# High-dimensional labeled data analysis with Gabriel graphs

Save this PDF as:

Size: px
Start display at page:

Download "High-dimensional labeled data analysis with Gabriel graphs"

## Transcription

1 High-dimensional labeled data analysis with Gabriel graphs Michaël Aupetit CEA - DAM Département Analyse Surveillance Environnement BP Bruyères-Le-Châtel, France Abstract. We propose the use of the Gabriel graph for the exploratory analysis of potentially high dimensional labeled data. Gabriel graph is a subgraph of the Delaunay triangulation, which connects two data points v i and v j for which there is no other point v k inside the open ball with diameter [v iv j]. If all the Gabriel neighbors of a datum have a different class than its own, this datum is said to be isolated. While if some of its Gabriel neighbors have the same class as its own and some others have not, then this datum is said to be border. Isolated and border data together with Gabriel graph, allow to get informations about the topology of the different classes in the data space. It is complementary with classical and neural projection techniques. 1 Introduction Exploratory data analysis is an important and active field of researches, which has to deal with the exponential growth of high-dimensional data bases in many domains. Here we consider the case of labeled data in potentially high dimensional space, and propose the use of a topological graph to extract some information about the topology of the different classes. Duda et Hart [5] define a class-similarity graph as a graph which connect pairs of centers of gravity of data of different classes, which are closer than a threshold. Another approach proposed by Melnik [10] creatse links between data if all the points sampled on a link are given the same label by a classifier. If the sampling is sufficiently high, the different connected components of the graph represent regions of different classes. We propose the use of a topological graph called Gabriel graph to extract informations about connexity of the different classes from a labeled data set. Gabriel graph [8] is a subgraph of the Delaunay triangulation [7] of the data set. It has been studied in the field of classification, as a way to edit and

2 condense large data sets [12], by keeping only relevant data which take part to the decision boundary of a nearest neighbor classifier. Recently, it has been proposed in [13], that these data which are preserved in the edited data set, and that we call border data hereafter, are similar to support vectors in the context of Support Vector Machines [2], which determine the decision boundary. We define normal, border and isolated data and study their use with Gabriel graphs to reveal the topology of high dimensional labeled data, which is complementary with classical (Principal Component Analysis... ) or neural (Curvilinear Component Analysis [3], Self-Organizing Maps [9]... ) projection techniques. 2 Normal, border and isolated data Considering a set of N data v and a graph G(v,L) with L a set of edges or links between the data. Two data v i and v j are neighbors of each other if l ij = {v i,v j } L. We define different qualities w.r.t. G(v,L) (Figure 1a) : Border: a datum v v for which there is at least one of its neighbors through G, which has not the same class as its own. Isolated: a datum v v for which all the neighbors through the graph G, have a class different from its own. Isolated data are also Border. Normal: a datum v v for which all the neighbors through the graph G, have the same class as its own. In the following, we choose a topological graph G for which the previous definitions have a relevant meaning w.r.t. the topology of the classes in the data space. 3 Voronoï, Delaunay and Gabriel graphs Considering a set v of N data in E, a bounded domain of R D, the Voronoï region V i associated to a datum v i is defined as the region of E which contains all the points for which v i is the closest datum among all the data v [7]. The Delaunay triangulation DT(v) of v is the set of edges drawn between pairs of data whose Voronoï regions share a common boundary [7] (Figure 1b). Although DT would be ideally suited for being the graph G we expect, it has a O(N D 2 ) computing time, making DT construction intractable for highdimensional data spaces. We propose to use the Gabriel graph [8] of v which approximates DT(v) and which takes O(D.N 3 ) time for its computation. The Gabriel graph GG(v) is the set of edges l ij subset of DT(v), for which the open ball with diameter [v i v j ] contains no other data than v i and v j : GG(v) = { l ij v v k v, (v k v i ) 2 +(v k v j ) 2 > (v i v j ) 2} (Figure 1c) The brute force algorithm to compute GG(v) is straight forward from the above definition. A heuristic proposed in [1] may improve noticeably the computing time.

