Unsupervised Learning

Size: px
Start display at page:

Download "Unsupervised Learning"

Transcription

1 Unsupervised Learning

2 Unsupervised learning Until now, we have assumed our training samples are labeled by their category membership. Methods that use labeled samples are said to be supervised. However, there are problems where the definition of the classes and even the number of the classes may be unknown. Machine learning methods which deal with such data are said to be unsupervised. Questions: Why would one even be interested in learning from unlabeled samples? Is it even possible in principle to learn anything of value from unlabeled samples?

3 Why unsupervised learning (in random order) 1. To limit the cost of the often surprisingly costly process of collecting and labeling a large set of sample patterns. E.g., videos are virtually free, but accurately labeling the video pixels is expensive and time consuming. 2. To obtain a larger training set than the one available using semi-supervised learning. Train a classifier on a small set of samples, then tune it up to make it run without supervision on a large, unlabeled set. Or, in the reverse direction, let a large set of unlabeled data group automatically, then label the groupings found. 3. To detect a gradual change of patterns over time. 4. To find features that will be useful for categorization. 5. To gain insight into the nature or structure of the data during the early stages of an investigation.

4 Unsupervised learning: clustering In practice, unsupervised learning methods implement what is usually referred to as data clustering. Qualitatively and generally, the problem of data clustering can be defined as: Grouping of objects into meaningful categories Given a representation of N objects, find k clusters based on a similarity measure.

5 Data clustering The problem can be tackled from several points of view: Statistics: represent the density function for all data as the mixture of a number of different distributions S i w i p y wi (y w i ) and fit a set of weights w i and component densities p y wi to the given data

6 Data clustering The problem can be tackled from several points of view: Geometry/topology : Partition the pattern space such that data belonging to each partition are highly homogeneous (i.e., they are similar to one another) More directly related with classification: Group (label) data such that average intra-group distance is minimized and average inter-group distance is maximized (yet another optimization problem!)

7 Data clustering Why data clustering? Natural Classification: degree of similarity among species. Data exploration: discover underlying structure, generate hypotheses, detect anomalies. Data Compression: for organizing/indexing/storing/broadcasting data. Applications: useful to any scientific field that collects data! Relevance: 2340 papers about data clustering indexed in Scopus in 2014!

8 Data clustering: examples 800,000 scientific papers clustered into 776 topics based on how often the papers were cited together by the authors of other papers

9 Data clustering Given a set of N unlabeled examples D = (x 1 ; x 2 ; ; x N ) in a d-dimensional feature space, D is partitioned into a number of disjoint subsets Dj 's: D = j=1,k Dj where i j D i D j = where the points in each subset are similar to each other according to a given criterion.

10 Data clustering A partition is denoted by p = (D 1 ;D 2 ;.. ; D k ) and the problem of data clustering is thus formulated as p * = argmin f(p) p where f( ) is formulated according to.

11 Data clustering A general optimization (minimization) algorithm for a classification function J(Y, W) (Y being the dataset and W the ordered set of labels assigned to each sample) can be described as follows: Choose an initial classifier W 0 repeat (step i) Change the classification such that J decreases until the classification is the same as the previous one. If the variables were continuous, a gradient method could be used. However, here, we are dealing with discrete variables.

12 Data clustering A reasonable algorithm (based on the simplifying assumption that the optimization problem is separable, i.e., that the minimum of an n-dimensional function can be found by minimizing it along each dimension separately) would assign to each sample the label that causes the largest (negative) J. NB Since the problem is non-separable, there is no guarantee that J decreases as the sum of J s. It may even increase! A better but slower solution, which guarantees monotonicity, would be to change, in each step, the label that causes the greatest negative J.

13 K-means clustering K-means clustering is developed by choosing the Euclidean distance as the similarity criterion and J = S k=1,nc Sy (i) ~w k y (i) - m k as the function to be optimized. y (i) is the i th sample and m k is the centroid of the k th cluster. y (i) ~w k refers to all samples y (i) assigned to cluster k Then M {m 1, m 2,.., m Nc } is the set of reference vectors, each of which represents the prototype for a class. J is minimized by choosing m k as the sample mean of the data having label w k.

