Cluster analysis. Agnieszka Nowak - Brzezinska
|
|
- Allan Mathews
- 5 years ago
- Views:
Transcription
1 Cluster analysis Agnieszka Nowak - Brzezinska
2 Outline of lecture What is cluster analysis? Clustering algorithms Measures of Cluster Validity
3 What is Cluster Analysis? Finding groups of objects such that the objects in a group will be similar (or related) to one another and different from (or unrelated to) the objects in other groups Intra-cluster distances are minimized Inter-cluster distances are maximized
4 Applications of Cluster Analysis Understanding Group genes and proteins that have similar functionality, or group stocks with similar price fluctuations Summarization Reduce the size of large data sets Clustering precipitation in Australia
5 Notion of a Cluster can be Ambiguous How many clusters? Six Clusters Two Clusters Four Clusters
6 Types of Clusterings A clustering is a set of clusters Important distinction between hierarchical and partitional sets of clusters Partitional Clustering A division data objects into non-overlapping subsets (clusters) such that each data object is in exactly one subset Hierarchical clustering A set of nested clusters organized as a hierarchical tree
7 Partitional Clustering Original Points A Partitional Clustering
8 Hierarchical Clustering p1 p2 p3 p4 p1 p2 p3 p4 Traditional Hierarchical Clustering Traditional Dendrogram
9 Clustering Algorithms K-means Hierarchical clustering Graph based clustering
10 K-means Clustering Partitional clustering approach Each cluster is associated with a centroid (center point) Each point is assigned to the cluster with the closest centroid Number of clusters, K, must be specified The basic algorithm is very simple
11 y Illustration 3 Iteration x
12 y y y y y y Illustration 3 Iteration 1 3 Iteration 2 3 Iteration x x x 3 Iteration 4 3 Iteration 5 3 Iteration x x x
13 y y y Two different K-means Clusterings Original Points x x Optimal Clustering x Sub-optimal Clustering
14 Solutions to Initial Centroids Problem Multiple runs Helps, but probability is not on your side Sample and use hierarchical clustering to determine initial centroids Select more than k initial centroids and then select among these initial centroids Select most widely separated Bisecting K-means Not as susceptible to initialization issues
15 Evaluating K-means Clusters Most common measure is Sum of Squared Error (SSE) For each point, the error is the distance to the nearest cluster To get SSE, we square these errors and sum them. SSE K i 1 x C i dist 2 ( m, x) x is a data point in cluster C i and m i is the representative point for cluster C i can show that m i corresponds to the center (mean) of the cluster Given two clusters, we can choose the one with the smaller error One easy way to reduce SSE is to increase K, the number of clusters A good clustering with smaller K can have a lower SSE than a poor clustering with higher K i
16 Limitations of K-means K-means has problems when clusters are of differing Sizes Densities Non-globular shapes K-means has problems when the data contains outliers. The number of clusters (K) is difficult to determine.
17 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
18 Strengths of Hierarchical Clustering Do not have to assume any particular number of clusters Any desired number of clusters can be obtained by cutting the dendogram at the proper level They may correspond to meaningful taxonomies Example in biological sciences (e.g., animal kingdom, phylogeny reconstruction, )
19 Hierarchical Clustering Two main types of hierarchical clustering Agglomerative: Start with the points as individual clusters At each step, merge the closest pair of clusters until only one cluster (or k clusters) left Divisive: Start with one, all-inclusive cluster At each step, split a cluster until each cluster contains a point (or there are k clusters) Traditional hierarchical algorithms use a similarity or distance matrix Merge or split one cluster at a time
20 Agglomerative Clustering Algorithm More popular hierarchical clustering technique Basic algorithm is straightforward 1. Compute the proximity matrix 2. Let each data point be a cluster 3. Repeat 4. Merge the two closest clusters 5. Update the proximity matrix 6. Until only a single cluster remains Key operation is the computation of the proximity of two clusters Different approaches to defining the distance between clusters distinguish the different algorithms
