Hierarchical and Ensemble Clustering
|
|
- Morgan Sanders
- 6 years ago
- Views:
Transcription
1 Hierarchical and Ensemble Clustering Ke Chen Reading: [7.8-7., EA], [25.5, KPM], [Fred & Jain, 25] COMP24 Machine Learning
2 Outline Introduction Cluster Distance Measures Agglomerative Algorithm Example and Demo Key Concepts in Hierarchal Clustering Clustering Ensemble via Evidence Accumulation Summary COMP24 Machine Learning 2
3 Introduction Hierarchical Clustering Approach A typical clustering analysis approach via partitioning data set sequentially Construct nested partitions layer by layer via grouping objects into a tree of clusters (without the need to know the number of clusters in advance) Use (generalised) distance matrix as clustering criteria Agglomerative vs. Divisive Agglomerative: a bottom-up strategy Initially each data object is in its own (atomic) cluster Then merge these atomic clusters into larger and larger clusters Divisive: a top-down strategy Initially all objects are in one single cluster Then the cluster is subdivided into smaller and smaller clusters Clustering Ensemble Using multiple clustering results for robustness and overcoming weaknesses of single clustering algorithms. COMP24 Machine Learning 3
4 Introduction: Illustration Illustrative Example: Agglomerative vs. Divisive Agglomerative and divisive clustering on the data set {a, b, c, d,e } Step Step Step 2 Step 3 Step 4 Agglomerative a a b b c d e d e c d e a b c d e Cluster distance Termination condition Divisive Step 4 Step 3 Step 2 Step Step COMP24 Machine Learning 4
5 Cluster Distance Measures Single link: smallest distance between an element in one cluster and an element in the other, i.e., d(c i, C j ) = min{d(x ip, x jq )} Complete link: largest distance between an element in one cluster and an element in the other, i.e., d(c i, C j ) = max{d(x ip, x jq )} Average: avg distance between elements in one cluster and elements in the other, i.e., single link (min) complete link (max) average d(c i, C j ) = avg{d(x ip, x jq )} d(c, C)= COMP24 Machine Learning 5
6 Cluster Distance Measures Example: Given a data set of five objects characterised by a single continuous feature, assume that there are two clusters: C: {a, b} and C2: {c, d, e}. a b c d e Feature Calculate the distance matrix. 2. Calculate three cluster distances between C and C2. a b c d e a b c d 4 3 e Single link dist(c,c2) = min{ d(a,c), d(a,d), d(a,e), d(b,c), d(b,d), d(b,e)} = min{3, 4, 5, 2, 3, 4} = 2 Complete link dist(c,c2) = max{ d(a,c), d(a,d), d(a,e), d(b,c), d(b,d), d(b,e)} = max{3, 4, 5, 2, 3, 4} = 5 Average d(a,c) + d(a,d) + d(a,e) + d(b,c) + d(b,d) + d(b,e) dist(c,c2) = = = = COMP24 Machine Learning 6
7 Agglomerative Algorithm The Agglomerative algorithm is carried out in three steps: ) Convert all object features into a distance matrix 2) Set each object as a cluster (thus if we have N objects, we will have N clusters at the beginning) 3) Repeat until number of cluster is one (or known # of clusters) Merge two closest clusters Update distance matrix COMP24 Machine Learning 7
8 Example Problem: clustering analysis with agglomerative algorithm data matrix Euclidean distance distance matrix COMP24 Machine Learning 8
9 Example Merge two closest clusters (iteration ) COMP24 Machine Learning 9
10 Example Update distance matrix (iteration ) COMP24 Machine Learning
11 Example Merge two closest clusters (iteration 2) COMP24 Machine Learning
12 Example Update distance matrix (iteration 2) COMP24 Machine Learning 2
13 Example Merge two closest clusters/update distance matrix (iteration 3) COMP24 Machine Learning 3
14 Example Merge two closest clusters/update distance matrix (iteration 4) COMP24 Machine Learning 4
15 Example Final result (meeting termination condition) COMP24 Machine Learning 5
16 Key Concepts in Hierarchal Clustering Dendrogram tree representation lifetime In the beginning we have 6 clusters: A, B, C, D, E and F 2. We merge clusters D and F into cluster (D, F) at distance.5 3. We merge cluster A and cluster B into (A, B) at distance.7 4. We merge clusters E and (D, F) into ((D, F), E) at distance. 5. We merge clusters ((D, F), E) and C into (((D, F), E), C) at distance.4 6. We merge clusters (((D, F), E), C) and (A, B) into ((((D, F), E), C), (A, B)) at distance The last cluster contain all the objects, thus conclude the computation object COMP24 Machine Learning 6
17 Key Concepts in Hierarchal Clustering Lifetime vs K-cluster Lifetime 6 Lifetime The distance between that a cluster is created and that it disappears (merges with other clusters during clustering). e.g. lifetime of A, B, C, D, E and F are.7,.7,.4,.5,. and.5, respectively, the life time of (A, B) is =.79, lifetime K-cluster Lifetime The distance from that K clusters emerge to that K clusters vanish (due to the reduction to K- clusters). e.g. 5-cluster lifetime is =.2 4-cluster lifetime is. -.7 =.29 3-cluster lifetime is.4. =.4 object 2-cluster lifetime is =.9 COMP24 Machine Learning 7