14 Unsupervised learning K-means clustering In practice: The algorithm partitions the input space S into a predefined number of subspaces, induced by the Euclidian distance. Each subspace s i of S is defined as: s i ={x j ϵs d(x j,m i ) = min t d(x j,m t )} This induces a so-called Voronoi tessellation of the input space (example limited to 2D patterns)

15 K-means clustering Randomly initialize m {m 1, m 2, m 3, m 4,..., m Nc } repeat Classify N samples according to nearest m i Recompute m i (as the mean of the patterns assigned to cluster i) until there is no change in m

16

17

18

19

20

21

22

23

24

25 Improving on k-means The main problem with k-means is the need to set a priori the number of desired clusters. A large number of algorithms have been proposed that overcome this limitation, by determining an optimal number of clusters at runtime. The basic idea behind these algorithms is splitting and merging : A cluster is split into two clusters when a measure of homogeneity falls below a certain threshold Two clusters are merged into one when a separation measure falls below a certain threshold

26 Isodata N D = approximate (desired) number of clusters T= threshold for (minimum) number of samples in a cluster Set Nc = N D 1. Cluster data into Nc clusters, eliminating data and clusters with fewer than T members and decreasing Nc accordingly. Exit if classification has not changed, 2. If Nc N D /2 or (Nc < 2 N D and iteration is odd) : a. Split clusters whose samples are sufficiently disjointed and increase Nc accordingly. b. If any clusters have been split go to Merge any pair of clusters whose samples are sufficiently close and/or overlapping and decrease Nc accordingly. 4. Go to step 1.

27 Isodata (cluster computation) 1. Cluster data into Nc clusters, eliminating data and clusters with fewer than T members and decreasing Nc accordingly. Exit if classification has not changed, For each cluster k the following quantities are computed: d k = (1/N k ) S y(i)~wk y (i) - m k avg. distance of samples from the mean (centroid) of cluster k s k 2 = max { (1/N k ) S y(i)~wk (y(i) j - m kj ) 2 } j largest variance along the coordinate axes. d = 1 N Nc k=1 N kd k overall average distance of samples N k = number of samples in cluster k

28 Isodata (split) s s 2 = max. spread threshold for splitting (no splitting below s s2 ) For k = 1,.., Nc If s k 2 > s s 2 If (d k > d and ( N k > 2T + 1 or Nc N D /2 or (Nc < 2 N D and iteration odd) ): split cluster k and increase Nc accordingly. Splitting means replacing the original center with two new centers displaced slightly (usually a fraction of s m ) in opposite directions along the axis m of largest variance.

29 Isodata (merge) D m = maximum distance separation for merging N max = maximum number of clusters that can be merged For i = 1,.., Nc For j = 1,.., Nc i. Compute d ij = m i - m j ii. Sort d ij < D m in ascending order For all sorted d ij, if neither cluster i or j have been merged: While the number of merges < N max Merge clusters i and j and decrease Nc accordingly end while The new center m of the merged cluster is computed as: m = (N i m i + N j m j )/(N i +N j )

Unsupervised Learning

Unsupervised Learning Unsupervised Learning Unsupervised learning Until now, we have assumed our training samples are labeled by their category membership. Methods that use labeled samples are said to be supervised. However,

More information

Unsupervised Learning and Clustering

Unsupervised Learning and Clustering Unsupervised Learning and Clustering Selim Aksoy Department of Computer Engineering Bilkent University saksoy@cs.bilkent.edu.tr CS 551, Spring 2008 CS 551, Spring 2008 c 2008, Selim Aksoy (Bilkent University)

More information

Unsupervised Learning and Clustering

Unsupervised Learning and Clustering Unsupervised Learning and Clustering Selim Aksoy Department of Computer Engineering Bilkent University saksoy@cs.bilkent.edu.tr CS 551, Spring 2009 CS 551, Spring 2009 c 2009, Selim Aksoy (Bilkent University)

More information

Clustering. Mihaela van der Schaar. January 27, Department of Engineering Science University of Oxford

Clustering. Mihaela van der Schaar. January 27, Department of Engineering Science University of Oxford Department of Engineering Science University of Oxford January 27, 2017 Many datasets consist of multiple heterogeneous subsets. Cluster analysis: Given an unlabelled data, want algorithms that automatically

More information

Unsupervised Learning : Clustering

Unsupervised 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 information

Supervised vs. Unsupervised Learning

Supervised vs. Unsupervised Learning Clustering Supervised vs. Unsupervised Learning So far we have assumed that the training samples used to design the classifier were labeled by their class membership (supervised learning) We assume now

More information

INF4820, Algorithms for AI and NLP: Evaluating Classifiers Clustering

INF4820, Algorithms for AI and NLP: Evaluating Classifiers Clustering INF4820, Algorithms for AI and NLP: Evaluating Classifiers Clustering Erik Velldal University of Oslo Sept. 18, 2012 Topics for today 2 Classification Recap Evaluating classifiers Accuracy, precision,

More information

Clustering CS 550: Machine Learning

Clustering CS 550: Machine Learning Clustering CS 550: Machine Learning This slide set mainly uses the slides given in the following links: http://www-users.cs.umn.edu/~kumar/dmbook/ch8.pdf http://www-users.cs.umn.edu/~kumar/dmbook/dmslides/chap8_basic_cluster_analysis.pdf

More information

Based on Raymond J. Mooney s slides

Based on Raymond J. Mooney s slides Instance Based Learning Based on Raymond J. Mooney s slides University of Texas at Austin 1 Example 2 Instance-Based Learning Unlike other learning algorithms, does not involve construction of an explicit