21 Starting Situation Start with clusters of individual points and a proximity matrix p1 p1 p2 p3 p4 p5... p2 p3 p4 p5... Proximity Matrix... p1 p2 p3 p4 p9 p10 p11 p12
22 Intermediate Situation After some merging steps, we have some clusters C1 C2 C3 C4 C5 C1 C3 C4 C1 C2 C3 C4 C5 Proximity Matrix C2 C5... p1 p2 p3 p4 p9 p10 p11 p12
23 Intermediate Situation We want to merge the two closest clusters (C2 and C5) and update the proximity matrix. C1 C2 C1 C2 C3 C4 C5 C3 C4 C3 C5 C4 Proximity Matrix C1 C2 C5... p1 p2 p3 p4 p9 p10 p11 p12
24 After Merging The question is How do we update the proximity matrix? C1 C2 U C5 C3 C4 C3 C4 C1 C2 U C5 C3 C4??????? C1 Proximity Matrix C2 U C5... p1 p2 p3 p4 p9 p10 p11 p12
25 How to Define Inter-Cluster Similarity p1 p2 p3 p4 p5... Similarity? p1 p2 MIN MAX Group Average Distance Between Centroids p3 p4 p5... Proximity Matrix
26 How to Define Inter-Cluster Similarity p1 p2 p3 p4 p5... p1 p2 p3 p4 p5 MIN MAX Group Average Distance Between Centroids... Proximity Matrix
27 How to Define Inter-Cluster Similarity p1 p2 p3 p4 p5... p1 p2 p3 p4 p5 MIN MAX Group Average Distance Between Centroids... Proximity Matrix
28 How to Define Inter-Cluster Similarity p1 p2 p3 p4 p5... p1 p2 p3 p4 p5 MIN MAX Group Average Distance Between Centroids... Proximity Matrix
29 How to Define Inter-Cluster Similarity p1 p1 p2 p3 p4 p5... p2 p3 p4 MIN MAX Group Average Distance Between Centroids p5... Proximity Matrix
30 Hierarchical Clustering: Group Average Compromise between Single and Complete Link Strengths Less susceptible to noise and outliers Limitations Biased towards globular clusters
31 Hierarchical Clustering: Time and Space requirements O(N 2 ) space since it uses the proximity matrix. N is the number of points. O(N 3 ) time in many cases There are N steps and at each step the size, N 2, proximity matrix must be updated and searched Complexity can be reduced to O(N 2 log(n) ) time for some approaches
32 Hierarchical Clustering: Problems and Limitations Once a decision is made to combine two clusters, it cannot be undone No objective function is directly minimized Different schemes have problems with one or more of the following: Sensitivity to noise and outliers (MIN) Difficulty handling different sized clusters and non-convex shapes (Group average, MAX) Breaking large clusters (MAX)
33 Types of data in clustering analysis Interval-scaled attributes: Binary attributes: Nominal, ordinal, and ratio attributes: Attributes of mixed types:
34 Interval-scaled attributes Continuous measurements of a roughly linear scale E.g. weight, height, temperature, etc. Standardize data in preprocessing so that all attributes have equal weight Exceptions: height may be a more important attribute associated with basketball players
35 Similarity and Dissimilarity Between Objects Distances are normally used to measure the similarity or dissimilarity between two data objects (objects=records) Minkowski distance: where i = (x i1, x i2,, x ip ) and j = (x j1, x j2,, x jp ) are two p- dimensional data objects, and q is a positive integer If q = 1, d is Manhattan distance q q p p q q j x i x j x i x j x i x j i d )... ( ), ( ), ( p p j x i x j x i x j x i x j i d
36 Similarity and Dissimilarity Between Objects (Cont.) If q = 2, d is Euclidean distance: d( i, j) Properties d(i,j) 0 d(i,i) = 0 ( x i d(i,j) = d(j,i) x j x i d(i,j) d(i,k) + d(k,j) 2 x j... x i p p Can also use weighted distance, or other dissimilarity measures. 2 x j 2 )
37 Binary Attributes A contingency table for binary data Object i Object j 1 0 sum 1 a b a b 0 c d c d sum a c b d p Simple matching coefficient (if the binary attribute is symmetric): d( i, j) b c a b c d Jaccard coefficient (if the binary attribute is asymmetric): d( i, j) b c a b c
38 Example i j Dissimilarity between Binary gender is a symmetric attribute Attributes Name Gender Fever Cough Test-1 Test-2 Test-3 Test-4 Jack M Y N P N N N Mary F Y N P N P N Jim M Y P N N N N remaining attributes are asymmetric let the values Y and P be set to 1, and the value N be set to 0 d( d( d( 0 1 jack, mary ) jack, jim) jim, mary )
39 Nominal Attributes A generalization of the binary attribute in that it can take more than 2 states, e.g., red, yellow, blue, green Method 1: Simple matching m: # of attributes that are same for both records, p: total # of attributes d( i, j) p p m Method 2: rewrite the database and create a new binary attribute for each of the m states For an object with color yellow, the yellow attribute is set to 1, while the remaining attributes are set to 0.