3 (a) (b) (c) Figure 1: (a) from top to bottom: border, isolated and normal data (circle at the center) (classes in gray levels). (b) Voronoï diagram (thin lines) and Delaunay triangulation (bold lines) of the data (circles). (c) Gabriel graph (bold lines) of the data with border and isolated data of class, and border data of class. 4 How to use Gabriel graph Applying the definitions given in section 2 with the Gabriel graph, allows to analyze the topology of the labeled data set (Figure 2). 4.1 Basic insights Border data are data of each class, closest to the class decision boundary than any other data. The identification of a border datum is a warning signal to the expert to pay more attention about its labeling. The middle point of each edge joining two border data of different classes, is a sample of the decision boundary in the sense of the nearest neighbor classifier 1. Hence, by projecting these middle points (e.g. using CCA [3]), we can visualize the decision boundary. Isolated data are subset of border data. Isolated data may reveal either outliers (error in labeling) or overlapping of the classes. The identification of an isolated datum is a warning signal to the expert that its labeling of this datum is probably erroneous because all its neighbors have a different class than its own. Normal data labeling need no particular attention not touching decision boundaries. 4.2 Advanced analysis We propose to prune the original graph G in order to reveal the different connected components w.r.t classes and qualities. All the following constructions hold for any graph G but we focus on Gabriel graph here. 1 Anewdatumnotinv is labeled with the class of the closest datum to it among v

4 G 5 G 2 G 4 G 3 Decision boundary samples Figure 2: Number of nodes x (edges (y) ) in (between) corresponding connected components of G 2 and G 4, are indicated beside nodes (edges) of G 3 and G 5. i) G : Construct the Gabriel graph of v. ii) G 2 : Clear edges in G connecting data pairs of different classes. iii) G 3 : Create the graph G 3 which associates a vertex to each connected components of G 2. If two of these connected components are linked in G, connect the corresponding vertices in G 3.G 3 is the class graph. iv) G 4 : Clear edges in G 2 which connect data pairs of different qualities. v) G 5 : Create the graph G 5 which associates a vertex to each connected components of G 4. If two of these connected components are linked in G, connect the corresponding vertices in G 5.G 5 is the class&quality graph. The drawing of the class graph shows the topology of the classes, the way they are connected or not, and the density of the connections between the different components. Considering the class&quality graph, the same analysis may be done and allows to visualize the number of border and isolated components. 5 Analysis of Iris database The Iris benchmark database [6, 11] is a set of 150 data, with 4 attributes (sepal and petal length and width, of Iris plants) and 3 classes (Iris Setosa (St), Versicolor (Vs) and Virginica (Vg)). There are 50 data of each classes. After a prior normalization of the data, the analysis technique we propose gives the following results (Figure 3): There is no isolated data in any of the classes which each consists of only one connected component (b). Hence, there is no overlapping in the data space despite what suggests 2-dimensional linear projection using PCA

5 (b) (a) (c) (d) Figure 3: Iris data base: (a) Projection onto the two first principal components (St +, Vs O, Vg ). (b) class graph. (c) class&quality graph. (d) Nonlinear projection using CCA [3], of the center of gravity of each G 2 s connected component, and of the decision boundary samples between St and Vs (diamonds), and between Vs and Vg (triangles). (a) or the class-preserving projection presented in [4]. So the decision boundary considering each pair of classes, is homeomorph to a 3-flat. Classes St and Vg are not connected (b) so two different clasiffiers may be considered: one separating St from Vs, and another Vs from Vg (d). There are 68 links between Vs and Vg, while only 8 between St and Vs (c). And there are only 6 border data in St (12% of this class), while 30 in Vs (60%) and 24 in Vg (48%). The same border component (28 data) of Vs is connected to both St and Vg. Moreover, the component of 44 St normal data is connected to St border data with only 19 links. This is the opposite for Vs (20 normal data and 60 links) and Vg (26 normal data and 38 links). All this suggests that St is well clustered having a little part in contact with Vs, while Vs and Vg are more spread along their common boundary. This approach helps us to grasp the topology of the data in the data space, and to detect eventual misleading projections of the data in lower dimensional spaces: it is complementary to classical and neural projection techniques. 6 Conclusion We propose to define the quality of data as isolated, border or normal according to the class of their neighbors on a graph. These qualities together with Gabriel graphs allow to discover the way the different classes are connected, the number of data of different classes which are in contact, to identify outliers