More information

Clustering. Supervised vs. Unsupervised Learning

Clustering. Supervised vs. Unsupervised Learning Clustering Supervised vs. Unsupervised Learning So far we have assumed that the training samples used to design the classifier were labeled by their class membership (supervised learning) We assume now

More information

University of Florida CISE department Gator Engineering. Clustering Part 2

University of Florida CISE department Gator Engineering. Clustering Part 2 Clustering Part 2 Dr. Sanjay Ranka Professor Computer and Information Science and Engineering University of Florida, Gainesville Partitional Clustering Original Points A Partitional Clustering Hierarchical

More information

Clustering and Visualisation of Data

Clustering and Visualisation of Data Clustering and Visualisation of Data Hiroshi Shimodaira January-March 28 Cluster analysis aims to partition a data set into meaningful or useful groups, based on distances between data points. In some

More information

Clustering & Dimensionality Reduction. 273A Intro Machine Learning

Clustering & Dimensionality Reduction. 273A Intro Machine Learning Clustering & Dimensionality Reduction 273A Intro Machine Learning What is Unsupervised Learning? In supervised learning we were given attributes & targets (e.g. class labels). In unsupervised learning

More information

Spectral Classification

Spectral Classification Spectral Classification Spectral Classification Supervised versus Unsupervised Classification n Unsupervised Classes are determined by the computer. Also referred to as clustering n Supervised Classes

More information

Classification. Vladimir Curic. Centre for Image Analysis Swedish University of Agricultural Sciences Uppsala University

Classification. Vladimir Curic. Centre for Image Analysis Swedish University of Agricultural Sciences Uppsala University Classification Vladimir Curic Centre for Image Analysis Swedish University of Agricultural Sciences Uppsala University Outline An overview on classification Basics of classification How to choose appropriate

More information

Accelerating Unique Strategy for Centroid Priming in K-Means Clustering

Accelerating Unique Strategy for Centroid Priming in K-Means Clustering IJIRST International Journal for Innovative Research in Science & Technology Volume 3 Issue 07 December 2016 ISSN (online): 2349-6010 Accelerating Unique Strategy for Centroid Priming in K-Means Clustering

More information

INF4820 Algorithms for AI and NLP. Evaluating Classifiers Clustering

INF4820 Algorithms for AI and NLP. Evaluating Classifiers Clustering INF4820 Algorithms for AI and NLP Evaluating Classifiers Clustering Erik Velldal & Stephan Oepen Language Technology Group (LTG) September 23, 2015 Agenda Last week Supervised vs unsupervised learning.

More information

Classification. Vladimir Curic. Centre for Image Analysis Swedish University of Agricultural Sciences Uppsala University

Classification. Vladimir Curic. Centre for Image Analysis Swedish University of Agricultural Sciences Uppsala University Classification Vladimir Curic Centre for Image Analysis Swedish University of Agricultural Sciences Uppsala University Outline An overview on classification Basics of classification How to choose appropriate

More information

Clustering. CE-717: Machine Learning Sharif University of Technology Spring Soleymani

Clustering. CE-717: Machine Learning Sharif University of Technology Spring Soleymani Clustering CE-717: Machine Learning Sharif University of Technology Spring 2016 Soleymani Outline Clustering Definition Clustering main approaches Partitional (flat) Hierarchical Clustering validation

More information

Cluster Analysis: Agglomerate Hierarchical Clustering

Cluster Analysis: Agglomerate Hierarchical Clustering Cluster Analysis: Agglomerate Hierarchical Clustering Yonghee Lee Department of Statistics, The University of Seoul Oct 29, 2015 Contents 1 Cluster Analysis Introduction Distance matrix Agglomerative Hierarchical

More information

CSE 5243 INTRO. TO DATA MINING

CSE 5243 INTRO. TO DATA MINING CSE 5243 INTRO. TO DATA MINING Cluster Analysis: Basic Concepts and Methods Huan Sun, CSE@The Ohio State University 09/25/2017 Slides adapted from UIUC CS412, Fall 2017, by Prof. Jiawei Han 2 Chapter 10.

