Unsupervised learning: Clustering


 Janel Strickland
 3 years ago
 Views:
Transcription
1 Unsupervised learning: Clustering Salissou Moutari Centre for Statistical Science and Operational Research CenSSOR 17 th September 2013 Unsupervised learning: Clustering 1/52
2 Outline 1 Introduction What is Unsupervised learning? Fundamental aspects of clustering 2 Clustering algorithms Hierarchical clustering Partitional clustering 3 Clustering evaluation metrics Unsupervised learning: Clustering h mn 2/52
3 Introduction What is Unsupervised learning? What is Unsupervised learning? Problem Given a set of records (e.g. observations or variables) with no target attribute, organise them into groups, without advance knowledge of the definitions of the groups. Unsupervised learning Unsupervised learning consists of approaches, which attempt to address the above problem by exploring the unlabelled data to find some intrinsic natural structures within them. Unsupervised learning: Clustering h mn 3/52
4 Introduction What is Unsupervised learning? What is Unsupervised learning? Problem Given a set of records (e.g. observations or variables) with no target attribute, organise them into groups, without advance knowledge of the definitions of the groups. Unsupervised learning Unsupervised learning consists of approaches, which attempt to address the above problem by exploring the unlabelled data to find some intrinsic natural structures within them. Unsupervised learning: Clustering h mn 3/52
5 Introduction What is Unsupervised learning? What is Unsupervised learning? Examples of unsupervised learning approaches Clustering Selforganising maps Association rule Blind signal separation etc. This session will focus on Clustering. Why Clustering? Clustering is one of the most utilised unsupervised learning techniques. Unsupervised learning: Clustering h mn 4/52
6 Introduction What is Unsupervised learning? What is Unsupervised learning? Examples of unsupervised learning approaches Clustering Selforganising maps Association rule Blind signal separation etc. This session will focus on Clustering. Why Clustering? Clustering is one of the most utilised unsupervised learning techniques. Unsupervised learning: Clustering h mn 4/52
7 Introduction What is Unsupervised learning? What is Unsupervised learning? Examples of unsupervised learning approaches Clustering Selforganising maps Association rule Blind signal separation etc. This session will focus on Clustering. Why Clustering? Clustering is one of the most utilised unsupervised learning techniques. Unsupervised learning: Clustering h mn 4/52
8 Introduction What is Unsupervised learning? What is Unsupervised learning? Examples of unsupervised learning approaches Clustering Selforganising maps Association rule Blind signal separation etc. This session will focus on Clustering. Why Clustering? Clustering is one of the most utilised unsupervised learning techniques. Unsupervised learning: Clustering h mn 4/52
9 Introduction Fundamental aspects of clustering Fundamental aspects of clustering Definition Clustering, also termed Cluster Analysis is the collection of methods for grouping unlabelled data into subsets (called clusters) that are believed to reflect the underlying structure of the data, based on similarity groups within the data. What is clustering for? Identification of new tumor classes using gene expression profiles; Identification of groups of coregulated genes, e.g. using a large number of yeast experiments; Grouping similar proteins together with respect to their chemical structure and/or functionality etc; Detect experimental artifacts. Unsupervised learning: Clustering h mn 5/52
10 Introduction Fundamental aspects of clustering Fundamental aspects of clustering Definition Clustering, also termed Cluster Analysis is the collection of methods for grouping unlabelled data into subsets (called clusters) that are believed to reflect the underlying structure of the data, based on similarity groups within the data. What is clustering for? Identification of new tumor classes using gene expression profiles; Identification of groups of coregulated genes, e.g. using a large number of yeast experiments; Grouping similar proteins together with respect to their chemical structure and/or functionality etc; Detect experimental artifacts. Unsupervised learning: Clustering h mn 5/52
11 Introduction Fundamental aspects of clustering Fundamental aspects of clustering Definition Clustering, also termed Cluster Analysis is the collection of methods for grouping unlabelled data into subsets (called clusters) that are believed to reflect the underlying structure of the data, based on similarity groups within the data. What is clustering for? Identification of new tumor classes using gene expression profiles; Identification of groups of coregulated genes, e.g. using a large number of yeast experiments; Grouping similar proteins together with respect to their chemical structure and/or functionality etc; Detect experimental artifacts. Unsupervised learning: Clustering h mn 5/52
12 Introduction Fundamental aspects of clustering Fundamental aspects of clustering Basic concepts Clustering deals with data for which the groups are unknown and undefined. Thus we need to conceptualise the groups. Intraclusters distance: Interclusters distance: Intracluster distance Intercluster distance Unsupervised learning: Clustering h mn 6/52
13 Challenges Introduction Fundamental aspects of clustering Notion of a Cluster can 1 Definition of the intercluster and intracluster distances. 2 The number of clusters. 3 The type of clusters. 4 Clusters quality. How many clusters? for these data? Unsupervised learning: Clustering h mn 7/52
14 Challenges Introduction Fundamental aspects of clustering Notion of a Cluster can 1 Definition of the intercluster and intracluster distances. 2 The number of clusters. 3 The type of clusters. 4 Clusters quality. How many clusters? for these data? Unsupervised learning: Clustering h mn 7/52
15 Introduction Fundamental aspects of clustering Challenges Two clusters? How many clusters? r can be Ambiguous Why not six clusters? Two Clusters Tan,Steinbach, Kumar Introduction to Data Mining Six Clusters Unsupervised learning: Clustering h mn 8/52
16 Challenges Introduction Fundamental aspects of clustering Definition of intraclusters distance Type of distance measurement to be used to determine how close two data points are to each other. It is commonly called the distance, similarity or dissimilarity measure. Definition of interclusters distance Type of distance measurement to be used to determine how close two clusters are to each other. It is commonly called the linkage function or linkage criteria. It is is often both data (cluster shape) and context dependent and may depend on the distance measure. Unsupervised learning: Clustering h mn 9/52
17 Introduction Fundamental aspects of clustering Distance measures Fundamental axioms Assume that the data are in an ndimensional Euclidean space, and let x =[x 1, x 2,...,x n ], y =[y 1, y 2,...,y n ]andz =[z 1, z 2,...,z n ]define three data points. Fundamental axioms of a distance measure d are: 1 d(x, x) =0 2 d(x, y) =d(y, x) 3 d(x, y) apple d(x, z)+d(z, y) Remark The choice of a distance measure will influence the shape of the clusters, as some elements may be close to one another according to one distance and farther away according to another. Unsupervised learning: Clustering h mn 10 / 52
18 Introduction Fundamental aspects of clustering Distance measures Fundamental axioms Assume that the data are in an ndimensional Euclidean space, and let x =[x 1, x 2,...,x n ], y =[y 1, y 2,...,y n ]andz =[z 1, z 2,...,z n ]define three data points. Fundamental axioms of a distance measure d are: 1 d(x, x) =0 2 d(x, y) =d(y, x) 3 d(x, y) apple d(x, z)+d(z, y) Remark The choice of a distance measure will influence the shape of the clusters, as some elements may be close to one another according to one distance and farther away according to another. Unsupervised learning: Clustering h mn 10 / 52