6 allowing to notice data likely to have an erroneous label, to pay more attention to the labeling of data near decision boundaries, and to visualize a sampling of the decision boundary in the sense of the nearest neighbor. This approach is complementary with classical and neural projection techniques. New visualizations tools remain to create to apprehend complex graphs obtained in case of strong overlapping of the classes. We experiment this approach on a large set of 5-dimensional data in the field of sismic events classification. References [1] Bhattacharya, B.K., Poulsen, R.S. & Toussaint, G.T.(1981) Application of Proximity Graphs to Editing Nearest Neighbor Decision Rule. Int. Symp. on Information Theory, SantaMonica. [2] Burges, C.(2002) A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery,2(2): [3] Demartines, P. & Hérault, J. (1997) Curvilinear Component Analysis: a Self- Organising Neural Network for Non-Linear Mapping of Data Sets. IEEE Trans. on Neural Networks,8(1): [4] Dhillon, I.S., Modha, D.S. & Spangler, W.S. (2002) Class Visualization of high-dimensional data with applications Computational Statistics & Data Analysis,41: [5] Duda, R.O., & Hart, P.E. (1973) Pattern Classification ans Scene Analysis. J. Wiley & Sons eds. [6] Fisher, R.A.(1936) The use of multiple measurements in taxonomic problems Annual Eugenics,7(2): [7] Fortune, S. (1992) Voronoï diagrams and Delaunay triangulations. Computing in Euclidean geometry. D.Z. Du, F. Hwang eds, World Scientific, [8] Gabriel, K.R. & Sokal, R.R.(1969) A new statistical approach to geographic variation analysis. Syst. Zoology,18: [9] Kohonen, T. (1997) Exploration of very large databases by self-organizing maps. Proc. of IEEE Int. Conf. on Neural Networks, ICNN 97, 1:PL1-PL6. [10] Melnik, O. (2002) Decision Region Connectivity Analysis: A method for analyzing high-dimensional classifiers. Machine Learning. 48(1-3): [11] Merz, C.J., Murphy, P.M. & Aha, D.W. (1997) UCI repository of machine learning databases. Dept. of Inf. and Comp. Sc., Univ. of California at Irvine, [12] Toussaint, G. (2002) Proximity Graphs for Nearest Neighbor Decision Rules: Recent Progress. Proc. of INTERFACE 2002, 34 th Symp. on Computing and Statistics, Montreal, Canada. [13] Zhang, W., & King, I. (2002) A Study of the Relationship Between Support Vector Machine and Gabriel Graph. Proc. of IEEE Int. Joint Conf. on Neural Networks, IJCNN 2002.

### Visualization of large data sets using MDS combined with LVQ.

Visualization of large data sets using MDS combined with LVQ. Antoine Naud and Włodzisław Duch Department of Informatics, Nicholas Copernicus University, Grudziądzka 5, 87-100 Toruń, Poland. www.phys.uni.torun.pl/kmk

### Data Mining: Exploring Data. Lecture Notes for Chapter 3. Slides by Tan, Steinbach, Kumar adapted by Michael Hahsler

Data Mining: Exploring Data Lecture Notes for Chapter 3 Slides by Tan, Steinbach, Kumar adapted by Michael Hahsler Topics Exploratory Data Analysis Summary Statistics Visualization What is data exploration?