40 Ordinal Attributes An ordinal attribute can be discrete or continuous Order is important, e.g., rank Can be treated like interval-scaled replacing x if by their rank map the range of each variable onto [0, 1] by replacing i-th object in the f-th attribute by r 1 if z if M 1 compute the dissimilarity using methods for interval-scaled attributes f r { 1,..., M } if f
41
42 Eucliedean distance
43 Other measures spheric manhattan
44 Different measures
45 y The distance between two point Calculate the distance between A (2,3) and B(7,8). D (A,B) = square ((7-2) 2 + (8-3) 2 ) = square ( ) = square (50) = B A x A B
46 y 3 points A(2,3), B(7,8) and C(5,1). Calculate: D (A,B) = square ((7-2) 2 + (8-3) 2 ) = square ( ) = square (50) = 7.07 D (A,C) = square ((5-2) 2 + (3-1) 2 ) = square (9 + 4) = square (13) = 3.60 D (B,C) = square ((7-5) 2 + (3-8) 2 ) = square (4 + 25) = square (29) = B A C x A B C
47 D (A,B) = square (( ) 2 + ( ) 2 + ( ) 2 + ( ) 2 + ( ) 2 ) = square ( ) = square (0.03) = 0.17 D (A,C) = square (( ) 2 + ( ) 2 + ( ) 2 + ( ) 2 + ( ) 2 ) = square ( ) = square (0.69) = 0.83 D (B,C) = square (( ) 2 + ( ) 2 + ( ) 2 + ( ) 2 + ( ) 2 ) = square ( ) = square (0.74) = 0.86 Many attributes V1 V2 V3 V4 V5 A B C
48 Hierarchical Clustering Use distance matrix as clustering criteria. This method does not require the number of clusters k as an input, but needs a termination condition. Step 0 Step 1 Step 2 Step 3 Step 4 a a b b a b c d e c c d e d d e e Step 4 Step 3 Step 2 Step 1 Step 0 agglomerative (AGNES) divisive (DIANA)
49 AGNES-Explored Given a set of N items to be clustered, and an NxN distance (or similarity) matrix, the basic process of Johnson's (1967) hierarchical clustering is this: Start by assigning each item to its own cluster, so that if you have N items, you now have N clusters, each containing just one item. Let the distances (similarities) between the clusters equal the distances (similarities) between the items they contain. Find the closest (most similar) pair of clusters and merge them into a single cluster, so that now you have one less cluster.
50 AGNES Compute distances (similarities) between the new cluster and each of the old clusters. Repeat steps 2 and 3 until all items are clustered into a single cluster of size N. Step 3 can be done in different ways, which is what distinguishes single-link from completelink and average-link clustering
51 data VAR 1 VAR
52 Distance matrix P_1 P_2 P_3 P_4 P_5 P_6 P_7 P_8 P_9 P_10 P_1 0 5,00 4,00 2,00 5,10 4,12 1,00 5,83 6,08 6,40 P_2 5,00 0 6,40 7,00 1,00 7,21 5,10 3,00 8,49 4,00 P_3 4,00 6,40 0 4,47 5,83 1,00 3,00 5,10 2,24 5,00 P_4 2,00 7,00 4,47 0 7,07 4,12 2,24 7,62 6,08 8,06 P_5 5,10 1,00 5,83 7,07 0 6,71 5,00 2,00 7,81 3,00 P_6 4,12 7,21 1,00 4,12 6,71 0 3,16 6,08 2,00 6,00 P_7 1,00 5,10 3,00 2,24 5,00 3,16 0 5,39 5,10 5,83 P_8 5,83 3,00 5,10 7,62 2,00 6,08 5,39 0 6,71 1,00 P_9 6,08 8,49 2,24 6,08 7,81 2,00 5,10 6,71 0 6,32 P_10 6,40 4,00 5,00 8,06 3,00 6,00 5,83 1,00 6,32 0
53 P_1 0 P_17 1 step P_1 P_2 P_3 P_4 P_5 P_6 P_7 P_8 P_9 P_10 P_2 5 0 P_3 4 6,4 0 P_ ,47 0 P_ P_ P_7 P_17 1 P_ P_ P_ P_ Find the minimal distance...