19 Distance measures Introduction Fundamental aspects of clustering Examples of distance metrics Some commonly used metrics for clustering include: Euclidian distance (L 2 norm): d(x, y) = p P n i=1 (x i y i ) 2 nx Manhattan distance (L 1 norm): d(x, y) = kx i y i k i=1 Chebychev maximum distance (L 1 norm): d(x, y) = Minkowski distance (L p norm): d(x, y) = max i=1,...,n kx i! 1/p nx kx i y i k p Mahalanobis distance: d(x, y) = p P n i=1 (x i y i )R 1 (x i y i ), where R denotes the covariance matrix associated to the data. i=1 y i k Unsupervised learning: Clustering h mn 11 / 52
20 Linkage criteria Introduction Fundamental aspects of clustering Examples of linkage criteria or linkage functions Let C 1 and C 2 be two candidate clusters and let d be the chosen distance metric. Commonly used linkage functions between C 1 and C2 include: Single linkage: f (C 1, C 2 )=min{d(x, y) : x 2 C 1, y 2 C 2 } Complete linkage: f (C 1, C 2 )=max{d(x, y) : x 2 C 1, y 2 C 2 } 1 X X Average linkage: f (C 1, C 2 )= d(x, y) C 1 C 2 x2c 1 y2c 2 Ward s criterion: The distance between C 1 and C 2 is given by where µ i is the centre of cluster i. f (C 1, C 2 )= C 1 C 2 C 1 + C 2 µ 1 µ 2 2, Unsupervised learning: Clustering h mn 12 / 52
21 Clustering algorithms Clustering algorithms Hierarchical clustering Create a hierarchical decomposition of a data set by finding successive clusters using previously established clusters. Hierarchical clustering methods produce a tree diagram known as dendrogram or phenogram, which can be built in two distinct ways: Bottomup known as Agglomerative clustering and Topdown called Divisive clustering. Partitional clustering Decompose the data set into a set of disjoint clusters, i.e. a set of nonoverlapping clusters such that each data point is in exactly one subset cluster. Unsupervised learning: Clustering h mn 13 / 52
22 Clustering algorithms Clustering algorithms Hierarchical clustering Create a hierarchical decomposition of a data set by finding successive clusters using previously established clusters. Hierarchical clustering methods produce a tree diagram known as dendrogram or phenogram, which can be built in two distinct ways: Bottomup known as Agglomerative clustering and Topdown called Divisive clustering. Partitional clustering Decompose the data set into a set of disjoint clusters, i.e. a set of nonoverlapping clusters such that each data point is in exactly one subset cluster. Unsupervised learning: Clustering h mn 13 / 52
23 Clustering algorithms Hierarchical clustering Hierarchical clustering Agglomerative clustering Start with the points as individual clusters; At each step, merge the closest pair of clusters until all the data points are in a single cluster or until certain termination conditions are satisfied. Divisive clustering Start with one, allinclusive cluster; At each step, split a cluster until each cluster contains a single data point or until certain termination conditions are satisfied. Unsupervised learning: Clustering h mn 14 / 52
24 Clustering algorithms Hierarchical clustering Hierarchical clustering Agglomerative clustering Start with the points as individual clusters; At each step, merge the closest pair of clusters until all the data points are in a single cluster or until certain termination conditions are satisfied. Divisive clustering Start with one, allinclusive cluster; At each step, split a cluster until each cluster contains a single data point or until certain termination conditions are satisfied. Unsupervised learning: Clustering h mn 14 / 52
25 Clustering algorithms Hierarchical clustering Agglomerative clustering Algorithm The algorithm forms clusters in a bottomup manner, as follows: 1 Initially, put each data point in its own cluster. 2 Among all current clusters, pick the two clusters which optimise the chosen linkage function. 3 Replace these two clusters with a new cluster, formed by merging the two original ones. 4 Repeat the steps 2 and 3 until there is only one remaining cluster in the pool, or until certain termination conditions are satisfied. Unsupervised learning: Clustering h mn 15 / 52
26 Clustering algorithms Hierarchical clustering Agglomerative clustering: Illustration with R Distance measure The function dist(x, method="metric") returns the distance matrix of anumericalmatrixx using a specified metric, which must be one of the followings: "euclidean", "maximum", "manhattan", "canberra", "binary" or "minkowski". Clustering The function hclust(d, method="linkage") performs hierarchical agglomerative clustering using a given distance matrix d and a specified linkage function, which must be one of the followings: "single", "complete", "average", "mcquitty", "median" or "centroid". Unsupervised learning: Clustering h mn 16 / 52
27 Clustering algorithms Hierarchical clustering Agglomerative clustering: Illustration with R Let us consider the following data set X : Unsupervised learning: Clustering h mn 17 / 52
28 Clustering algorithms Hierarchical clustering Agglomerative clustering: Illustration with R Rscript library(stats) d<dist(x, method="euclidean") hc<hclust(d, method="single") ggdendrogram(hc, theme dendro=false) Agglomerative clustering using euclidian distance measure and single linkage. Unsupervised learning: Clustering h mn 18 / 52
29 Clustering algorithms Hierarchical clustering Agglomerative clustering: Illustration with R Single linkage: Impact of the choice of the distance measure. Euclidian distance Chebychev distance Unsupervised learning: Clustering h mn 19 / 52
30 Clustering algorithms Hierarchical clustering Agglomerative clustering: Illustration with R Complete linkage: Impact of the choice of the distance measure. Euclidian distance Chebychev distance Unsupervised learning: Clustering h mn 20 / 52
31 Clustering algorithms Hierarchical clustering Agglomerative clustering: Illustration with R Average linkage: Impact of the choice of the distance measure. Euclidian distance Chebychev distance Unsupervised learning: Clustering h mn 21 / 52
32 Clustering algorithms Hierarchical clustering Agglomerative clustering: Illustration with R Euclidean distance: Impact of the choice of the linkage function. Single linkage Complete linkage Average linkage Unsupervised learning: Clustering h mn 22 / 52
33 Clustering algorithms Hierarchical clustering Agglomerative clustering: Illustration with R Chebychev distance: Impact of the choice of the linkage function. Single linkage Complete linkage Average linkage Unsupervised learning: Clustering h mn 23 / 52
34 Clustering algorithms Hierarchical clustering Agglomerative clustering Advantages No apriori information about the number of clusters required; Easy to implement; The obtained results may correspond to meaningful taxonomies. Limitations The algorithm does not enable to undo what was done previously Interpretation of the hierarchy can be complex or even confusing Depending on the type of distance matrix used, the algorithm 1 can be sensitivity to noise and outliers, 2 tends to break large clusters. 3 can hardly handle di erent sized clusters. Unsupervised learning: Clustering h mn 24 / 52
35 Clustering algorithms Hierarchical clustering Agglomerative clustering Advantages No apriori information about the number of clusters required; Easy to implement; The obtained results may correspond to meaningful taxonomies. Limitations The algorithm does not enable to undo what was done previously Interpretation of the hierarchy can be complex or even confusing Depending on the type of distance matrix used, the algorithm 1 can be sensitivity to noise and outliers, 2 tends to break large clusters. 3 can hardly handle di erent sized clusters. Unsupervised learning: Clustering h mn 24 / 52