18 Demo Agglomerative Demo COMP24 Machine Learning 8
19 Relevant Issues How to determine the number of clusters If the number of clusters known, termination condition is given! The K-cluster lifetime as the range of threshold value on the dendrogram tree that leads to the identification of K clusters Heuristic rule: cut a dendrogram tree with maximum life time to find a proper K Major weakness of agglomerative clustering methods Can never undo what was done previously Sensitive to cluster distance measures and noise/outliers Less efficient: O (n 2 logn), where n is the number of total objects There are several variants to overcome its weaknesses BIRCH: scalable to a large data set ROCK: clustering categorical data CHAMELEON: hierarchical clustering using dynamic modelling COMP24 Machine Learning 9
20 Motivation Clustering Ensemble A single clustering algorithm may be affected by various factors Sensitive to initialisation and noise/outliers, e.g. the K-means is sensitive to initial centroids! Sensitive to distance metrics but hard to find a proper one Hard to decide a single best algorithm that can handle all types of cluster shapes and sizes An effective treatments: clustering ensemble Utilise the results obtained by multiple clustering analyses for robustness COMP24 Machine Learning 2
21 Clustering Ensemble Clustering Ensemble via Evidence Accumulation (Fred & Jain, 25) A simple clustering ensemble algorithm to overcome the main weaknesses of different clustering methods by exploiting their synergy via evidence accumulation Algorithm summary Initial clustering analysis by using either different clustering algorithms or running a single clustering algorithm on different conditions, leading to multiple partitions e.g. the K-mean with various initial centroid settings and different K, the agglomerative algorithm with different distance metrics and forced to terminated with different number of clusters Converting clustering results on different partitions into binary distance matrices Evidence accumulation: form a collective distance matrix based on all the binary distance matrices Apply a hierarchical clustering algorithm (with a proper cluster distance metric) to the collective distance matrix and use the maximum K-cluster lifetime to decide K COMP24 Machine Learning 2
22 Clustering Ensemble Example: convert clustering results into binary Distance matrix Cluster 2 (C2) D distance Matrix Cluster (C) A B C D = A B C D A B C D COMP24 Machine Learning 22
23 Clustering Ensemble Example: convert clustering results into binary Distance matrix A B C D Cluster (C) Cluster 2 (C2) = D 2 A D C B D C A B distance Matrix 23 Cluster 3 (C3) COMP24 Machine Learning
24 Clustering Ensemble Evidence accumulation: form the collective distance matrix 24 = D 2 = D = + = D D 2 D C COMP24 Machine Learning
25 Clustering Ensemble Application to non-convex dataset Data set of 4 data points Initial clustering analysis: K-mean (K=2,,), 3 initial settings per K totally 3 partitions Converting clustering results to binary distance matrices for the collective distance matrix Applying the Agglomerative algorithm to the collective distance matrix (single-link) Cut the dendrogram tree with the maximum K-cluster lifetime to decide K COMP24 Machine Learning 25
26 Summary Hierarchical algorithm is a sequential clustering algorithm Use distance matrix to construct a tree of clusters (dendrogram) Hierarchical representation without the need of knowing # of clusters (can set termination condition with known # of clusters) Major weakness of agglomerative clustering methods Can never undo what was done previously Sensitive to cluster distance measures and noise/outliers Less efficient: O (n 2 logn), where n is the number of total objects Clustering ensemble based on evidence accumulation Initial clustering with different conditions, e.g., K-means on different K, initialisations Evidence accumulation collective distance matrix Apply agglomerative algorithm to collective distance matrix and max k-cluster lifetime Online tutorial: how to use hierarchical clustering functions in Matlab: COMP24 Machine Learning 26
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
More information[7.3, EA], [9.1, CMB]
K-means Clustering Ke Chen Reading: [7.3, EA], [9.1, CMB] Outline Introduction K-means Algorithm Example How K-means partitions? K-means Demo Relevant Issues Application: Cell Neulei Detection Summary
More informationHierarchical 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
More informationClustering 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
More informationCS570: Introduction to Data Mining
CS570: Introduction to Data Mining Scalable Clustering Methods: BIRCH and Others Reading: Chapter 10.3 Han, Chapter 9.5 Tan Cengiz Gunay, Ph.D. Slides courtesy of Li Xiong, Ph.D., 2011 Han, Kamber & Pei.