54 P_1 0 P_17 1 step P_1 P_2 P_3 P_4 P_5 P_6 P_7 P_8 P_9 P_10 P_2 5 0 P_3 4 6,4 0 P_ ,47 0 P_ P_ P_7 P_17 1 P_ P_ P_ P_ Find the minimal distance...
55 P_1 0 P_17 1 step P_1 P_2 P_3 P_4 P_5 P_6 P_7 P_8 P_9 P_10 P_2 5 0 P_3 4 6,4 0 P_ ,47 0 P_ P_ P_7 P_17 1 P_ P_ P_ P_ Find the minimal distance...
56 2 step P_17 0 P_17 P_2 P_3 P_4 P_5 P_6 P_8 P_9 P_10 P_2 5 0 P_25 P_25 P_3 3 6,4 0 P_ , P_ P_ P_ P_ P_
57 2 step P_17 0 P_17 P_2 P_3 P_4 P_5 P_6 P_8 P_9 P_10 P_2 5 0 P_25 P_25 P_3 3 6,4 0 P_ , P_ P_ P_ P_ P_
58 3 step P_17 P_25 P_3 P_4 P_6 P_8 P_9 P_10 P_17 0 P_ P_36 P_3 P_3 3 5,83 0 P_ ,47 0 P_ P_ P_6 P_36 P_ P_ Find the minimal distance...
59 3 step P_17 P_25 P_3 P_4 P_6 P_8 P_9 P_10 P_17 0 P_ P_36 P_3 P_3 3 5,83 0 P_ ,47 0 P_ P_ P_6 P_36 P_ P_ Find the minimal distance...
60 3 step P_17 P_25 P_3 P_4 P_6 P_8 P_9 P_10 P_17 0 P_ P_36 P_3 P_3 3 5,83 0 P_ ,47 0 P_ P_ P_6 P_36 P_ P_ Find the minimal distance...
61 4 step P_17 P_25 P_36 P_4 P_810 P_9 P_10 P_17 0 P_ P_36 3 5,83 0 P_ ,12 0 P_8 P_ P_ P_ P_10 0 Find the minimal distance...
62 4 step P_17 P_25 P_36 P_4 P_810 P_9 P_10 P_17 0 P_ P_36 3 5,83 0 P_ ,12 0 P_8 P_ P_ P_ P_10 0 Find the minimal distance...
63 4 step P_17 P_25 P_36 P_4 P_810 P_9 P_10 P_17 0 P_ P_36 3 5,83 0 P_ ,12 0 P_8 P_ P_ P_ P_10 0 Find the minimal distance...
64 5 step P_174 P_25 P_36 P_4 P_810 P_9 P_174 0 P_ P_36 3 5,83 0 P_ ,12 0 P_4 P_ P_ Find the minimal distance...
65 5 step P_174 P_25 P_36 P_4 P_810 P_9 P_174 0 P_ P_36 3 5,83 0 P_ ,12 0 P_4 P_ P_ Find the minimal distance...
66 5 step P_174 P_25 P_36 P_4 P_810 P_9 P_174 0 P_ P_36 3 5,83 0 P_ ,12 0 P_4 P_ P_ Find the minimal distance...
67 6 step P_174 P_25810 P_36 P_810 P_9 P_174 0 P_ P_36 3 5,83 0 P_ P_ Find the minimal distance...
68 6 step P_174 P_25810 P_36 P_810 P_9 P_174 0 P_ P_36 3 5,83 0 P_ P_ Find the minimal distance...
69 6 step P_174 P_25810 P_36 P_810 P_9 P_174 0 P_ P_36 3 5,83 0 P_ P_ Find the minimal distance...