36 Clustering algorithms Hierarchical clustering Divisive clustering Algorithm The algorithm forms clusters in a updown manner, as follows: 1 Initially, put all objects in one cluster. 2 Among all current clusters, pick the one which satisfies a specified criterion and split it using a specified method. 3 Replace this cluster with the new clusters, formed by splitting the original one. 4 Repeat the steps 2 and 3 until all clusters are singletons or or until certain termination conditions are satisfied. Unsupervised learning: Clustering h mn 25 / 52
37 Clustering algorithms Hierarchical clustering Divisive clustering: Illustration with R Clustering The function diana(x, diss = inherits(x, "dist"), metric = "metric") performs hierarchical divisive clustering a numerical matrix X using a specified distance metric, which must be one of the followings: "euclidean" or "manhattan". Let us consider the following data set X : Unsupervised learning: Clustering h mn 26 / 52
38 Clustering algorithms Hierarchical clustering Divisive clustering: Illustration with R Rscript library(cluster) dc<diana(x, diss=inherits(x, "dist"), metric="euclidean") plot(dc) Divisive clustering using euclidian distance measure. Unsupervised learning: Clustering h mn 27 / 52
39 Clustering algorithms Hierarchical clustering Divisive clustering: Illustration with R Impact of the choice of the distance measure Euclidian distance Manhattan distance Unsupervised learning: Clustering h mn 28 / 52
40 Divisive clustering Clustering algorithms Hierarchical clustering Advantages No apriori information about the number of clusters required; The obtained result may correspond to meaningful taxonomies. Limitations The algorithm does not enable to undo what was done previously; Computational di culties when considering all possible divisions into two groups; Depending on the type of distance matrix used, the algorithm 1 can be sensitivity to noise and outliers 2 tends to break large clusters Unsupervised learning: Clustering h mn 29 / 52
41 Clustering algorithms Partitional clustering Partitional clustering Basic concept Given, k the number of clusters, partitional clustering algorithms construct a partition of a data set into k clusters that optimises the chosen partitioning criterion. Partitionning techniques 1 Global optimal method: Exhaustive enumeration of all partitions (NP hard problem) 2 Heuristic methods: e.g. kmeans clustering Each cluster is represented by its centre kmedoids clustering or PAM (Partition Around Medoids): Each cluster is represented by one of its components Unsupervised learning: Clustering h mn 30 / 52
42 Clustering algorithms Partitional clustering Partitional clustering Basic concept Given, k the number of clusters, partitional clustering algorithms construct a partition of a data set into k clusters that optimises the chosen partitioning criterion. Partitionning techniques 1 Global optimal method: Exhaustive enumeration of all partitions (NP hard problem) 2 Heuristic methods: e.g. kmeans clustering Each cluster is represented by its centre kmedoids clustering or PAM (Partition Around Medoids): Each cluster is represented by one of its components Unsupervised learning: Clustering h mn 30 / 52
43 kmeans clustering Clustering algorithms Partitional clustering Basic concept Given an integer k asetx of n points (n Euclidean space, denoted by k) in a mdimensional X = {x i =(x i1,...,x im ) T 2 R m, i =1,...,n}. Find an assignment of the n points into k disjoint clusters C =(C 1,...,C k ) centered at cluster means µ j (j =1,...,k), based on a certain criteria, e.g. by minimising f (X, C) = kx X C j j=1 i=1 x (j) i µ j 2, where C j is the number of points in the cluster C j,andx (j) i in C j. is the point i Unsupervised learning: Clustering h mn 31 / 52
44 Clustering algorithms Partitional clustering kmeans clustering Algorithm The kmeans clustering algorithm can be summarised as follows: 1 Select k data points randomly in a domain containing all the points in the data set. These k points represent the centres of the initial clusters. 2 Assign each point to the cluster that has the closest centre. 3 Recompute the cluster centers (means) using the current cluster memberships. 4 Repeat the steps 2 and 3 until the centres no longer change, or until certain termination conditions are satisfied. Unsupervised learning: Clustering h mn 32 / 52
45 Clustering algorithms Partitional clustering kmeans clustering: Illustration with R Clustering The function kmeans(x, centers, iter.max = 1000, nstart = 10) performs kmeans clustering given a numerical matrix of data x, the maximum number of iterations, and the number of random initial sets to be chosen when centres is greater than 1. Let us consider the following data set X : Unsupervised learning: Clustering h mn 33 / 52
46 Clustering algorithms Partitional clustering kmean clustering: Illustration with R Rscript library(stats) kc < kmeans(x, centers= 4, iter.max=1000, nstart=10000) kmean clustering using four clusters. Unsupervised learning: Clustering h mn 34 / 52
47 Clustering algorithms Partitional clustering kmean clustering: Illustration with R Impact of the choice of the number of clusters Three clusters Four clusters Unsupervised learning: Clustering h mn 35 / 52
48 Clustering algorithms Partitional clustering kmean clustering: Illustration with R Impact of the choice of the number of clusters Five clusters Six clusters Unsupervised learning: Clustering h mn 36 / 52
49 Clustering algorithms Partitional clustering kmean Clustering: Illustration with R Impact of the choice of the number of clusters Number of clusters vs Within clusters sum of squares. Unsupervised learning: Clustering h mn 37 / 52
50 Clustering algorithms Partitional clustering kmean clustering Advantages Relatively easy to implement. A simple iterative algorithm works quite well in practice. Limitations Need to specify k, the number of clusters, in advance. Applicable only when the mean is defined, hence it can t handle categorical data. Not suitable to discover clusters with nonconvex shapes. Unable to handle noisy data and outliers. Unsupervised learning: Clustering h mn 38 / 52
51 kmedoids clustering Clustering algorithms Partitional clustering Basic concept Given an integer k asetx of n points (n Euclidean space, denoted by k) in a mdimensional X = {x i =(x i1,...,x im ) T 2 R m, i =1,...,n}. Find an assignment of the n points into k disjoint clusters C =(C 1,...,C k ) centered at cluster points m j (j =1,...,k) called medoids, based on a certain criteria, e.g. by minimising f (X, C) = kx X C j j=1 i=1 x (j) i m j, where C j is the number of points in the cluster C j,andx (j) i in C j. is the point i Unsupervised learning: Clustering h mn 39 / 52
52 Clustering algorithms Partitional clustering kmedoids clustering PAM (Partitioning Around Medoids) Algorithm The PAM is a kmedoids clustering algorithm, which is similar to the kmeans algorithm. It can be summarised as follows: 1 Select randomly k data points from the given data set. These k points represent the medoids of the initial clusters. 2 Assign each point to the cluster that has the closest medoid. 3 Iteratively replace one of the medoids by one of the nonmedoids which improve the chosen criterion. 4 Repeat the steps 2 and 3 until the medoids no longer change, or until certain termination conditions are satisfied. Unsupervised learning: Clustering h mn 40 / 52
53 Clustering algorithms Partitional clustering kmedoids clustering PAM Algorithm Advantages: Works e ectively for small data sets Limitations: Does not scale well for large data sets CLARA (Clustering Large Applications) Based on multiple sampling from the data set and application of PAM on each sample, it provides the best clustering as the output. Advantages: Deals with larger data sets than PAM Limitations: E ciency depends on the sample size Unsupervised learning: Clustering h mn 41 / 52