### Visualising Class Distribution on Self-Organising Maps

Visualising Class Distribution on Self-Organising Maps Rudolf Mayer, Taha Abdel Aziz, and Andreas Rauber Institute for Software Technology and Interactive Systems Vienna University of Technology Favoritenstrasse

### Data topology visualization for the Self-Organizing Map

Data topology visualization for the Self-Organizing Map Kadim Taşdemir and Erzsébet Merényi Rice University - Electrical & Computer Engineering 6100 Main Street, Houston, TX, 77005 - USA Abstract. The

### INTERACTIVE DATA EXPLORATION USING MDS MAPPING

INTERACTIVE DATA EXPLORATION USING MDS MAPPING Antoine Naud and Włodzisław Duch 1 Department of Computer Methods Nicolaus Copernicus University ul. Grudziadzka 5, 87-100 Toruń, Poland Abstract: Interactive

### Extracting Fuzzy Rules from Data for Function Approximation and Pattern Classification

Extracting Fuzzy Rules from Data for Function Approximation and Pattern Classification Chapter 9 in Fuzzy Information Engineering: A Guided Tour of Applications, ed. D. Dubois, H. Prade, and R. Yager,

### Analysis Tools and Libraries for BigData

+ Analysis Tools and Libraries for BigData Lecture 02 Abhijit Bendale + Office Hours 2 n Terry Boult (Waiting to Confirm) n Abhijit Bendale (Tue 2:45 to 4:45 pm). Best if you email me in advance, but I

### Solving Geometric Problems with the Rotating Calipers *

Solving Geometric Problems with the Rotating Calipers * Godfried Toussaint School of Computer Science McGill University Montreal, Quebec, Canada ABSTRACT Shamos [1] recently showed that the diameter of

### Methodology for Emulating Self Organizing Maps for Visualization of Large Datasets

Methodology for Emulating Self Organizing Maps for Visualization of Large Datasets Macario O. Cordel II and Arnulfo P. Azcarraga College of Computer Studies *Corresponding Author: macario.cordel@dlsu.edu.ph

### Character Image Patterns as Big Data

22 International Conference on Frontiers in Handwriting Recognition Character Image Patterns as Big Data Seiichi Uchida, Ryosuke Ishida, Akira Yoshida, Wenjie Cai, Yaokai Feng Kyushu University, Fukuoka,

### Data Exploration Data Visualization

Data Exploration Data Visualization What is data exploration? A preliminary exploration of the data to better understand its characteristics. Key motivations of data exploration include Helping to select

### An Analysis on Density Based Clustering of Multi Dimensional Spatial Data

An Analysis on Density Based Clustering of Multi Dimensional Spatial Data K. Mumtaz 1 Assistant Professor, Department of MCA Vivekanandha Institute of Information and Management Studies, Tiruchengode,

### Introduction to Machine Learning Using Python. Vikram Kamath

Introduction to Machine Learning Using Python Vikram Kamath Contents: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Introduction/Definition Where and Why ML is used Types of Learning Supervised Learning Linear Regression

### Iris Sample Data Set. Basic Visualization Techniques: Charts, Graphs and Maps. Summary Statistics. Frequency and Mode

Iris Sample Data Set Basic Visualization Techniques: Charts, Graphs and Maps CS598 Information Visualization Spring 2010 Many of the exploratory data techniques are illustrated with the Iris Plant data

### 8 Visualization of high-dimensional data

8 VISUALIZATION OF HIGH-DIMENSIONAL DATA 55 { plik roadmap8.tex January 24, 2005} 8 Visualization of high-dimensional data 8. Visualization of individual data points using Kohonen s SOM 8.. Typical Kohonen

### ViSOM A Novel Method for Multivariate Data Projection and Structure Visualization

IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 13, NO. 1, JANUARY 2002 237 ViSOM A Novel Method for Multivariate Data Projection and Structure Visualization Hujun Yin Abstract When used for visualization of

### Self Organizing Maps: Fundamentals

Self Organizing Maps: Fundamentals Introduction to Neural Networks : Lecture 16 John A. Bullinaria, 2004 1. What is a Self Organizing Map? 2. Topographic Maps 3. Setting up a Self Organizing Map 4. Kohonen