More informationBBS654 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
More informationCSE 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.
More informationData Mining. Dr. Raed Ibraheem Hamed. University of Human Development, College of Science and Technology Department of Computer Science
Data Mining Dr. Raed Ibraheem Hamed University of Human Development, College of Science and Technology Department of Computer Science 06 07 Department of CS - DM - UHD Road map Cluster Analysis: Basic
More informationCSE 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
More informationHierarchical Clustering 4/5/17
Hierarchical Clustering 4/5/17 Hypothesis Space Continuous inputs Output is a binary tree with data points as leaves. Useful for explaining the training data. Not useful for making new predictions. Direction
More informationUnsupervised Learning. Unsupervised Learning. What is Clustering? Unsupervised Learning I Clustering 9/7/2017. Clustering
Unsupervised Learning Clustering Centroid models (K-mean) Connectivity models (hierarchical clustering) Density models (DBSCAN) Graph-based models Subspace models (Biclustering) Feature extraction techniques
More informationHierarchical 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
More informationData 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
More informationCluster Validation. Ke Chen. Reading: [25.1.2, KPM], [Wang et al., 2009], [Yang & Chen, 2011] COMP24111 Machine Learning
Cluster Validation Ke Chen Reading: [5.., KPM], [Wang et al., 9], [Yang & Chen, ] COMP4 Machine Learning Outline Motivation and Background Internal index Motivation and general ideas Variance-based internal
More informationMachine 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.
More informationCluster 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
More informationHierarchy. No or very little supervision Some heuristic quality guidances on the quality of the hierarchy. Jian Pei: CMPT 459/741 Clustering (2) 1
Hierarchy An arrangement or classification of things according to inclusiveness A natural way of abstraction, summarization, compression, and simplification for understanding Typical setting: organize
More informationLecture 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
More informationDistances, 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
More informationLesson 3. Prof. Enza Messina
Lesson 3 Prof. Enza Messina Clustering techniques are generally classified into these classes: PARTITIONING ALGORITHMS Directly divides data points into some prespecified number of clusters without a hierarchical
More informationDATA 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)
More informationCSE 5243 INTRO. TO DATA MINING
CSE 5243 INTRO. TO DATA MINING Cluster Analysis: Basic Concepts and Methods Huan Sun, CSE@The Ohio State University 09/28/2017 Slides adapted from UIUC CS412, Fall 2017, by Prof. Jiawei Han 2 Chapter 10.