54 Clustering algorithms Partitional clustering kmedoids clustering: Illustration with R CLARA The function clara(x, k, metric = "metric", samples = r) performs CLARA clustering given a numerical matrix of data x, the number of cluster, the distance metric, and the number of samples to be drawn from the data set X. Let us consider the following data set X : Unsupervised learning: Clustering h mn 42 / 52
55 Clustering algorithms Partitional clustering kmedoids clustering: Illustration with R Rscript library(cluster) km < clara(x, k, metric = "euclidean", samples = 10) CLARA clustering using 5 clusters and 10 samples. Unsupervised learning: Clustering h mn 43 / 52
56 Clustering algorithms Partitional clustering kmedoids clustering: Illustration with R CLARA: Impact of the choice of the distance metric Euclidean distance Manhattan distance Unsupervised learning: Clustering h mn 44 / 52
57 Clustering evaluation metrics So... which method to use for the data set X?!!!?? Hierarchical clustering? If yes Agglomerative or Divisive? For either method 1 which metric distance and/or linkage function? 2 where to cut the dendrogram? Partitional clustering? If yes kmeans or CLARA? For either method 1 which metric distance? 2 how many clusters? Unsupervised learning: Clustering h mn 45 / 52
58 Clustering evaluation metrics So... which method to use for the data set X?!!!?? Hierarchical clustering? If yes Agglomerative or Divisive? For either method 1 which metric distance and/or linkage function? 2 where to cut the dendrogram? Partitional clustering? If yes kmeans or CLARA? For either method 1 which metric distance? 2 how many clusters? Unsupervised learning: Clustering h mn 45 / 52
59 Clustering evaluation metrics So... which method to use for the data set X?!!!?? Hierarchical clustering? If yes Agglomerative or Divisive? For either method 1 which metric distance and/or linkage function? 2 where to cut the dendrogram? Partitional clustering? If yes kmeans or CLARA? For either method 1 which metric distance? 2 how many clusters? Unsupervised learning: Clustering h mn 45 / 52
60 Clustering evaluation metrics So... which method to use for the data set X?!!!?? Hierarchical clustering? If yes Agglomerative or Divisive? For either method 1 which metric distance and/or linkage function? 2 where to cut the dendrogram? Partitional clustering? If yes kmeans or CLARA? For either method 1 which metric distance? 2 how many clusters? Unsupervised learning: Clustering h mn 45 / 52
61 Clustering evaluation metrics So... which method to use for the data set X?!!!?? Hierarchical clustering? If yes Agglomerative or Divisive? For either method 1 which metric distance and/or linkage function? 2 where to cut the dendrogram? Partitional clustering? If yes kmeans or CLARA? For either method 1 which metric distance? 2 how many clusters? Unsupervised learning: Clustering h mn 45 / 52
62 Clustering evaluation metrics Clustering evaluation metrics Silhouette Coe cient Provides a graphical representation of how well each object lies within its cluster. The silhouette coe cient of a data point i is defined as s i = (b i a i ) max(a i, b i ), where a i denotes the average distance between the data point i and all other data points in its cluster, and b i denotes the minimum average distance between i and the data points in other clusters. Data points with large silhouette coe cient s i are wellclustered, those with small s i tend to lie between clusters. Unsupervised learning: Clustering h mn 46 / 52
63 Clustering evaluation metrics Clustering evaluation metrics Classificationoriented measures Use of the classification approach to compare clustering techniques with the ground truth. Some of these measures are 1 Entropy 2 Purity 3 Recall 4 F measure Unsupervised learning: Clustering h mn 47 / 52
64 Clustering evaluation metrics Clustering evaluation metrics Entropy Measures the degree to which each cluster consists of data points from a single class. The entropy of a cluster i is given by E i = lx j=1 n ij n i log nij n i, where n ij is the number of data points of class i in cluster j, n i is the number of data points in cluster i and l is the number of classes. The total entropy for a set of clusters is given by E = kx i=1 n i n E i, where k is the number of clusters and n is the total number of data points. Unsupervised learning: Clustering h mn 48 / 52
65 Clustering evaluation metrics Clustering evaluation metrics Purity Measures the extent to which a cluster contains data points of a single class. Using the previous notations, the purity for a cluster i is given by Pur i =max j n ij n i, whereas the overall purity of a clustering is given by Pur = kx i=1 n i n Pur i. Unsupervised learning: Clustering h mn 49 / 52
66 Clustering evaluation metrics Clustering evaluation metrics Precision Measures the fraction of a cluster that consists of objects of a specified class. Using the previous notations, the precision of cluster i with respect to class j is given by Pre(i, j) = n ij n i Recall Measures the extent to which a cluster contains all objects of a specified class. The recall of cluster i with respect to class j is given by Rec(i, j) = n ij n j, where n ij is the number of data points of class i in cluster j and n j is the number of data points in class j. Unsupervised learning: Clustering h mn 50 / 52
67 Clustering evaluation metrics Clustering evaluation metrics F measure It combines the precision and the recall to measure the extent to which a cluster contains only data points of a particular class and all points of that class. The F measure of cluster i with respect to class j is given by F (i, j) = 2Pre(i, j) Rec(i, j) Pre(i, j)+rec(i, j). Unsupervised learning: Clustering h mn 51 / 52
68 End End Thank you for your attention! Unsupervised learning: Clustering h mn 52 / 52
Clustering. Danilo Croce Web Mining & Retrieval a.a. 2015/201 16/03/2016
Clustering Danilo Croce Web Mining & Retrieval a.a. 2015/201 16/03/2016 1 Supervised learning vs. unsupervised learning Supervised learning: discover patterns in the data that relate data attributes with
More informationCluster Analysis. Isabel M. Rodrigues. Lisboa, 2014. Instituto Superior Técnico
Instituto Superior Técnico Lisboa, 2014 Introduction: Cluster analysis What is? Finding groups of objects such that the objects in a group will be similar (or related) to one another and different from
More informationDATA MINING CLUSTER ANALYSIS: BASIC CONCEPTS
DATA MINING CLUSTER ANALYSIS: BASIC CONCEPTS 1 AND ALGORITHMS Chiara Renso KDDLAB ISTI CNR, Pisa, Italy WHAT IS CLUSTER ANALYSIS? Finding groups of objects such that the objects in a group will be similar
More informationNeural Networks Lesson 5  Cluster Analysis
Neural Networks Lesson 5  Cluster Analysis Prof. Michele Scarpiniti INFOCOM Dpt.  Sapienza University of Rome http://ispac.ing.uniroma1.it/scarpiniti/index.htm michele.scarpiniti@uniroma1.it Rome, 29
More informationClustering UE 141 Spring 2013
Clustering UE 141 Spring 013 Jing Gao SUNY Buffalo 1 Definition of Clustering Finding groups of obects such that the obects in a group will be similar (or related) to one another and different from (or
More informationData Mining Clustering (2) Sheets are based on the those provided by Tan, Steinbach, and Kumar. Introduction to Data Mining
Data Mining Clustering (2) Toon Calders Sheets are based on the those provided by Tan, Steinbach, and Kumar. Introduction to Data Mining Outline Partitional Clustering Distancebased Kmeans, Kmedoids,
More informationClustering. Adrian Groza. Department of Computer Science Technical University of ClujNapoca
Clustering Adrian Groza Department of Computer Science Technical University of ClujNapoca Outline 1 Cluster Analysis What is Datamining? Cluster Analysis 2 Kmeans 3 Hierarchical Clustering What is Datamining?