### Data Mining for Customer Service Support. Senioritis Seminar Presentation Megan Boice Jay Carter Nick Linke KC Tobin

Data Mining for Customer Service Support Senioritis Seminar Presentation Megan Boice Jay Carter Nick Linke KC Tobin Traditional Hotline Services Problem Traditional Customer Service Support (manufacturing)

### PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 4: LINEAR MODELS FOR CLASSIFICATION

PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 4: LINEAR MODELS FOR CLASSIFICATION Introduction In the previous chapter, we explored a class of regression models having particularly simple analytical

### Data Mining Cluster Analysis: Basic Concepts and Algorithms. Lecture Notes for Chapter 8. Introduction to Data Mining

Data Mining Cluster Analysis: Basic Concepts and Algorithms Lecture Notes for Chapter 8 by Tan, Steinbach, Kumar 1 What is Cluster Analysis? Finding groups of objects such that the objects in a group will

### Visualization of textual data: unfolding the Kohonen maps.

Visualization of textual data: unfolding the Kohonen maps. CNRS - GET - ENST 46 rue Barrault, 75013, Paris, France (e-mail: ludovic.lebart@enst.fr) Ludovic Lebart Abstract. The Kohonen self organizing

### The Role of Size Normalization on the Recognition Rate of Handwritten Numerals

The Role of Size Normalization on the Recognition Rate of Handwritten Numerals Chun Lei He, Ping Zhang, Jianxiong Dong, Ching Y. Suen, Tien D. Bui Centre for Pattern Recognition and Machine Intelligence,

### Visualization of Topology Representing Networks

Visualization of Topology Representing Networks Agnes Vathy-Fogarassy 1, Agnes Werner-Stark 1, Balazs Gal 1 and Janos Abonyi 2 1 University of Pannonia, Department of Mathematics and Computing, P.O.Box

### Support Vector Machines with Clustering for Training with Very Large Datasets

Support Vector Machines with Clustering for Training with Very Large Datasets Theodoros Evgeniou Technology Management INSEAD Bd de Constance, Fontainebleau 77300, France theodoros.evgeniou@insead.fr Massimiliano

### COM CO P 5318 Da t Da a t Explora Explor t a ion and Analysis y Chapte Chapt r e 3

COMP 5318 Data Exploration and Analysis Chapter 3 What is data exploration? A preliminary exploration of the data to better understand its characteristics. Key motivations of data exploration include Helping

### International Journal of Computer Science Trends and Technology (IJCST) Volume 2 Issue 3, May-Jun 2014

RESEARCH ARTICLE OPEN ACCESS A Survey of Data Mining: Concepts with Applications and its Future Scope Dr. Zubair Khan 1, Ashish Kumar 2, Sunny Kumar 3 M.Tech Research Scholar 2. Department of Computer

### An Introduction to Data Mining. Big Data World. Related Fields and Disciplines. What is Data Mining? 2/12/2015

An Introduction to Data Mining for Wind Power Management Spring 2015 Big Data World Every minute: Google receives over 4 million search queries Facebook users share almost 2.5 million pieces of content

### Data Mining: Exploring Data. Lecture Notes for Chapter 3. Introduction to Data Mining

Data Mining: Exploring Data Lecture Notes for Chapter 3 Introduction to Data Mining by Tan, Steinbach, Kumar What is data exploration? A preliminary exploration of the data to better understand its characteristics.