More information

CHAPTER 4 K-MEANS AND UCAM CLUSTERING ALGORITHM

CHAPTER 4 K-MEANS AND UCAM CLUSTERING ALGORITHM CHAPTER 4 K-MEANS AND UCAM CLUSTERING 4.1 Introduction ALGORITHM Clustering has been used in a number of applications such as engineering, biology, medicine and data mining. The most popular clustering

More information

Unsupervised Learning. Presenter: Anil Sharma, PhD Scholar, IIIT-Delhi

Unsupervised 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 information

CHAPTER 4: CLUSTER ANALYSIS

CHAPTER 4: CLUSTER ANALYSIS CHAPTER 4: CLUSTER ANALYSIS WHAT IS CLUSTER ANALYSIS? A cluster is a collection of data-objects similar to one another within the same group & dissimilar to the objects in other groups. Cluster analysis

More information

Unsupervised Learning

Unsupervised 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 information

INF4820 Algorithms for AI and NLP. Evaluating Classifiers Clustering

INF4820 Algorithms for AI and NLP. Evaluating Classifiers Clustering INF4820 Algorithms for AI and NLP Evaluating Classifiers Clustering Murhaf Fares & Stephan Oepen Language Technology Group (LTG) September 27, 2017 Today 2 Recap Evaluation of classifiers Unsupervised

More information

Keywords Clustering, Goals of clustering, clustering techniques, clustering algorithms.

Keywords 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 information

A Comparative study of Clustering Algorithms using MapReduce in Hadoop

A Comparative study of Clustering Algorithms using MapReduce in Hadoop A Comparative study of Clustering Algorithms using MapReduce in Hadoop Dweepna Garg 1, Khushboo Trivedi 2, B.B.Panchal 3 1 Department of Computer Science and Engineering, Parul Institute of Engineering

More information

Cluster Analysis. Mu-Chun Su. Department of Computer Science and Information Engineering National Central University 2003/3/11 1

Cluster Analysis. Mu-Chun Su. Department of Computer Science and Information Engineering National Central University 2003/3/11 1 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 information

INF 4300 Classification III Anne Solberg The agenda today:

INF 4300 Classification III Anne Solberg The agenda today: INF 4300 Classification III Anne Solberg 28.10.15 The agenda today: More on estimating classifier accuracy Curse of dimensionality and simple feature selection knn-classification K-means clustering 28.10.15

More information

Gene Clustering & Classification

Gene 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 information

CSE 5243 INTRO. TO DATA MINING

CSE 5243 INTRO. TO DATA MINING CSE 5243 INTRO. TO DATA MINING Cluster Analysis: Basic Concepts and Methods Huan Sun, CSE@The Ohio State University Slides adapted from UIUC CS412, Fall 2017, by Prof. Jiawei Han 2 Chapter 10. Cluster

More information

CSE 158. Web Mining and Recommender Systems. Midterm recap

CSE 158. Web Mining and Recommender Systems. Midterm recap CSE 158 Web Mining and Recommender Systems Midterm recap Midterm on Wednesday! 5:10 pm 6:10 pm Closed book but I ll provide a similar level of basic info as in the last page of previous midterms CSE 158

More information

INF4820. Clustering. Erik Velldal. Nov. 17, University of Oslo. Erik Velldal INF / 22

INF4820. Clustering. Erik Velldal. Nov. 17, University of Oslo. Erik Velldal INF / 22 INF4820 Clustering Erik Velldal University of Oslo Nov. 17, 2009 Erik Velldal INF4820 1 / 22 Topics for Today More on unsupervised machine learning for data-driven categorization: clustering. The task

More information

Clustering algorithms

Clustering algorithms Clustering algorithms Machine Learning Hamid Beigy Sharif University of Technology Fall 1393 Hamid Beigy (Sharif University of Technology) Clustering algorithms Fall 1393 1 / 22 Table of contents 1 Supervised

More information

Using Machine Learning to Optimize Storage Systems

Using Machine Learning to Optimize Storage Systems Using Machine Learning to Optimize Storage Systems Dr. Kiran Gunnam 1 Outline 1. Overview 2. Building Flash Models using Logistic Regression. 3. Storage Object classification 4. Storage Allocation recommendation

More information

Machine Learning for OR & FE

Machine Learning for OR & FE Machine Learning for OR & FE Unsupervised Learning: Clustering Martin Haugh Department of Industrial Engineering and Operations Research Columbia University Email: martin.b.haugh@gmail.com (Some material

More information

Semi-Supervised Clustering with Partial Background Information

Semi-Supervised Clustering with Partial Background Information Semi-Supervised Clustering with Partial Background Information Jing Gao Pang-Ning Tan Haibin Cheng Abstract Incorporating background knowledge into unsupervised clustering algorithms has been the subject

More information

Lesson 3. Prof. Enza Messina

Lesson 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 information

Data Mining. Dr. Raed Ibraheem Hamed. University of Human Development, College of Science and Technology Department of Computer Science

Data Mining. Dr. Raed Ibraheem Hamed. University of Human Development, College of Science and Technology Department of Computer Science Data Mining Dr. Raed Ibraheem Hamed University of Human Development, College of Science and Technology Department of Computer Science 2016 201 Road map What is Cluster Analysis? Characteristics of Clustering

More information

Cluster Analysis. Ying Shen, SSE, Tongji University

Cluster Analysis. Ying Shen, SSE, Tongji University Cluster Analysis Ying Shen, SSE, Tongji University Cluster analysis Cluster analysis groups data objects based only on the attributes in the data. The main objective is that The objects within a group