More informationText Clustering. Clustering
Text Clustering 1 Clustering Partition unlabeled examples into disoint subsets of clusters, such that: Examples within a cluster are very similar Examples in different clusters are very different Discover
More informationChapter 7. Cluster Analysis
Chapter 7. Cluster Analysis. What is Cluster Analysis?. A Categorization of Major Clustering Methods. Partitioning Methods. Hierarchical Methods 5. DensityBased Methods 6. GridBased Methods 7. ModelBased
More informationClustering & Association
Clustering  Overview What is cluster analysis? Grouping data objects based only on information found in the data describing these objects and their relationships Maximize the similarity within objects
More informationCluster Analysis using R
Cluster analysis or clustering is the task of assigning a set of objects into groups (called clusters) so that the objects in the same cluster are more similar (in some sense or another) to each other
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 4/8/2004 Hierarchical
More informationExample: Document Clustering. Clustering: Definition. Notion of a Cluster can be Ambiguous. Types of Clusterings. Hierarchical Clustering
Overview Prognostic Models and Data Mining in Medicine, part I Cluster Analsis What is Cluster Analsis? KMeans Clustering Hierarchical Clustering Cluster Validit Eample: Microarra data analsis 6 Summar
More informationDistance based clustering
// Distance based clustering Chapter ² ² Clustering Clustering is the art of finding groups in data (Kaufman and Rousseeuw, 99). What is a cluster? Group of objects separated from other clusters Means
More informationCluster Analysis: Basic Concepts and Algorithms
Cluster Analsis: Basic Concepts and Algorithms What does it mean clustering? Applications Tpes of clustering Kmeans Intuition Algorithm Choosing initial centroids Bisecting Kmeans Postprocessing Strengths
More informationCLASSIFICATION AND CLUSTERING. Anveshi Charuvaka
CLASSIFICATION AND CLUSTERING Anveshi Charuvaka Learning from Data Classification Regression Clustering Anomaly Detection Contrast Set Mining Classification: Definition Given a collection of records (training
More informationClustering. 15381 Artificial Intelligence Henry Lin. Organizing data into clusters such that there is
Clustering 15381 Artificial Intelligence Henry Lin Modified from excellent slides of Eamonn Keogh, Ziv BarJoseph, and Andrew Moore What is Clustering? Organizing data into clusters such that there is
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 by Tan, Steinbach, Kumar 1 What is Cluster Analysis? Finding groups of objects such that the objects in a group will
More informationL15: statistical clustering
Similarity measures Criterion functions Cluster validity Flat clustering algorithms kmeans ISODATA L15: statistical clustering Hierarchical clustering algorithms Divisive Agglomerative CSCE 666 Pattern
More informationFig. 1 A typical Knowledge Discovery process [2]
Volume 4, Issue 7, July 2014 ISSN: 2277 128X International Journal of Advanced Research in Computer Science and Software Engineering Research Paper Available online at: www.ijarcsse.com A Review on Clustering
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 informationROBERTO BATTITI, MAURO BRUNATO. The LION Way: Machine Learning plus Intelligent Optimization. LIONlab, University of Trento, Italy, Apr 2015
ROBERTO BATTITI, MAURO BRUNATO. The LION Way: Machine Learning plus Intelligent Optimization. LIONlab, University of Trento, Italy, Apr 2015 http://intelligentoptimization.org/lionbook Roberto Battiti
More informationInformation Retrieval and Web Search Engines
Information Retrieval and Web Search Engines Lecture 7: Document Clustering December 10 th, 2013 WolfTilo Balke and Kinda El Maarry Institut für Informationssysteme Technische Universität Braunschweig
More informationSocial Media Mining. Data Mining Essentials
Introduction Data production rate has been increased dramatically (Big Data) and we are able store much more data than before E.g., purchase data, social media data, mobile phone data Businesses and customers
More informationKMeans Cluster Analysis. Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 1
KMeans Cluster Analsis Chapter 3 PPDM Class Tan,Steinbach, Kumar Introduction to Data Mining 4/18/4 1 What is Cluster Analsis? Finding groups of objects such that the objects in a group will be similar
More informationMedical Information Management & Mining. You Chen Jan,15, 2013 You.chen@vanderbilt.edu
Medical Information Management & Mining You Chen Jan,15, 2013 You.chen@vanderbilt.edu 1 Trees Building Materials Trees cannot be used to build a house directly. How can we transform trees to building materials?
More informationChapter ML:XI (continued)
Chapter ML:XI (continued) XI. Cluster Analysis Data Mining Overview Cluster Analysis Basics Hierarchical Cluster Analysis Iterative Cluster Analysis DensityBased Cluster Analysis Cluster Evaluation Constrained
More informationUNSUPERVISED MACHINE LEARNING TECHNIQUES IN GENOMICS
UNSUPERVISED MACHINE LEARNING TECHNIQUES IN GENOMICS Dwijesh C. Mishra I.A.S.R.I., Library Avenue, New Delhi110 012 dcmishra@iasri.res.in What is Learning? "Learning denotes changes in a system that enable
More informationCluster Analysis: Basic Concepts and Methods
10 Cluster Analysis: Basic Concepts and Methods Imagine that you are the Director of Customer Relationships at AllElectronics, and you have five managers working for you. You would like to organize all
More informationStatistical Databases and Registers with some datamining
Unsupervised learning  Statistical Databases and Registers with some datamining a course in Survey Methodology and O cial Statistics Pages in the book: 501528 Department of Statistics Stockholm University
More informationDistances, Clustering, and Classification. Heatmaps
Distances, Clustering, and Classification Heatmaps 1 Distance Clustering organizes things that are close into groups What does it mean for two genes to be close? What does it mean for two samples to be
More informationData Mining Project Report. Document Clustering. Meryem UzunPer
Data Mining Project Report Document Clustering Meryem UzunPer 504112506 Table of Content Table of Content... 2 1. Project Definition... 3 2. Literature Survey... 3 3. Methods... 4 3.1. Kmeans algorithm...