### Comparison of Non-linear Dimensionality Reduction Techniques for Classification with Gene Expression Microarray Data

CMPE 59H Comparison of Non-linear Dimensionality Reduction Techniques for Classification with Gene Expression Microarray Data Term Project Report Fatma Güney, Kübra Kalkan 1/15/2013 Keywords: Non-linear

### Determining optimal window size for texture feature extraction methods

IX Spanish Symposium on Pattern Recognition and Image Analysis, Castellon, Spain, May 2001, vol.2, 237-242, ISBN: 84-8021-351-5. Determining optimal window size for texture feature extraction methods Domènec

### Equational Reasoning as a Tool for Data Analysis

AUSTRIAN JOURNAL OF STATISTICS Volume 31 (2002), Number 2&3, 231-239 Equational Reasoning as a Tool for Data Analysis Michael Bulmer University of Queensland, Brisbane, Australia Abstract: A combination

### ACEAT-493 Data Visualization by PCA, LDA, and ICA

ACEAT-493 Data Visualization by PCA, LDA, and ICA Tsun-Yu Yang a, Chaur-Chin Chen a,b a Institute of Information Systems and Applications, National Tsing Hua U., Taiwan b Department of Computer Science,

### A Computational Framework for Exploratory Data Analysis

A Computational Framework for Exploratory Data Analysis Axel Wismüller Depts. of Radiology and Biomedical Engineering, University of Rochester, New York 601 Elmwood Avenue, Rochester, NY 14642-8648, U.S.A.

### Visual analysis of self-organizing maps

488 Nonlinear Analysis: Modelling and Control, 2011, Vol. 16, No. 4, 488 504 Visual analysis of self-organizing maps Pavel Stefanovič, Olga Kurasova Institute of Mathematics and Informatics, Vilnius University

### Graphical Representation of Multivariate Data

Graphical Representation of Multivariate Data One difficulty with multivariate data is their visualization, in particular when p > 3. At the very least, we can construct pairwise scatter plots of variables.

### The Scientific Data Mining Process

Chapter 4 The Scientific Data Mining Process When I use a word, Humpty Dumpty said, in rather a scornful tone, it means just what I choose it to mean neither more nor less. Lewis Carroll [87, p. 214] In

### Connecting Segments for Visual Data Exploration and Interactive Mining of Decision Rules

Journal of Universal Computer Science, vol. 11, no. 11(2005), 1835-1848 submitted: 1/9/05, accepted: 1/10/05, appeared: 28/11/05 J.UCS Connecting Segments for Visual Data Exploration and Interactive Mining

### Face Recognition using SIFT Features

Face Recognition using SIFT Features Mohamed Aly CNS186 Term Project Winter 2006 Abstract Face recognition has many important practical applications, like surveillance and access control.

### Decision Tree Learning on Very Large Data Sets

Decision Tree Learning on Very Large Data Sets Lawrence O. Hall Nitesh Chawla and Kevin W. Bowyer Department of Computer Science and Engineering ENB 8 University of South Florida 4202 E. Fowler Ave. Tampa

### CITY UNIVERSITY OF HONG KONG 香 港 城 市 大 學. Self-Organizing Map: Visualization and Data Handling 自 組 織 神 經 網 絡 : 可 視 化 和 數 據 處 理

CITY UNIVERSITY OF HONG KONG 香 港 城 市 大 學 Self-Organizing Map: Visualization and Data Handling 自 組 織 神 經 網 絡 : 可 視 化 和 數 據 處 理 Submitted to Department of Electronic Engineering 電 子 工 程 學 系 in Partial Fulfillment

### Data Mining using Rule Extraction from Kohonen Self-Organising Maps

Data Mining using Rule Extraction from Kohonen Self-Organising Maps James Malone, Kenneth McGarry, Stefan Wermter and Chris Bowerman School of Computing and Technology, University of Sunderland, St Peters

### Class visualization of high-dimensional data with applications

Computational Statistics & Data Analysis 41 (22) 59 9 www.elsevier.com/locate/csda Class visualization of high-dimensional data with applications Inderjit S. Dhillon a;, Dharmendra S. Modha b, W. Scott

### Neural 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

### 3F3: Signal and Pattern Processing

3F3: Signal and Pattern Processing Lecture 3: Classification Zoubin Ghahramani zoubin@eng.cam.ac.uk Department of Engineering University of Cambridge Lent Term Classification We will represent data by