More informationUnsupervised 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)
More informationHierarchical 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
More informationUnsupervised Learning Hierarchical Methods
Unsupervised Learning Hierarchical Methods Road Map. Basic Concepts 2. BIRCH 3. ROCK The Principle Group data objects into a tree of clusters Hierarchical methods can be Agglomerative: bottom-up approach
More informationCluster Analysis: Agglomerate Hierarchical Clustering
Cluster Analysis: Agglomerate Hierarchical Clustering Yonghee Lee Department of Statistics, The University of Seoul Oct 29, 2015 Contents 1 Cluster Analysis Introduction Distance matrix Agglomerative Hierarchical
More informationData 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
More information5/15/16. 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
More informationGene Clustering & Classification
BINF, Introduction to Computational Biology Gene Clustering & Classification Young-Rae Cho Associate Professor Department of Computer Science Baylor University Overview Introduction to Gene Clustering
More informationKnowledge Discovery in Databases
Ludwig-Maximilians-Universität München Institut für Informatik Lehr- und Forschungseinheit für Datenbanksysteme Lecture notes Knowledge Discovery in Databases Summer Semester 2012 Lecture 8: Clustering
More informationUniversity 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
More informationTypes of general clustering methods. Clustering Algorithms for general similarity measures. Similarity between clusters
Types of general clustering methods Clustering Algorithms for general similarity measures agglomerative versus divisive algorithms agglomerative = bottom-up build up clusters from single objects divisive
More informationWhat is Cluster Analysis? COMP 465: Data Mining Clustering Basics. Applications of Cluster Analysis. Clustering: Application Examples 3/17/2015
// What is Cluster Analysis? COMP : Data Mining Clustering Basics Slides Adapted From : Jiawei Han, Micheline Kamber & Jian Pei Data Mining: Concepts and Techniques, rd ed. Cluster: A collection of data
More informationECLT 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
More informationECLT 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
More informationClustering part II 1
Clustering part II 1 Clustering What is Cluster Analysis? Types of Data in Cluster Analysis A Categorization of Major Clustering Methods Partitioning Methods Hierarchical Methods 2 Partitioning Algorithms:
More informationUnsupervised Learning
Outline Unsupervised Learning Basic concepts K-means algorithm Representation of clusters Hierarchical clustering Distance functions Which clustering algorithm to use? NN Supervised learning vs. unsupervised
More informationCluster 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
More information4. Ad-hoc I: Hierarchical clustering
4. Ad-hoc I: Hierarchical clustering Hierarchical versus Flat Flat methods generate a single partition into k clusters. The number k of clusters has to be determined by the user ahead of time. Hierarchical
More informationCluster 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
More informationExploiting Parallelism to Support Scalable Hierarchical Clustering
Exploiting Parallelism to Support Scalable Hierarchical Clustering Rebecca Cathey, Eric Jensen, Steven Beitzel, Ophir Frieder, David Grossman Information Retrieval Laboratory http://ir.iit.edu Background
More informationCluster 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,
More informationClustering Algorithms for general similarity measures
Types of general clustering methods Clustering Algorithms for general similarity measures general similarity measure: specified by object X object similarity matrix 1 constructive algorithms agglomerative
More informationPAM algorithm. Types of Data in Cluster Analysis. A Categorization of Major Clustering Methods. Partitioning i Methods. Hierarchical Methods
Whatis Cluster Analysis? Clustering Types of Data in Cluster Analysis Clustering part II A Categorization of Major Clustering Methods Partitioning i Methods Hierarchical Methods Partitioning i i Algorithms:
More informationClustering. 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
More informationClustering 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
More informationClustering. Informal goal. General types of clustering. Applications: Clustering in information search and analysis. Example applications in search
Informal goal Clustering Given set of objects and measure of similarity between them, group similar objects together What mean by similar? What is good grouping? Computation time / quality tradeoff 1 2
More informationHierarchical Clustering
Hierarchical Clustering Build a tree-based hierarchical taxonomy (dendrogram) from a set animal of documents. vertebrate invertebrate fish reptile amphib. mammal worm insect crustacean One approach: recursive
More information10701 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