70 7 step P_174 0 P_174 P_25810 P_369 P_9 P_ P_ P_ Find the minimal distance...
71 7 step P_174 0 P_174 P_25810 P_369 P_9 P_ P_ P_ Find the minimal distance...
72 7 step P_174 0 P_174 P_25810 P_369 P_9 P_ P_ P_ Find the minimal distance...
73 8 step P_ P_174 P_25810 P_369 P_ P_ P_ Find the minimal distance...
74 8 step P_ P_174 P_25810 P_369 P_ P_ P_ Find the minimal distance...
75 8 step P_ P_174 P_25810 P_369 P_ P_ P_ Find the minimal distance...
76 9 step P_ P_174 P_25810 P_369 P_ P_ P_ Find the minimal distance... 9 step P_ P_ P_25810 P_ Find the minimal distance...
77 9 step P_ P_174 P_25810 P_369 P_ It is now only ONE GROUP P_ P_ P_ STEPS OF THE ALGORITHM Find the minimal distance... 9 step P_ P_ P_25810 P_ Find the minimal distance...
78 9 step P_ P_174 P_25810 P_369 P_ Powstanie jedna grupa P_ P_ P_ Find the minimal distance... 9 iteracji algorytmu 9 step P_ P_ P_25810 P_ Find the minimal distance...
79 Dendrogram
80 Single Linkage Complete linkage Average Linkage
81 The number of clusters
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
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 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 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 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 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 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 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 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 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 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 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 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 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 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 informationClustering 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 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 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 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 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 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 informationDATA MINING - 1DL105, 1Dl111. An introductory class in data mining
1 DATA MINING - 1DL105, 1Dl111 Fall 007 An introductory class in data mining http://user.it.uu.se/~udbl/dm-ht007/ alt. http://www.it.uu.se/edu/course/homepage/infoutv/ht07 Kjell Orsborn Uppsala Database
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 informationWhat is Cluster Analysis?
Cluster Analysis What is Cluster Analysis? Finding groups of objects (data points) such that the objects in a group will be similar (or related) to one another and different from (or unrelated to) the
More informationData Mining: Concepts and Techniques. Chapter March 8, 2007 Data Mining: Concepts and Techniques 1
Data Mining: Concepts and Techniques Chapter 7.1-4 March 8, 2007 Data Mining: Concepts and Techniques 1 1. What is Cluster Analysis? 2. Types of Data in Cluster Analysis Chapter 7 Cluster Analysis 3. A
More informationCluster Analysis. CSE634 Data Mining
Cluster Analysis CSE634 Data Mining Agenda Introduction Clustering Requirements Data Representation Partitioning Methods K-Means Clustering K-Medoids Clustering Constrained K-Means clustering Introduction
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 informationUnsupervised Learning. Andrea G. B. Tettamanzi I3S Laboratory SPARKS Team
Unsupervised Learning Andrea G. B. Tettamanzi I3S Laboratory SPARKS Team Table of Contents 1)Clustering: Introduction and Basic Concepts 2)An Overview of Popular Clustering Methods 3)Other Unsupervised
More informationClustering fundamentals
Elena Baralis, Tania Cerquitelli Politecnico di Torino What is Cluster Analsis? Finding groups of objects such that the objects in a group will be similar (or related) to one another and different from
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 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 informationMultiDimensional 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
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 informationStatistics 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
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 (modified by Predrag Radivojac, 07) Old Faithful Geyser Data
More informationUnsupervised Learning : Clustering
Unsupervised Learning : Clustering Things to be Addressed Traditional Learning Models. Cluster Analysis K-means Clustering Algorithm Drawbacks of traditional clustering algorithms. Clustering as a complex
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 informationCluster Analysis: Basic Concepts and Algorithms
Cluster Analysis: Basic Concepts and Algorithms Data Warehousing and Mining Lecture 10 by Hossen Asiful Mustafa What is Cluster Analysis? Finding groups of objects such that the objects in a group will
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 informationData 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 What is Cluster Analsis? Finding groups of objects such that the
More informationRoad map. Basic concepts
Clustering Basic concepts Road map K-means algorithm Representation of clusters Hierarchical clustering Distance functions Data standardization Handling mixed attributes Which clustering algorithm to use?