More information10810 /02710 Computational Genomics. Clustering expression data
10810 /02710 Computational Genomics Clustering expression data What is Clustering? Organizing data into clusters such that there is high intracluster similarity low intercluster similarity Informally,
More informationLecture 20: Clustering
Lecture 20: Clustering Wrapup of neural nets (from last lecture Introduction to unsupervised learning Kmeans clustering COMP424, Lecture 20  April 3, 2013 1 Unsupervised learning In supervised learning,
More informationClustering. Data Mining. Abraham Otero. Data Mining. Agenda
Clustering 1/46 Agenda Introduction Distance Knearest neighbors Hierarchical clustering Quick reference 2/46 1 Introduction It seems logical that in a new situation we should act in a similar way as in
More informationAn Introduction to Cluster Analysis for Data Mining
An Introduction to Cluster Analysis for Data Mining 10/02/2000 11:42 AM 1. INTRODUCTION... 4 1.1. Scope of This Paper... 4 1.2. What Cluster Analysis Is... 4 1.3. What Cluster Analysis Is Not... 5 2. OVERVIEW...
More informationCluster Analysis: Basic Concepts and Algorithms
8 Cluster Analysis: Basic Concepts and Algorithms Cluster analysis divides data into groups (clusters) that are meaningful, useful, or both. If meaningful groups are the goal, then the clusters should
More informationData Mining Cluster Analysis: Basic Concepts and Algorithms. Clustering Algorithms. Lecture Notes for Chapter 8. Introduction to Data Mining
Data Mining Cluster Analsis: Basic Concepts and Algorithms Lecture Notes for Chapter 8 Introduction to Data Mining b Tan, Steinbach, Kumar Clustering Algorithms Kmeans and its variants Hierarchical clustering
More informationData Clustering. Dec 2nd, 2013 Kyrylo Bessonov
Data Clustering Dec 2nd, 2013 Kyrylo Bessonov Talk outline Introduction to clustering Types of clustering Supervised Unsupervised Similarity measures Main clustering algorithms kmeans Hierarchical Main
More informationData Mining Clustering. Sheets are based on the those provided by Tan, Steinbach, and Kumar. Introduction to Data Mining
Data Mining Clustering Toon Calders Sheets are based on the those provided b Tan, Steinbach, and Kumar. Introduction to Data Mining What is Cluster Analsis? Finding groups of objects such that the objects
More informationMachine Learning using MapReduce
Machine Learning using MapReduce What is Machine Learning Machine learning is a subfield of artificial intelligence concerned with techniques that allow computers to improve their outputs based on previous
More informationUnsupervised Learning and Data Mining. Unsupervised Learning and Data Mining. Clustering. Supervised Learning. Supervised Learning
Unsupervised Learning and Data Mining Unsupervised Learning and Data Mining Clustering Decision trees Artificial neural nets Knearest neighbor Support vectors Linear regression Logistic regression...
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 4/8/4 What is
More informationARTIFICIAL INTELLIGENCE (CSCU9YE) LECTURE 6: MACHINE LEARNING 2: UNSUPERVISED LEARNING (CLUSTERING)
ARTIFICIAL INTELLIGENCE (CSCU9YE) LECTURE 6: MACHINE LEARNING 2: UNSUPERVISED LEARNING (CLUSTERING) Gabriela Ochoa http://www.cs.stir.ac.uk/~goc/ OUTLINE Preliminaries Classification and Clustering Applications
More informationCluster Algorithms. Adriano Cruz adriano@nce.ufrj.br. 28 de outubro de 2013
Cluster Algorithms Adriano Cruz adriano@nce.ufrj.br 28 de outubro de 2013 Adriano Cruz adriano@nce.ufrj.br () Cluster Algorithms 28 de outubro de 2013 1 / 80 Summary 1 KMeans Adriano Cruz adriano@nce.ufrj.br
More informationThere are a number of different methods that can be used to carry out a cluster analysis; these methods can be classified as follows:
Statistics: Rosie Cornish. 2007. 3.1 Cluster Analysis 1 Introduction This handout is designed to provide only a brief introduction to cluster analysis and how it is done. Books giving further details are
More informationRobotics 2 Clustering & EM. Giorgio Grisetti, Cyrill Stachniss, Kai Arras, Maren Bennewitz, Wolfram Burgard
Robotics 2 Clustering & EM Giorgio Grisetti, Cyrill Stachniss, Kai Arras, Maren Bennewitz, Wolfram Burgard 1 Clustering (1) Common technique for statistical data analysis to detect structure (machine learning,
More informationCluster analysis Cosmin Lazar. COMO Lab VUB
Cluster analysis Cosmin Lazar COMO Lab VUB Introduction Cluster analysis foundations rely on one of the most fundamental, simple and very often unnoticed ways (or methods) of understanding and learning,
More informationClustering: Techniques & Applications. Nguyen Sinh Hoa, Nguyen Hung Son. 15 lutego 2006 Clustering 1
Clustering: Techniques & Applications Nguyen Sinh Hoa, Nguyen Hung Son 15 lutego 2006 Clustering 1 Agenda Introduction Clustering Methods Applications: Outlier Analysis Gene clustering Summary and Conclusions
More informationComparison and Analysis of Various Clustering Methods in Data mining On Education data set Using the weak tool
Comparison and Analysis of Various Clustering Metho in Data mining On Education data set Using the weak tool Abstract: Data mining is used to find the hidden information pattern and relationship between
More informationFlat Clustering KMeans Algorithm
Flat Clustering KMeans Algorithm 1. Purpose. Clustering algorithms group a set of documents into subsets or clusters. The cluster algorithms goal is to create clusters that are coherent internally, but
More informationMachine Learning and Data Mining. Clustering. (adapted from) Prof. Alexander Ihler
Machine Learning and Data Mining Clustering (adapted from) Prof. Alexander Ihler Unsupervised learning Supervised learning Predict target value ( y ) given features ( x ) Unsupervised learning Understand
More informationClustering Hierarchical clustering and kmean clustering
Clustering Hierarchical clustering and kmean clustering Genome 373 Genomic Informatics Elhanan Borenstein The clustering problem: A quick review partition genes into distinct sets with high homogeneity
More informationData Mining. Cluster Analysis: Advanced Concepts and Algorithms
Data Mining Cluster Analysis: Advanced Concepts and Algorithms Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 1 More Clustering Methods Prototypebased clustering Densitybased clustering Graphbased
More informationSummary Data Mining & Process Mining (1BM46) Content. Made by S.P.T. Ariesen