More informationCluster 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
More informationUnsupervised Learning and Clustering
Unsupervised Learning and Clustering Selim Aksoy Department of Computer Engineering Bilkent University saksoy@cs.bilkent.edu.tr CS 551, Spring 2008 CS 551, Spring 2008 c 2008, Selim Aksoy (Bilkent University)
More informationClustering Analysis Basics
Clustering Analysis Basics Ke Chen Reading: [Ch. 7, EA], [5., KPM] Outline Introduction Data Types and Representations Distance Measures Major Clustering Methodologies Summary Introduction Cluster: A collection/group
More informationCS7267 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,
More informationMachine 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
More informationUnsupervised Learning. Supervised learning vs. unsupervised learning. What is Cluster Analysis? Applications of Cluster Analysis
7 Supervised learning vs unsupervised learning Unsupervised Learning Supervised learning: discover patterns in the data that relate data attributes with a target (class) attribute These patterns are then
More informationData 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
More informationClustering. 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
More informationNotes. Reminder: HW2 Due Today by 11:59PM. Review session on Thursday. Midterm next Tuesday (10/10/2017)
1 Notes Reminder: HW2 Due Today by 11:59PM TA s note: Please provide a detailed ReadMe.txt file on how to run the program on the STDLINUX. If you installed/upgraded any package on STDLINUX, you should
More information9/17/2009. Wenyan Li (Emily Li) Sep. 15, Introduction to Clustering Analysis
Introduction ti to K-means Algorithm Wenan Li (Emil Li) Sep. 5, 9 Outline Introduction to Clustering Analsis K-means Algorithm Description Eample of K-means Algorithm Other Issues of K-means Algorithm
More informationApplications. Foreground / background segmentation Finding skin-colored regions. Finding the moving objects. Intelligent scissors
Segmentation I Goal Separate image into coherent regions Berkeley segmentation database: http://www.eecs.berkeley.edu/research/projects/cs/vision/grouping/segbench/ Slide by L. Lazebnik Applications Intelligent
More informationINF4820. Clustering. Erik Velldal. Nov. 17, University of Oslo. Erik Velldal INF / 22
INF4820 Clustering Erik Velldal University of Oslo Nov. 17, 2009 Erik Velldal INF4820 1 / 22 Topics for Today More on unsupervised machine learning for data-driven categorization: clustering. The task
More informationMachine 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
More informationCLUSTERING ALGORITHMS
CLUSTERING ALGORITHMS Number of possible clusterings Let X={x 1,x 2,,x N }. Question: In how many ways the N points can be Answer: Examples: assigned into m groups? S( N, m) 1 m! m i 0 ( 1) m 1 m i i N
More informationBig Data Analytics! Special Topics for Computer Science CSE CSE Feb 9
Big Data Analytics! Special Topics for Computer Science CSE 4095-001 CSE 5095-005! Feb 9 Fei Wang Associate Professor Department of Computer Science and Engineering fei_wang@uconn.edu Clustering I What
More informationClustering and Visualisation of Data
Clustering and Visualisation of Data Hiroshi Shimodaira January-March 28 Cluster analysis aims to partition a data set into meaningful or useful groups, based on distances between data points. In some
More informationClustering: 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
More informationHierarchical clustering
Aprendizagem Automática Hierarchical clustering Ludwig Krippahl Hierarchical clustering Summary Hierarchical Clustering Agglomerative Clustering Divisive Clustering Clustering Features 1 Aprendizagem Automática
More informationMachine 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
More informationClustering. 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
More informationObjective of clustering
Objective of clustering Discover structures and patterns in high-dimensional data. Group data with similar patterns together. This reduces the complexity and facilitates interpretation. Expression level
More informationPerformance impact of dynamic parallelism on different clustering algorithms
Performance impact of dynamic parallelism on different clustering algorithms Jeffrey DiMarco and Michela Taufer Computer and Information Sciences, University of Delaware E-mail: jdimarco@udel.edu, taufer@udel.edu
More informationCSE 347/447: DATA MINING
CSE 347/447: DATA MINING Lecture 6: Clustering II W. Teal Lehigh University CSE 347/447, Fall 2016 Hierarchical Clustering Definition Produces a set of nested clusters organized as a hierarchical tree
More informationCS 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
More informationNotes. Reminder: HW2 Due Today by 11:59PM. Review session on Thursday. Midterm next Tuesday (10/09/2018)
1 Notes Reminder: HW2 Due Today by 11:59PM TA s note: Please provide a detailed ReadMe.txt file on how to run the program on the STDLINUX. If you installed/upgraded any package on STDLINUX, you should