### Online data visualization using the neural gas network

Online data visualization using the neural gas network Pablo A. Estévez, Cristián J. Figueroa Department of Electrical Engineering, University of Chile, Casilla 412-3, Santiago, Chile Abstract A high-quality

### Visualizing class probability estimators

Visualizing class probability estimators Eibe Frank and Mark Hall Department of Computer Science University of Waikato Hamilton, New Zealand {eibe, mhall}@cs.waikato.ac.nz Abstract. Inducing classifiers

### Example: 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? K-Means Clustering Hierarchical Clustering Cluster Validit Eample: Microarra data analsis 6 Summar

### Data Mining and Visualization

Data Mining and Visualization Jeremy Walton NAG Ltd, Oxford Overview Data mining components Functionality Example application Quality control Visualization Use of 3D Example application Market research

### 1 Introduction. Abstract

Systematic Methods for Multivariate Data Visualization and Numerical Assessment of Class Separability and Overlap in Automated Visual Industrial Quality Control * Andreas Konig, Olaf Bulmahn, and Manfred

### Geometry and Topology from Point Cloud Data

Geometry and Topology from Point Cloud Data Tamal K. Dey Department of Computer Science and Engineering The Ohio State University Dey (2011) Geometry and Topology from Point Cloud Data WALCOM 11 1 / 51

### Face Recognition using Principle Component Analysis

Face Recognition using Principle Component Analysis Kyungnam Kim Department of Computer Science University of Maryland, College Park MD 20742, USA Summary This is the summary of the basic idea about PCA

### Knowledge Discovery from patents using KMX Text Analytics

Knowledge Discovery from patents using KMX Text Analytics Dr. Anton Heijs anton.heijs@treparel.com Treparel Abstract In this white paper we discuss how the KMX technology of Treparel can help searchers

### Cluster 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 Prototype-based Fuzzy c-means

### Load balancing in a heterogeneous computer system by self-organizing Kohonen network

Bull. Nov. Comp. Center, Comp. Science, 25 (2006), 69 74 c 2006 NCC Publisher Load balancing in a heterogeneous computer system by self-organizing Kohonen network Mikhail S. Tarkov, Yakov S. Bezrukov Abstract.

### Data Mining: Exploring Data. Lecture Notes for Chapter 3. Introduction to Data Mining

Data Mining: Exploring Data Lecture Notes for Chapter 3 Introduction to Data Mining by Tan, Steinbach, Kumar Tan,Steinbach, Kumar Introduction to Data Mining 8/05/2005 1 What is data exploration? A preliminary

### Tracking Groups of Pedestrians in Video Sequences

Tracking Groups of Pedestrians in Video Sequences Jorge S. Marques Pedro M. Jorge Arnaldo J. Abrantes J. M. Lemos IST / ISR ISEL / IST ISEL INESC-ID / IST Lisbon, Portugal Lisbon, Portugal Lisbon, Portugal

### Data Mining. Practical Machine Learning Tools and Techniques. Classification, association, clustering, numeric prediction

Data Mining Practical Machine Learning Tools and Techniques Slides for Chapter 2 of Data Mining by I. H. Witten and E. Frank Input: Concepts, instances, attributes Terminology What s a concept? Classification,

### TOWARDS SIMPLE, EASY TO UNDERSTAND, AN INTERACTIVE DECISION TREE ALGORITHM

TOWARDS SIMPLE, EASY TO UNDERSTAND, AN INTERACTIVE DECISION TREE ALGORITHM Thanh-Nghi Do College of Information Technology, Cantho University 1 Ly Tu Trong Street, Ninh Kieu District Cantho City, Vietnam

### TIETS34 Seminar: Data Mining on Biometric identification

TIETS34 Seminar: Data Mining on Biometric identification Youming Zhang Computer Science, School of Information Sciences, 33014 University of Tampere, Finland Youming.Zhang@uta.fi Course Description Content