Summary Data Mining & Process Mining (1BM46) Made by S.P.T. Ariesen Content Data Mining part... 2 Lecture 1... 2 Lecture 2:... 4 Lecture 3... 7 Lecture 4... 9 Process mining part... 13 Lecture 5... 13
More informationClustering and Data Mining in R
Clustering and Data Mining in R Workshop Supplement Thomas Girke December 10, 2011 Introduction Data Preprocessing Data Transformations Distance Methods Cluster Linkage Hierarchical Clustering Approaches
More informationClustering Techniques: A Brief Survey of Different Clustering Algorithms
Clustering Techniques: A Brief Survey of Different Clustering Algorithms Deepti Sisodia Technocrates Institute of Technology, Bhopal, India Lokesh Singh Technocrates Institute of Technology, Bhopal, India
More information. Learn the number of classes and the structure of each class using similarity between unlabeled training patterns
Outline Part 1: of data clustering NonSupervised Learning and Clustering : Problem formulation cluster analysis : Taxonomies of Clustering Techniques : Data types and Proximity Measures : Difficulties
More informationCluster Analysis: Advanced Concepts
Cluster Analysis: Advanced Concepts and dalgorithms Dr. Hui Xiong Rutgers University Introduction to Data Mining 08/06/2006 1 Introduction to Data Mining 08/06/2006 1 Outline Prototypebased Fuzzy cmeans
More informationAn Enhanced Clustering Algorithm to Analyze Spatial Data
International Journal of Engineering and Technical Research (IJETR) ISSN: 23210869, Volume2, Issue7, July 2014 An Enhanced Clustering Algorithm to Analyze Spatial Data Dr. Mahesh Kumar, Mr. Sachin Yadav
More informationA comparison of various clustering methods and algorithms in data mining
Volume :2, Issue :5, 3236 May 2015 www.allsubjectjournal.com eissn: 23494182 pissn: 23495979 Impact Factor: 3.762 R.Tamilselvi B.Sivasakthi R.Kavitha Assistant Professor A comparison of various clustering
More informationStandardization and Its Effects on KMeans Clustering Algorithm
Research Journal of Applied Sciences, Engineering and Technology 6(7): 3993303, 03 ISSN: 0407459; eissn: 0407467 Maxwell Scientific Organization, 03 Submitted: January 3, 03 Accepted: February 5, 03
More informationHierarchical Cluster Analysis Some Basics and Algorithms
Hierarchical Cluster Analysis Some Basics and Algorithms Nethra Sambamoorthi CRMportals Inc., 11 Bartram Road, Englishtown, NJ 07726 (NOTE: Please use always the latest copy of the document. Click on this
More informationSteven M. Ho!and. Department of Geology, University of Georgia, Athens, GA 306022501
CLUSTER ANALYSIS Steven M. Ho!and Department of Geology, University of Georgia, Athens, GA 306022501 January 2006 Introduction Cluster analysis includes a broad suite of techniques designed to find groups
More informationData Clustering Techniques Qualifying Oral Examination Paper
Data Clustering Techniques Qualifying Oral Examination Paper Periklis Andritsos University of Toronto Department of Computer Science periklis@cs.toronto.edu March 11, 2002 1 Introduction During a cholera
More informationSTATISTICA. Clustering Techniques. Case Study: Defining Clusters of Shopping Center Patrons. and
Clustering Techniques and STATISTICA Case Study: Defining Clusters of Shopping Center Patrons STATISTICA Solutions for Business Intelligence, Data Mining, Quality Control, and Webbased Analytics Table
More informationPERFORMANCE ANALYSIS OF CLUSTERING ALGORITHMS IN DATA MINING IN WEKA
PERFORMANCE ANALYSIS OF CLUSTERING ALGORITHMS IN DATA MINING IN WEKA Prakash Singh 1, Aarohi Surya 2 1 Department of Finance, IIM Lucknow, Lucknow, India 2 Department of Computer Science, LNMIIT, Jaipur,
More informationText Analytics. Text Clustering. Ulf Leser
Text Analytics Text Clustering Ulf Leser Content of this Lecture (Text) clustering Cluster quality Clustering algorithms Application Ulf Leser: Text Analytics, Winter Semester 2010/2011 2 Clustering Clustering
More informationTerritorial Analysis for Ratemaking. Philip Begher, Dario Biasini, Filip Branitchev, David Graham, Erik McCracken, Rachel Rogers and Alex Takacs
Territorial Analysis for Ratemaking by Philip Begher, Dario Biasini, Filip Branitchev, David Graham, Erik McCracken, Rachel Rogers and Alex Takacs Department of Statistics and Applied Probability University
More informationIntroduction to Statistical Machine Learning
CHAPTER Introduction to Statistical Machine Learning We start with a gentle introduction to statistical machine learning. Readers familiar with machine learning may wish to skip directly to Section 2,
More informationSPECIAL PERTURBATIONS UNCORRELATED TRACK PROCESSING
AAS 07228 SPECIAL PERTURBATIONS UNCORRELATED TRACK PROCESSING INTRODUCTION James G. Miller * Two historical uncorrelated track (UCT) processing approaches have been employed using general perturbations
More informationClustering Very Large Data Sets with Principal Direction Divisive Partitioning
Clustering Very Large Data Sets with Principal Direction Divisive Partitioning David Littau 1 and Daniel Boley 2 1 University of Minnesota, Minneapolis MN 55455 littau@cs.umn.edu 2 University of Minnesota,
More informationEM Clustering Approach for MultiDimensional Analysis of Big Data Set
EM Clustering Approach for MultiDimensional Analysis of Big Data Set Amhmed A. Bhih School of Electrical and Electronic Engineering Princy Johnson School of Electrical and Electronic Engineering Martin
More informationComputational Complexity between KMeans and KMedoids Clustering Algorithms for Normal and Uniform Distributions of Data Points
Journal of Computer Science 6 (3): 363368, 2010 ISSN 15493636 2010 Science Publications Computational Complexity between KMeans and KMedoids Clustering Algorithms for Normal and Uniform Distributions
More informationPersonalized Hierarchical Clustering
Personalized Hierarchical Clustering Korinna Bade, Andreas Nürnberger Faculty of Computer Science, OttovonGuerickeUniversity Magdeburg, D39106 Magdeburg, Germany {kbade,nuernb}@iws.cs.unimagdeburg.de
More informationMachine Learning for NLP
Natural Language Processing SoSe 2015 Machine Learning for NLP Dr. Mariana Neves May 4th, 2015 (based on the slides of Dr. Saeedeh Momtazi) Introduction Field of study that gives computers the ability
More informationData Mining for Knowledge Management. Clustering
Data Mining for Knowledge Management Clustering Themis Palpanas University of Trento http://disi.unitn.eu/~themis Data Mining for Knowledge Management Thanks for slides to: Jiawei Han Eamonn Keogh Jeff