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 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, nd Edition by Tan, Steinbach, Karpatne, Kumar What is Cluster Analysis? Finding groups
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 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 informationCommunity Detection. Jian Pei: CMPT 741/459 Clustering (1) 2
Clustering Community Detection http://image.slidesharecdn.com/communitydetectionitilecturejune0-0609559-phpapp0/95/community-detection-in-social-media--78.jpg?cb=3087368 Jian Pei: CMPT 74/459 Clustering
More informationData Mining. Clustering. Hamid Beigy. Sharif University of Technology. Fall 1394
Data Mining Clustering Hamid Beigy Sharif University of Technology Fall 1394 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1394 1 / 31 Table of contents 1 Introduction 2 Data matrix and
More informationStatistics 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
More informationTan,Steinbach, Kumar Introduction to Data Mining 4/18/ Tan,Steinbach, Kumar Introduction to Data Mining 4/18/
Data Mining Cluster Analsis: Basic Concepts and Algorithms Lecture Notes for Chapter Introduction to Data Mining b Tan, Steinbach, Kumar What is Cluster Analsis? Finding groups of objects such that the
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 informationClustering Basic Concepts and Algorithms 1
Clustering Basic Concepts and Algorithms 1 Jeff Howbert Introduction to Machine Learning Winter 014 1 Machine learning tasks Supervised Classification Regression Recommender systems Reinforcement learning
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 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 informationData 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
More informationMachine Learning 15/04/2015. Supervised learning vs. unsupervised learning. What is Cluster Analysis? Applications of Cluster Analysis
// Supervised learning vs unsupervised learning Machine Learning Unsupervised Learning Supervised learning: discover patterns in the data that relate data attributes with a target (class) attribute These
More informationLecture 7 Cluster Analysis: Part A
Lecture 7 Cluster Analysis: Part A Zhou Shuigeng May 7, 2007 2007-6-23 Data Mining: Tech. & Appl. 1 Outline What is Cluster Analysis? Types of Data in Cluster Analysis A Categorization of Major Clustering
More informationTan,Steinbach, Kumar Introduction to Data Mining 4/18/ Tan,Steinbach, Kumar Introduction to Data Mining 4/18/
Data Mining Cluster Analsis: Basic Concepts and Algorithms Lecture Notes for Chapter Introduction to Data Mining b Tan, Steinbach, Kumar What is Cluster Analsis? Finding groups of objects such that the
More informationOnline Social Networks and Media. Community detection
Online Social Networks and Media Community detection 1 Notes on Homework 1 1. You should write your own code for generating the graphs. You may use SNAP graph primitives (e.g., add node/edge) 2. For the
More informationUnsupervised Learning. Presenter: Anil Sharma, PhD Scholar, IIIT-Delhi
Unsupervised Learning Presenter: Anil Sharma, PhD Scholar, IIIT-Delhi Content Motivation Introduction Applications Types of clustering Clustering criterion functions Distance functions Normalization Which
More informationClustering Tips and Tricks in 45 minutes (maybe more :)
Clustering Tips and Tricks in 45 minutes (maybe more :) Olfa Nasraoui, University of Louisville Tutorial for the Data Science for Social Good Fellowship 2015 cohort @DSSG2015@University of Chicago https://www.researchgate.net/profile/olfa_nasraoui
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 informationIntroduction to Clustering
Introduction to Clustering Ref: Chengkai Li, Department of Computer Science and Engineering, University of Texas at Arlington (Slides courtesy of Vipin Kumar) What is Cluster Analysis? Finding groups of
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 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 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:
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 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 informationHierarchical Clustering
What is clustering Partitioning of a data set into subsets. A cluster is a group of relatively homogeneous cases or observations Hierarchical Clustering Mikhail Dozmorov Fall 2016 2/61 What is clustering
More informationOlmo 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)
More informationHierarchical clustering
Aprendizagem Automática Hierarchical clustering Ludwig Krippahl Hierarchical clustering Summary Hierarchical Clustering Agglomerative Clustering Divisive Clustering Clustering Features 1 Aprendizagem Automática
More informationClustering Part 2. A Partitional Clustering
Universit of Florida CISE department Gator Engineering Clustering Part Dr. Sanja Ranka Professor Computer and Information Science and Engineering Universit of Florida, Gainesville Universit of Florida
More informationCS 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:
More informationData Mining 資料探勘. 分群分析 (Cluster Analysis) 1002DM04 MI4 Thu. 9,10 (16:10-18:00) B513
Data Mining 資料探勘 分群分析 (Cluster Analysis) DM MI Thu. 9, (6:-8:) B5 Min-Yuh Day 戴敏育 Assistant Professor 專任助理教授 Dept. of Information Management, Tamkang University 淡江大學資訊管理學系 http://mail. tku.edu.tw/myday/
More informationSYDE 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
More informationWorking 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
More informationChapter VIII.3: Hierarchical Clustering
Chapter VIII.3: Hierarchical Clustering 1. Basic idea 1.1. Dendrograms 1.2. Agglomerative and divisive 2. Cluster distances 2.1. Single link 2.2. Complete link 2.3. Group average and Mean distance 2.4.