More information

Data Mining Chapter 9: Descriptive Modeling Fall 2011 Ming Li Department of Computer Science and Technology Nanjing University

Data Mining Chapter 9: Descriptive Modeling Fall 2011 Ming Li Department of Computer Science and Technology Nanjing University Data Mining Chapter 9: Descriptive Modeling Fall 2011 Ming Li Department of Computer Science and Technology Nanjing University Descriptive model A descriptive model presents the main features of the data

More information

Introduction to Artificial Intelligence

Introduction to Artificial Intelligence Introduction to Artificial Intelligence COMP307 Machine Learning 2: 3-K Techniques Yi Mei yi.mei@ecs.vuw.ac.nz 1 Outline K-Nearest Neighbour method Classification (Supervised learning) Basic NN (1-NN)

More information

10701 Machine Learning. Clustering

10701 Machine Learning. Clustering 171 Machine Learning Clustering What is Clustering? Organizing data into clusters such that there is high intra-cluster similarity low inter-cluster similarity Informally, finding natural groupings among

More information

Machine Learning for Signal Processing Clustering. Bhiksha Raj Class Oct 2016

Machine Learning for Signal Processing Clustering. Bhiksha Raj Class Oct 2016 Machine Learning for Signal Processing Clustering Bhiksha Raj Class 11. 13 Oct 2016 1 Statistical Modelling and Latent Structure Much of statistical modelling attempts to identify latent structure in the

More information

Unsupervised Data Mining: Clustering. Izabela Moise, Evangelos Pournaras, Dirk Helbing

Unsupervised Data Mining: Clustering. Izabela Moise, Evangelos Pournaras, Dirk Helbing Unsupervised Data Mining: Clustering Izabela Moise, Evangelos Pournaras, Dirk Helbing Izabela Moise, Evangelos Pournaras, Dirk Helbing 1 1. Supervised Data Mining Classification Regression Outlier detection

More information

ECLT 5810 Clustering

ECLT 5810 Clustering ECLT 5810 Clustering What is Cluster Analysis? Cluster: a collection of data objects Similar to one another within the same cluster Dissimilar to the objects in other clusters Cluster analysis Grouping

More information

Olmo S. Zavala Romero. Clustering Hierarchical Distance Group Dist. K-means. Center of Atmospheric Sciences, UNAM.

Olmo S. Zavala Romero. Clustering Hierarchical Distance Group Dist. K-means. Center of Atmospheric Sciences, UNAM. Center of Atmospheric Sciences, UNAM November 16, 2016 Cluster Analisis Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster)

More information

BBS654 Data Mining. Pinar Duygulu. Slides are adapted from Nazli Ikizler

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 information

ECLT 5810 Clustering

ECLT 5810 Clustering ECLT 5810 Clustering What is Cluster Analysis? Cluster: a collection of data objects Similar to one another within the same cluster Dissimilar to the objects in other clusters Cluster analysis Grouping

More information

Behavioral Data Mining. Lecture 18 Clustering

Behavioral Data Mining. Lecture 18 Clustering Behavioral Data Mining Lecture 18 Clustering Outline Why? Cluster quality K-means Spectral clustering Generative Models Rationale Given a set {X i } for i = 1,,n, a clustering is a partition of the X i

More information

K-Means Clustering 3/3/17

K-Means Clustering 3/3/17 K-Means Clustering 3/3/17 Unsupervised Learning We have a collection of unlabeled data points. We want to find underlying structure in the data. Examples: Identify groups of similar data points. Clustering

More information

SYDE Winter 2011 Introduction to Pattern Recognition. Clustering

SYDE Winter 2011 Introduction to Pattern Recognition. Clustering SYDE 372 - Winter 2011 Introduction to Pattern Recognition Clustering Alexander Wong Department of Systems Design Engineering University of Waterloo Outline 1 2 3 4 5 All the approaches we have learned

More information

Data Informatics. Seon Ho Kim, Ph.D.

Data Informatics. Seon Ho Kim, Ph.D. Data Informatics Seon Ho Kim, Ph.D. seonkim@usc.edu Clustering Overview Supervised vs. Unsupervised Learning Supervised learning (classification) Supervision: The training data (observations, measurements,

More information

Clustering. SC4/SM4 Data Mining and Machine Learning, Hilary Term 2017 Dino Sejdinovic

Clustering. SC4/SM4 Data Mining and Machine Learning, Hilary Term 2017 Dino Sejdinovic Clustering SC4/SM4 Data Mining and Machine Learning, Hilary Term 2017 Dino Sejdinovic Clustering is one of the fundamental and ubiquitous tasks in exploratory data analysis a first intuition about the

