ) that appear most frequently in the data base. It is most often applied to binary-valued data X j. In this context the observations
CHAPTER 4: CLUSTER ANALYSIS
CHAPTER 4: CLUSTER ANALYSIS WHAT IS CLUSTER ANALYSIS? A cluster is a collection of data-objects similar to one another within the same group & dissimilar to the objects in other groups. Cluster analysis
Finding Clusters 1 / 60
Finding Clusters Types of Clustering Approaches: Linkage Based, e.g. Hierarchical Clustering Clustering by Partitioning, e.g. k-means Density Based Clustering, e.g. DBScan Grid Based Clustering 1 / 60
Lecture 4 Hierarchical clustering
CSE : Unsupervised learning Spring 00 Lecture Hierarchical clustering. Multiple levels of granularity So far we ve talked about the k-center, k-means, and k-medoid problems, all of which involve pre-specifying
Clustering in R d. Clustering. Widely-used clustering methods. The k-means optimization problem CSE 250B
Clustering in R d Clustering CSE 250B Two common uses of clustering: Vector quantization Find a finite set of representatives that provides good coverage of a complex, possibly infinite, high-dimensional
Hierarchical Clustering Lecture 9
Hierarchical Clustering Lecture 9 Marina Santini Acknowledgements Slides borrowed and adapted from: Data Mining by I. H. Witten, E. Frank and M. A. Hall 1 Lecture 9: Required Reading Witten et al. (2011:
CS7267 MACHINE LEARNING
S7267 MAHINE LEARNING HIERARHIAL LUSTERING Ref: hengkai Li, Department of omputer Science and Engineering, University of Texas at Arlington (Slides courtesy of Vipin Kumar) Mingon Kang, Ph.D. omputer Science,
Clustering. K-means clustering
Clustering K-means clustering Clustering Motivation: Identify clusters of data points in a multidimensional space, i.e. partition the data set {x 1,...,x N } into K clusters. Intuition: A cluster is a
Statistics 202: Data Mining. c Jonathan Taylor. Clustering Based in part on slides from textbook, slides of Susan Holmes.
Clustering Based in part on slides from textbook, slides of Susan Holmes December 2, 2012 1 / 1 Clustering Clustering Goal: Finding groups of objects such that the objects in a group will be similar (or
Big Data Infrastructure CS 489/698 Big Data Infrastructure (Winter 2017)
Big Data Infrastructure CS 489/698 Big Data Infrastructure (Winter 2017) Week 9: Data Mining (4/4) March 9, 2017 Jimmy Lin David R. Cheriton School of Computer Science University of Waterloo These slides
Machine Learning and Data Mining. Clustering (1): Basics. Kalev Kask
Machine Learning and Data Mining Clustering (1): Basics Kalev Kask Unsupervised learning Supervised learning Predict target value ( y ) given features ( x ) Unsupervised learning Understand patterns of
Cluster analysis. Agnieszka Nowak - Brzezinska
Cluster analysis Agnieszka Nowak - Brzezinska Outline of lecture What is cluster analysis? Clustering algorithms Measures of Cluster Validity What is Cluster Analysis? Finding groups of objects such that
Introduction to Data Mining
Introduction to Data Mining Lecture #14: Clustering Seoul National University 1 In This Lecture Learn the motivation, applications, and goal of clustering Understand the basic methods of clustering (bottom-up
Hierarchical clustering
Hierarchical clustering Rebecca C. Steorts, Duke University STA 325, Chapter 10 ISL 1 / 63 Agenda K-means versus Hierarchical clustering Agglomerative vs divisive clustering Dendogram (tree) Hierarchical
Unsupervised Learning and Clustering
Unsupervised Learning and Clustering Selim Aksoy Department of Computer Engineering Bilkent University saksoy@cs.bilkent.edu.tr CS 551, Spring 2009 CS 551, Spring 2009 c 2009, Selim Aksoy (Bilkent University)
Stats 170A: Project in Data Science Exploratory Data Analysis: Clustering Algorithms