More informationIdentification of noisy variables for nonmetric and symbolic data in cluster analysis
Identification of noisy variables for nonmetric and symbolic data in cluster analysis Marek Walesiak and Andrzej Dudek Wroclaw University of Economics, Department of Econometrics and Computer Science,
More informationHESSO Master of Science in Engineering. Clustering. Prof. Laura Elena Raileanu HESSO YverdonlesBains (HEIGVD)
HESSO Master of Science in Engineering Clustering Prof. Laura Elena Raileanu HESSO YverdonlesBains (HEIGVD) Plan Motivation Hierarchical Clustering KMeans Clustering 2 Problem Setup Arrange items
More informationCluster Analysis. Alison Merikangas Data Analysis Seminar 18 November 2009
Cluster Analysis Alison Merikangas Data Analysis Seminar 18 November 2009 Overview What is cluster analysis? Types of cluster Distance functions Clustering methods Agglomerative Kmeans Densitybased Interpretation
More informationClustering in Machine Learning. By: Ibrar Hussain Student ID:
Clustering in Machine Learning By: Ibrar Hussain Student ID: 11021083 Presentation An Overview Introduction Definition Types of Learning Clustering in Machine Learning Kmeans Clustering Example of kmeans
More informationData Mining 資 料 探 勘. 分 群 分 析 (Cluster Analysis)
Data Mining 資 料 探 勘 Tamkang University 分 群 分 析 (Cluster Analysis) DM MI Wed,, (: :) (B) MinYuh Day 戴 敏 育 Assistant Professor 專 任 助 理 教 授 Dept. of Information Management, Tamkang University 淡 江 大 學 資
More informationData visualization and clustering. Genomics is to no small extend a data science
Data visualization and clustering Genomics is to no small extend a data science [www.data2discovery.org] Data visualization and clustering Genomics is to no small extend a data science [Andersson et al.,
More informationProtein Protein Interaction Networks
Functional Pattern Mining from Genome Scale Protein Protein Interaction Networks YoungRae Cho, Ph.D. Assistant Professor Department of Computer Science Baylor University it My Definition of Bioinformatics
More informationVector Quantization and Clustering
Vector Quantization and Clustering Introduction Kmeans clustering Clustering issues Hierarchical clustering Divisive (topdown) clustering Agglomerative (bottomup) clustering Applications to speech recognition
More informationA Survey of Clustering Techniques
A Survey of Clustering Techniques Pradeep Rai Asst. Prof., CSE Department, Kanpur Institute of Technology, Kanpur0800 (India) Shubha Singh Asst. Prof., MCA Department, Kanpur Institute of Technology,
More informationSoSe 2014: MTANI: Big Data Analytics
SoSe 2014: MTANI: Big Data Analytics Lecture 4 21/05/2014 Sead Izberovic Dr. Nikolaos Korfiatis Agenda Recap from the previous session Clustering Introduction Distance mesures Hierarchical Clustering
More informationOn Clustering Validation Techniques
Journal of Intelligent Information Systems, 17:2/3, 107 145, 2001 c 2001 Kluwer Academic Publishers. Manufactured in The Netherlands. On Clustering Validation Techniques MARIA HALKIDI mhalk@aueb.gr YANNIS
More informationData Mining Essentials
This chapter is from Social Media Mining: An Introduction. By Reza Zafarani, Mohammad Ali Abbasi, and Huan Liu. Cambridge University Press, 2014. Draft version: April 20, 2014. Complete Draft and Slides
More informationUsing Data Mining for Mobile Communication Clustering and Characterization
Using Data Mining for Mobile Communication Clustering and Characterization A. Bascacov *, C. Cernazanu ** and M. Marcu ** * Lasting Software, Timisoara, Romania ** Politehnica University of Timisoara/Computer
More informationChapter 4 Data Mining A Short Introduction
Chapter 4 Data Mining A Short Introduction Data Mining  1 1 Today's Question 1. Data Mining Overview 2. Association Rule Mining 3. Clustering 4. Classification Data Mining  2 2 3. Clustering  Descriptive
More informationData Mining and Knowledge Discovery in Databases (KDD) State of the Art. Prof. Dr. T. Nouri Computer Science Department FHNW Switzerland
Data Mining and Knowledge Discovery in Databases (KDD) State of the Art Prof. Dr. T. Nouri Computer Science Department FHNW Switzerland 1 Conference overview 1. Overview of KDD and data mining 2. Data
More informationUSING THE AGGLOMERATIVE METHOD OF HIERARCHICAL CLUSTERING AS A DATA MINING TOOL IN CAPITAL MARKET 1. Vera Marinova Boncheva
382 [7] Reznik, A, Kussul, N., Sokolov, A.: Identification of user activity using neural networks. Cybernetics and computer techniques, vol. 123 (1999) 70 79. (in Russian) [8] Kussul, N., et al. : MultiAgent
More informationChapter 20: Data Analysis
Chapter 20: Data Analysis Database System Concepts, 6 th Ed. See www.dbbook.com for conditions on reuse Chapter 20: Data Analysis Decision Support Systems Data Warehousing Data Mining Classification
More informationData Mining KClustering Problem
Data Mining KClustering Problem Elham Karoussi Supervisor Associate Professor Noureddine Bouhmala This Master s Thesis is carried out as a part of the education at the University of Agder and is therefore
More informationA Method for Decentralized Clustering in Large MultiAgent Systems
A Method for Decentralized Clustering in Large MultiAgent Systems Elth Ogston, Benno Overeinder, Maarten van Steen, and Frances Brazier Department of Computer Science, Vrije Universiteit Amsterdam {elth,bjo,steen,frances}@cs.vu.nl
More informationWhat is Cluster Analysis?
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 a set of data objects
More informationChapter 4 Data Mining A Short Introduction. 2006/7, Karl Aberer, EPFLIC, Laboratoire de systèmes d'informations répartis Data Mining  1
Chapter 4 Data Mining A Short Introduction 2006/7, Karl Aberer, EPFLIC, Laboratoire de systèmes d'informations répartis Data Mining  1 1 Today's Question 1. Data Mining Overview 2. Association Rule Mining
More informationData Mining 5. Cluster Analysis
Data Mining 5. Cluster Analysis 5.2 Fall 2009 Instructor: Dr. Masoud Yaghini Outline Data Structures IntervalValued (Numeric) Variables Binary Variables Categorical Variables Ordinal Variables Variables
More informationClustering Connectionist and Statistical Language Processing
Clustering Connectionist and Statistical Language Processing Frank Keller keller@coli.unisb.de Computerlinguistik Universität des Saarlandes Clustering p.1/21 Overview clustering vs. classification supervised
More information