More information

Introduction to Machine Learning CMU-10701

Introduction to Machine Learning CMU-10701 Introduction to Machine Learning CMU-10701 Clustering and EM Barnabás Póczos & Aarti Singh Contents Clustering K-means Mixture of Gaussians Expectation Maximization Variational Methods 2 Clustering 3 K-

More information

COMS 4771 Clustering. Nakul Verma

COMS 4771 Clustering. Nakul Verma COMS 4771 Clustering Nakul Verma Supervised Learning Data: Supervised learning Assumption: there is a (relatively simple) function such that for most i Learning task: given n examples from the data, find

More information

Chapter DM:II. II. Cluster Analysis

Chapter 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 information

Machine Learning. Unsupervised Learning. Manfred Huber

Machine Learning. Unsupervised Learning. Manfred Huber Machine Learning Unsupervised Learning Manfred Huber 2015 1 Unsupervised Learning In supervised learning the training data provides desired target output for learning In unsupervised learning the training

More information

Association Rule Mining and Clustering

Association Rule Mining and Clustering Association Rule Mining and Clustering Lecture Outline: Classification vs. Association Rule Mining vs. Clustering Association Rule Mining Clustering Types of Clusters Clustering Algorithms Hierarchical:

More information

Network Traffic Measurements and Analysis

Network Traffic Measurements and Analysis DEIB - Politecnico di Milano Fall, 2017 Introduction Often, we have only a set of features x = x 1, x 2,, x n, but no associated response y. Therefore we are not interested in prediction nor classification,

More information

Clustering & Classification (chapter 15)

Clustering & Classification (chapter 15) Clustering & Classification (chapter 5) Kai Goebel Bill Cheetham RPI/GE Global Research goebel@cs.rpi.edu cheetham@cs.rpi.edu Outline k-means Fuzzy c-means Mountain Clustering knn Fuzzy knn Hierarchical

More information

What to come. There will be a few more topics we will cover on supervised learning

What to come. There will be a few more topics we will cover on supervised learning Summary so far Supervised learning learn to predict Continuous target regression; Categorical target classification Linear Regression Classification Discriminative models Perceptron (linear) Logistic regression

More information

CLASSIFICATION WITH RADIAL BASIS AND PROBABILISTIC NEURAL NETWORKS

CLASSIFICATION WITH RADIAL BASIS AND PROBABILISTIC NEURAL NETWORKS CLASSIFICATION WITH RADIAL BASIS AND PROBABILISTIC NEURAL NETWORKS CHAPTER 4 CLASSIFICATION WITH RADIAL BASIS AND PROBABILISTIC NEURAL NETWORKS 4.1 Introduction Optical character recognition is one of

More information

Data clustering & the k-means algorithm

Data clustering & the k-means algorithm April 27, 2016 Why clustering? Unsupervised Learning Underlying structure gain insight into data generate hypotheses detect anomalies identify features Natural classification e.g. biological organisms

More information

Pattern Clustering with Similarity Measures

Pattern Clustering with Similarity Measures Pattern Clustering with Similarity Measures Akula Ratna Babu 1, Miriyala Markandeyulu 2, Bussa V R R Nagarjuna 3 1 Pursuing M.Tech(CSE), Vignan s Lara Institute of Technology and Science, Vadlamudi, Guntur,

More information

Unsupervised Learning: Clustering

Unsupervised Learning: Clustering Unsupervised Learning: Clustering Vibhav Gogate The University of Texas at Dallas Slides adapted from Carlos Guestrin, Dan Klein & Luke Zettlemoyer Machine Learning Supervised Learning Unsupervised Learning

More information

Improving Cluster Method Quality by Validity Indices

Improving Cluster Method Quality by Validity Indices Improving Cluster Method Quality by Validity Indices N. Hachani and H. Ounalli Faculty of Sciences of Bizerte, Tunisia narjes hachani@yahoo.fr Faculty of Sciences of Tunis, Tunisia habib.ounalli@fst.rnu.tn

More information

Region-based Segmentation

Region-based Segmentation Region-based Segmentation Image Segmentation Group similar components (such as, pixels in an image, image frames in a video) to obtain a compact representation. Applications: Finding tumors, veins, etc.

More information

Unsupervised Learning Partitioning Methods

Unsupervised Learning Partitioning Methods Unsupervised Learning Partitioning Methods Road Map 1. Basic Concepts 2. K-Means 3. K-Medoids 4. CLARA & CLARANS Cluster Analysis Unsupervised learning (i.e., Class label is unknown) Group data to form

More information

Exploratory Analysis: Clustering

Exploratory Analysis: Clustering Exploratory Analysis: Clustering (some material taken or adapted from slides by Hinrich Schutze) Heejun Kim June 26, 2018 Clustering objective Grouping documents or instances into subsets or clusters Documents

More information

Machine Learning in Biology

Machine Learning in Biology Università degli studi di Padova Machine Learning in Biology Luca Silvestrin (Dottorando, XXIII ciclo) Supervised learning Contents Class-conditional probability density Linear and quadratic discriminant