More informationHomework # 4. Example: Age in years. Answer: Discrete, quantitative, ratio. a) Year that an event happened, e.g., 1917, 1950, 2000.
Homework # 4 1. Attribute Types Classify the following attributes as binary, discrete, or continuous. Further classify the attributes as qualitative (nominal or ordinal) or quantitative (interval or ratio).
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 informationCOMP20008 Elements of Data Processing. Outlier Detection and Clustering
COMP20008 Elements of Data Processing Outlier Detection and Clustering Today Outlier detection for high dimensional data (part I) A digression clustering algorithms K-means Hierarchical clustering Outlier
More informationUniversity of Florida CISE department Gator Engineering. Clustering Part 4
Clustering Part 4 Dr. Sanjay Ranka Professor Computer and Information Science and Engineering University of Florida, Gainesville DBSCAN DBSCAN is a density based clustering algorithm Density = number of
More informationChapter DM:II. II. Cluster Analysis
Chapter DM:II II. Cluster Analysis Cluster Analysis Basics Hierarchical Cluster Analysis Iterative Cluster Analysis Density-Based Cluster Analysis Cluster Evaluation Constrained Cluster Analysis DM:II-1
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 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 informationForestry Applied Multivariate Statistics. Cluster Analysis
1 Forestry 531 -- Applied Multivariate Statistics Cluster Analysis Purpose: To group similar entities together based on their attributes. Entities can be variables or observations. [illustration in Class]
More informationClustering Part 4 DBSCAN
Clustering Part 4 Dr. Sanjay Ranka Professor Computer and Information Science and Engineering University of Florida, Gainesville DBSCAN DBSCAN is a density based clustering algorithm Density = number of
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: Overview and K-means algorithm
Clustering: Overview and K-means algorithm Informal goal Given set of objects and measure of similarity between them, group similar objects together K-Means illustrations thanks to 2006 student Martin
More informationIntroduction to Computer Science
DM534 Introduction to Computer Science Clustering and Feature Spaces Richard Roettger: About Me Computer Science (Technical University of Munich and thesis at the ICSI at the University of California at
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 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 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 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 informationUniversity of Florida CISE department Gator Engineering. Clustering Part 5
Clustering Part 5 Dr. Sanjay Ranka Professor Computer and Information Science and Engineering University of Florida, Gainesville SNN Approach to Clustering Ordinary distance measures have problems Euclidean
More information9/29/13. Outline Data mining tasks. Clustering algorithms. Applications of clustering in biology
9/9/ I9 Introduction to Bioinformatics, Clustering algorithms Yuzhen Ye (yye@indiana.edu) School of Informatics & Computing, IUB Outline Data mining tasks Predictive tasks vs descriptive tasks Example
More informationToday 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
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 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 informationKeywords Clustering, Goals of clustering, clustering techniques, clustering algorithms.
Volume 3, Issue 5, May 2013 ISSN: 2277 128X International Journal of Advanced Research in Computer Science and Software Engineering Research Paper Available online at: www.ijarcsse.com A Survey of Clustering
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 information7.1 Euclidean and Manhattan distances between two objects The k-means partitioning algorithm... 21
Contents 7 Cluster Analysis 7 7.1 What Is Cluster Analysis?......................................... 7 7.2 Types of Data in Cluster Analysis.................................... 9 7.2.1 Interval-Scaled
More information