Stats 170A: Project in Data Science Exploratory Data Analysis: Clustering Algorithms Padhraic Smyth Department of Computer Science Bren School of Information and Computer Sciences University of California,
Cluster Analysis. Mu-Chun Su. Department of Computer Science and Information Engineering National Central University 2003/3/11 1
Cluster Analysis Mu-Chun Su Department of Computer Science and Information Engineering National Central University 2003/3/11 1 Introduction Cluster analysis is the formal study of algorithms and methods
Introduction to Machine Learning
Introduction to Machine Learning Clustering Varun Chandola Computer Science & Engineering State University of New York at Buffalo Buffalo, NY, USA chandola@buffalo.edu Chandola@UB CSE 474/574 1 / 19 Outline
Data Clustering. Danushka Bollegala
Data Clustering Danushka Bollegala Outline Why cluster data? Clustering as unsupervised learning Clustering algorithms k-means, k-medoids agglomerative clustering Brown s clustering Spectral clustering
Data Mining Concepts & Techniques
Data Mining Concepts & Techniques Lecture No 08 Cluster Analysis Naeem Ahmed Email: naeemmahoto@gmailcom Department of Software Engineering Mehran Univeristy of Engineering and Technology Jamshoro Outline
Mixture Models and the EM Algorithm
Mixture Models and the EM Algorithm Padhraic Smyth, Department of Computer Science University of California, Irvine c 2017 1 Finite Mixture Models Say we have a data set D = {x 1,..., x N } where x i is
Lecture Notes for Chapter 7. Introduction to Data Mining, 2 nd Edition. by Tan, Steinbach, Karpatne, Kumar
Data Mining Cluster Analysis: Basic Concepts and Algorithms Lecture Notes for Chapter 7 Introduction to Data Mining, 2 nd Edition by Tan, Steinbach, Karpatne, Kumar Hierarchical Clustering Produces a set
Unsupervised Learning: Clustering
Unsupervised Learning: Clustering Vibhav Gogate The University of Texas at Dallas Slides adapted from Carlos Guestrin, Dan Klein & Luke Zettlemoyer Machine Learning Supervised Learning Unsupervised Learning
Cluster Analysis. Prof. Thomas B. Fomby Department of Economics Southern Methodist University Dallas, TX April 2008 April 2010
Cluster Analysis Prof. Thomas B. Fomby Department of Economics Southern Methodist University Dallas, TX 7575 April 008 April 010 Cluster Analysis, sometimes called data segmentation or customer segmentation,
ECLT 5810 Clustering
ECLT 5810 Clustering What is Cluster Analysis? Cluster: a collection of data objects Similar to one another within the same cluster Dissimilar to the objects in other clusters Cluster analysis Grouping
Approaches to Clustering
Clustering A basic tool in data mining/pattern recognition: Divide a set of data into groups. Samples in one cluster are close and clusters are far apart. 6 5 4 3 1 1 3 1 1 3 4 5 6 Motivations: Discover
ECLT 5810 Clustering
ECLT 5810 Clustering What is Cluster Analysis? Cluster: a collection of data objects Similar to one another within the same cluster Dissimilar to the objects in other clusters Cluster analysis Grouping
SYDE Winter 2011 Introduction to Pattern Recognition. Clustering
SYDE 372 - Winter 2011 Introduction to Pattern Recognition Clustering Alexander Wong Department of Systems Design Engineering University of Waterloo Outline 1 2 3 4 5 All the approaches we have learned
Data Clustering Hierarchical Clustering, Density based clustering Grid based clustering
Data Clustering Hierarchical Clustering, Density based clustering Grid based clustering Team 2 Prof. Anita Wasilewska CSE 634 Data Mining All Sources Used for the Presentation Olson CF. Parallel algorithms
Clustering. SC4/SM4 Data Mining and Machine Learning, Hilary Term 2017 Dino Sejdinovic