More information

Contents Machine Learning concepts 4 Learning Algorithm 4 Predictive Model (Model) 4 Model, Classification 4 Model, Regression 4 Representation

Contents Machine Learning concepts 4 Learning Algorithm 4 Predictive Model (Model) 4 Model, Classification 4 Model, Regression 4 Representation Contents Machine Learning concepts 4 Learning Algorithm 4 Predictive Model (Model) 4 Model, Classification 4 Model, Regression 4 Representation Learning 4 Supervised Learning 4 Unsupervised Learning 4

More information

Clustering. CS294 Practical Machine Learning Junming Yin 10/09/06

Clustering. CS294 Practical Machine Learning Junming Yin 10/09/06 Clustering CS294 Practical Machine Learning Junming Yin 10/09/06 Outline Introduction Unsupervised learning What is clustering? Application Dissimilarity (similarity) of objects Clustering algorithm K-means,

More information

Clustering. Robert M. Haralick. Computer Science, Graduate Center City University of New York

Clustering. Robert M. Haralick. Computer Science, Graduate Center City University of New York 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 information

10/14/2017. Dejan Sarka. Anomaly Detection. Sponsors

10/14/2017. Dejan Sarka. Anomaly Detection. Sponsors Dejan Sarka Anomaly Detection Sponsors About me SQL Server MVP (17 years) and MCT (20 years) 25 years working with SQL Server Authoring 16 th book Authoring many courses, articles Agenda Introduction Simple

More information

Clustering. Partition unlabeled examples into disjoint subsets of clusters, such that:

Clustering. Partition unlabeled examples into disjoint subsets of clusters, such that: Text Clustering 1 Clustering Partition unlabeled examples into disjoint subsets of clusters, such that: Examples within a cluster are very similar Examples in different clusters are very different Discover

More information

Unsupervised Learning

Unsupervised Learning Networks for Pattern Recognition, 2014 Networks for Single Linkage K-Means Soft DBSCAN PCA Networks for Kohonen Maps Linear Vector Quantization Networks for Problems/Approaches in Machine Learning Supervised

More information

CHAPTER 3 A FAST K-MODES CLUSTERING ALGORITHM TO WAREHOUSE VERY LARGE HETEROGENEOUS MEDICAL DATABASES

CHAPTER 3 A FAST K-MODES CLUSTERING ALGORITHM TO WAREHOUSE VERY LARGE HETEROGENEOUS MEDICAL DATABASES 70 CHAPTER 3 A FAST K-MODES CLUSTERING ALGORITHM TO WAREHOUSE VERY LARGE HETEROGENEOUS MEDICAL DATABASES 3.1 INTRODUCTION In medical science, effective tools are essential to categorize and systematically

More information

Fuzzy Segmentation. Chapter Introduction. 4.2 Unsupervised Clustering.

Fuzzy Segmentation. Chapter Introduction. 4.2 Unsupervised Clustering. Chapter 4 Fuzzy Segmentation 4. Introduction. The segmentation of objects whose color-composition is not common represents a difficult task, due to the illumination and the appropriate threshold selection

More information

10601 Machine Learning. Hierarchical clustering. Reading: Bishop: 9-9.2

10601 Machine Learning. Hierarchical clustering. Reading: Bishop: 9-9.2 161 Machine Learning Hierarchical clustering Reading: Bishop: 9-9.2 Second half: Overview Clustering - Hierarchical, semi-supervised learning Graphical models - Bayesian networks, HMMs, Reasoning under

More information

Clustering. Informal goal. General types of clustering. Applications: Clustering in information search and analysis. Example applications in search

Clustering. 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 information

Introduction to Pattern Recognition Part II. Selim Aksoy Bilkent University Department of Computer Engineering

Introduction to Pattern Recognition Part II. Selim Aksoy Bilkent University Department of Computer Engineering Introduction to Pattern Recognition Part II Selim Aksoy Bilkent University Department of Computer Engineering saksoy@cs.bilkent.edu.tr RETINA Pattern Recognition Tutorial, Summer 2005 Overview Statistical

More information

Cluster Analysis. Angela Montanari and Laura Anderlucci

Cluster Analysis. Angela Montanari and Laura Anderlucci Cluster Analysis Angela Montanari and Laura Anderlucci 1 Introduction Clustering a set of n objects into k groups is usually moved by the aim of identifying internally homogenous groups according to a

More information

Lecture-17: Clustering with K-Means (Contd: DT + Random Forest)

Lecture-17: Clustering with K-Means (Contd: DT + Random Forest) Lecture-17: Clustering with K-Means (Contd: DT + Random Forest) Medha Vidyotma April 24, 2018 1 Contd. Random Forest For Example, if there are 50 scholars who take the measurement of the length of the