More informationConsensus Clustering. Javier Béjar URL - Spring 2019 CS - MAI
Consensus Clustering Javier Béjar URL - Spring 2019 CS - MAI Consensus Clustering The ensemble of classifiers is a well established strategy in supervised learning Unsupervised learning aims the same goal:
More informationLecture 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 4/8/4 What
More informationA Comparison of Document Clustering Techniques
A Comparison of Document Clustering Techniques M. Steinbach, G. Karypis, V. Kumar Present by Leo Chen Feb-01 Leo Chen 1 Road Map Background & Motivation (2) Basic (6) Vector Space Model Cluster Quality
More informationClustering and Dissimilarity Measures. Clustering. Dissimilarity Measures. Cluster Analysis. Perceptually-Inspired Measures
Clustering and Dissimilarity Measures Clustering APR Course, Delft, The Netherlands Marco Loog May 19, 2008 1 What salient structures exist in the data? How many clusters? May 19, 2008 2 Cluster Analysis
More informationTELCOM2125: Network Science and Analysis
School of Information Sciences University of Pittsburgh TELCOM2125: Network Science and Analysis Konstantinos Pelechrinis Spring 2015 2 Part 4: Dividing Networks into Clusters The problem l Graph partitioning
More informationUnderstanding 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
More informationData Mining Algorithms
for the original version: -JörgSander and Martin Ester - Jiawei Han and Micheline Kamber Data Management and Exploration Prof. Dr. Thomas Seidl Data Mining Algorithms Lecture Course with Tutorials Wintersemester
More informationClustering in Data Mining
Clustering in Data Mining Classification Vs Clustering When the distribution is based on a single parameter and that parameter is known for each object, it is called classification. E.g. Children, young,
More informationCluster 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
More informationNetwork 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,
More informationUNSUPERVISED LEARNING IN R. Introduction to hierarchical clustering
UNSUPERVISED LEARNING IN R Introduction to hierarchical clustering Hierarchical clustering Number of clusters is not known ahead of time Two kinds: bottom-up and top-down, this course bottom-up Hierarchical
More informationHard 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
More informationClassification. Vladimir Curic. Centre for Image Analysis Swedish University of Agricultural Sciences Uppsala University
Classification Vladimir Curic Centre for Image Analysis Swedish University of Agricultural Sciences Uppsala University Outline An overview on classification Basics of classification How to choose appropriate
More information10601 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
More informationChapter 6: Cluster Analysis
Chapter 6: Cluster Analysis The major goal of cluster analysis is to separate individual observations, or items, into groups, or clusters, on the basis of the values for the q variables measured on each
More informationFinding 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
More informationClustering 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
More informationCHAPTER 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
More informationInformation Retrieval and Web Search Engines
Information Retrieval and Web Search Engines Lecture 7: Document Clustering December 4th, 2014 Wolf-Tilo Balke and José Pinto Institut für Informationssysteme Technische Universität Braunschweig The Cluster
More informationA Review on Cluster Based Approach in Data Mining
A Review on Cluster Based Approach in Data Mining M. Vijaya Maheswari PhD Research Scholar, Department of Computer Science Karpagam University Coimbatore, Tamilnadu,India Dr T. Christopher Assistant professor,
More informationUnsupervised Learning. Clustering and the EM Algorithm. Unsupervised Learning is Model Learning
Unsupervised Learning Clustering and the EM Algorithm Susanna Ricco Supervised Learning Given data in the form < x, y >, y is the target to learn. Good news: Easy to tell if our algorithm is giving the
More informationCOMP33111: Tutorial and lab exercise 7
COMP33111: Tutorial and lab exercise 7 Guide answers for Part 1: Understanding clustering 1. Explain the main differences between classification and clustering. main differences should include being unsupervised
More informationA Spectral-based Clustering Algorithm for Categorical Data Using Data Summaries (SCCADDS)
A Spectral-based Clustering Algorithm for Categorical Data Using Data Summaries (SCCADDS) Eman Abdu eha90@aol.com Graduate Center The City University of New York Douglas Salane dsalane@jjay.cuny.edu Center
More informationData 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 4/8/004 What
More informationPart 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
More informationK-Means. Oct Youn-Hee Han
K-Means Oct. 2015 Youn-Hee Han http://link.koreatech.ac.kr ²K-Means algorithm An unsupervised clustering algorithm K stands for number of clusters. It is typically a user input to the algorithm Some criteria
More information