Clustering SC4/SM4 Data Mining and Machine Learning, Hilary Term 2017 Dino Sejdinovic Clustering is one of the fundamental and ubiquitous tasks in exploratory data analysis a first intuition about the
3. Cluster analysis Overview
Université Laval Multivariate analysis - February 2006 1 3.1. Overview 3. Cluster analysis Clustering requires the recognition of discontinuous subsets in an environment that is sometimes discrete (as
Unsupervised Learning and Data Mining
Unsupervised Learning and Data Mining Unsupervised Learning and Data Mining Clustering Supervised Learning ó Decision trees ó Artificial neural nets ó K-nearest neighbor ó Support vectors ó Linear regression
Segmentation Computer Vision Spring 2018, Lecture 27
Segmentation http://www.cs.cmu.edu/~16385/ 16-385 Computer Vision Spring 218, Lecture 27 Course announcements Homework 7 is due on Sunday 6 th. - Any questions about homework 7? - How many of you have
3. Cluster analysis Overview
Université Laval Analyse multivariable - mars-avril 2008 1 3.1. Overview 3. Cluster analysis Clustering requires the recognition of discontinuous subsets in an environment that is sometimes discrete (as
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 4/18/004 1
10601 Machine Learning. Hierarchical clustering. Reading: Bishop: 9-9.2
161 Machine Learning Hierarchical clustering Reading: Bishop: 9-9.2 Second half: Overview Clustering - Hierarchical, semi-supervised learning Graphical models - Bayesian networks, HMMs, Reasoning under
Multivariate Analysis
Multivariate Analysis Cluster Analysis Prof. Dr. Anselmo E de Oliveira anselmo.quimica.ufg.br anselmo.disciplinas@gmail.com Unsupervised Learning Cluster Analysis Natural grouping Patterns in the data
Clustering: K-means and Kernel K-means
Clustering: K-means and Kernel K-means Piyush Rai Machine Learning (CS771A) Aug 31, 2016 Machine Learning (CS771A) Clustering: K-means and Kernel K-means 1 Clustering Usually an unsupervised learning problem
10701 Machine Learning. Clustering
171 Machine Learning Clustering What is Clustering? Organizing data into clusters such that there is high intra-cluster similarity low inter-cluster similarity Informally, finding natural groupings among
Clustering: Classic Methods and Modern Views
Clustering: Classic Methods and Modern Views Marina Meilă University of Washington mmp@stat.washington.edu June 22, 2015 Lorentz Center Workshop on Clusters, Games and Axioms Outline Paradigms for clustering
Machine Learning and Data Mining. Clustering. (adapted from) Prof. Alexander Ihler
Machine Learning and Data Mining Clustering (adapted from) Prof. Alexander Ihler Overview What is clustering and its applications? Distance between two clusters. Hierarchical Agglomerative clustering.
MATH5745 Multivariate Methods Lecture 13
MATH5745 Multivariate Methods Lecture 13 April 24, 2018 MATH5745 Multivariate Methods Lecture 13 April 24, 2018 1 / 33 Cluster analysis. Example: Fisher iris data Fisher (1936) 1 iris data consists of
Lecture 10: Semantic Segmentation and Clustering
Lecture 10: Semantic Segmentation and Clustering Vineet Kosaraju, Davy Ragland, Adrien Truong, Effie Nehoran, Maneekwan Toyungyernsub Department of Computer Science Stanford University Stanford, CA 94305
Machine Learning. B. Unsupervised Learning B.1 Cluster Analysis. Lars Schmidt-Thieme
Machine Learning B. Unsupervised Learning B.1 Cluster Analysis Lars Schmidt-Thieme Information Systems and Machine Learning Lab (ISMLL) Institute for Computer Science University of Hildesheim, Germany
COMP 551 Applied Machine Learning Lecture 13: Unsupervised learning
COMP 551 Applied Machine Learning Lecture 13: Unsupervised learning Associate Instructor: Herke van Hoof (herke.vanhoof@mail.mcgill.ca) Slides mostly by: (jpineau@cs.mcgill.ca) Class web page: www.cs.mcgill.ca/~jpineau/comp551