More information

Computer Vision. Exercise Session 10 Image Categorization

Computer Vision. Exercise Session 10 Image Categorization Computer Vision Exercise Session 10 Image Categorization Object Categorization Task Description Given a small number of training images of a category, recognize a-priori unknown instances of that category

More information

Jarek Szlichta

Jarek Szlichta Jarek Szlichta http://data.science.uoit.ca/ Approximate terminology, though there is some overlap: Data(base) operations Executing specific operations or queries over data Data mining Looking for patterns

More information

High throughput Data Analysis 2. Cluster Analysis

High throughput Data Analysis 2. Cluster Analysis High throughput Data Analysis 2 Cluster Analysis Overview Why clustering? Hierarchical clustering K means clustering Issues with above two Other methods Quality of clustering results Introduction WHY DO

More information

Machine Learning. B. Unsupervised Learning B.1 Cluster Analysis. Lars Schmidt-Thieme, Nicolas Schilling

Machine Learning. B. Unsupervised Learning B.1 Cluster Analysis. Lars Schmidt-Thieme, Nicolas Schilling Machine Learning B. Unsupervised Learning B.1 Cluster Analysis Lars Schmidt-Thieme, Nicolas Schilling Information Systems and Machine Learning Lab (ISMLL) Institute for Computer Science University of Hildesheim,

More information

Mining di Dati Web. Lezione 3 - Clustering and Classification

Mining di Dati Web. Lezione 3 - Clustering and Classification Mining di Dati Web Lezione 3 - Clustering and Classification Introduction Clustering and classification are both learning techniques They learn functions describing data Clustering is also known as Unsupervised

More information

Hard clustering. Each object is assigned to one and only one cluster. Hierarchical clustering is usually hard. Soft (fuzzy) clustering

Hard clustering. Each object is assigned to one and only one cluster. Hierarchical clustering is usually hard. Soft (fuzzy) clustering An unsupervised machine learning problem Grouping a set of objects in such a way that objects in the same group (a cluster) are more similar (in some sense or another) to each other than to those in other

More information

Introduction to Mobile Robotics

Introduction to Mobile Robotics Introduction to Mobile Robotics Clustering Wolfram Burgard Cyrill Stachniss Giorgio Grisetti Maren Bennewitz Christian Plagemann Clustering (1) Common technique for statistical data analysis (machine learning,

More information

K-Means. Oct Youn-Hee Han

K-Means. Oct Youn-Hee Han K-Means Oct. 2015 Youn-Hee Han http://link.koreatech.ac.kr ²K-Means algorithm An unsupervised clustering algorithm K stands for number of clusters. It is typically a user input to the algorithm Some criteria

More information

Clustering Part 4 DBSCAN

Clustering 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 information

6. Dicretization methods 6.1 The purpose of discretization

6. Dicretization methods 6.1 The purpose of discretization 6. Dicretization methods 6.1 The purpose of discretization Often data are given in the form of continuous values. If their number is huge, model building for such data can be difficult. Moreover, many

More information

Understanding Clustering Supervising the unsupervised

Understanding Clustering Supervising the unsupervised Understanding Clustering Supervising the unsupervised Janu Verma IBM T.J. Watson Research Center, New York http://jverma.github.io/ jverma@us.ibm.com @januverma Clustering Grouping together similar data

More information

Clustering algorithms and autoencoders for anomaly detection

Clustering algorithms and autoencoders for anomaly detection Clustering algorithms and autoencoders for anomaly detection Alessia Saggio Lunch Seminars and Journal Clubs Université catholique de Louvain, Belgium 3rd March 2017 a Outline Introduction Clustering algorithms

More information

International Journal of Scientific Research & Engineering Trends Volume 4, Issue 6, Nov-Dec-2018, ISSN (Online): X

International Journal of Scientific Research & Engineering Trends Volume 4, Issue 6, Nov-Dec-2018, ISSN (Online): X Analysis about Classification Techniques on Categorical Data in Data Mining Assistant Professor P. Meena Department of Computer Science Adhiyaman Arts and Science College for Women Uthangarai, Krishnagiri,

More information

CSE 255 Lecture 6. Data Mining and Predictive Analytics. Community Detection

CSE 255 Lecture 6. Data Mining and Predictive Analytics. Community Detection CSE 255 Lecture 6 Data Mining and Predictive Analytics Community Detection Dimensionality reduction Goal: take high-dimensional data, and describe it compactly using a small number of dimensions Assumption:

More information

Data Mining and Data Warehousing Henryk Maciejewski Data Mining Clustering

Data Mining and Data Warehousing Henryk Maciejewski Data Mining Clustering Data Mining and Data Warehousing Henryk Maciejewski Data Mining Clustering Clustering Algorithms Contents K-means Hierarchical algorithms Linkage functions Vector quantization SOM Clustering Formulation

More information