### Visualization of Breast Cancer Data by SOM Component Planes

International Journal of Science and Technology Volume 3 No. 2, February, 2014 Visualization of Breast Cancer Data by SOM Component Planes P.Venkatesan. 1, M.Mullai 2 1 Department of Statistics,NIRT(Indian

### Data Mining: A Preprocessing Engine

Journal of Computer Science 2 (9): 735-739, 2006 ISSN 1549-3636 2005 Science Publications Data Mining: A Preprocessing Engine Luai Al Shalabi, Zyad Shaaban and Basel Kasasbeh Applied Science University,

### The Role of Visualization in Effective Data Cleaning

The Role of Visualization in Effective Data Cleaning Yu Qian Dept. of Computer Science The University of Texas at Dallas Richardson, TX 75083-0688, USA qianyu@student.utdallas.edu Kang Zhang Dept. of Computer

### Visualization of General Defined Space Data

International Journal of Computer Graphics & Animation (IJCGA) Vol.3, No.4, October 013 Visualization of General Defined Space Data John R Rankin La Trobe University, Australia Abstract A new algorithm

### Traffic Prediction in Wireless Mesh Networks Using Process Mining Algorithms

Traffic Prediction in Wireless Mesh Networks Using Process Mining Algorithms Kirill Krinkin Open Source and Linux lab Saint Petersburg, Russia kirill.krinkin@fruct.org Eugene Kalishenko Saint Petersburg

### Data Mining with R. Decision Trees and Random Forests. Hugh Murrell

Data Mining with R Decision Trees and Random Forests Hugh Murrell reference books These slides are based on a book by Graham Williams: Data Mining with Rattle and R, The Art of Excavating Data for Knowledge

### Visualization of Large Font Databases

Visualization of Large Font Databases Martin Solli and Reiner Lenz Linköping University, Sweden ITN, Campus Norrköping, Linköping University, 60174 Norrköping, Sweden Martin.Solli@itn.liu.se, Reiner.Lenz@itn.liu.se

### Robust Outlier Detection Technique in Data Mining: A Univariate Approach

Robust Outlier Detection Technique in Data Mining: A Univariate Approach Singh Vijendra and Pathak Shivani Faculty of Engineering and Technology Mody Institute of Technology and Science Lakshmangarh, Sikar,

### AMDr (3) Fig. 1 Cluster growth process. Fig. 3 Spread as a function of N with D=1,2,3,4

Statistical Approach to Clustering in Pattern Recognition Yujing Zeng Department of Electrical Engineering & Comp. Science OhioUniversity, Athens, OH 457 USA Abstract-- Clustering is a typical method of

### Data 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 k-means Hierarchical Main

### Visual Data Mining with Pixel-oriented Visualization Techniques

Visual Data Mining with Pixel-oriented Visualization Techniques Mihael Ankerst The Boeing Company P.O. Box 3707 MC 7L-70, Seattle, WA 98124 mihael.ankerst@boeing.com Abstract Pixel-oriented visualization

### Protein Protein Interaction Networks

Functional Pattern Mining from Genome Scale Protein Protein Interaction Networks Young-Rae Cho, Ph.D. Assistant Professor Department of Computer Science Baylor University it My Definition of Bioinformatics

### SCAN: A Structural Clustering Algorithm for Networks

SCAN: A Structural Clustering Algorithm for Networks Xiaowei Xu, Nurcan Yuruk, Zhidan Feng (University of Arkansas at Little Rock) Thomas A. J. Schweiger (Acxiom Corporation) Networks scaling: #edges connected

### Feature vs. Classifier Fusion for Predictive Data Mining a Case Study in Pesticide Classification

Feature vs. Classifier Fusion for Predictive Data Mining a Case Study in Pesticide Classification Henrik Boström School of Humanities and Informatics University of Skövde P.O. Box 408, SE-541 28 Skövde

### Topological Data Analysis Applications to Computer Vision

Topological Data Analysis Applications to Computer Vision Vitaliy Kurlin, http://kurlin.org Microsoft Research Cambridge and Durham University, UK Topological Data Analysis quantifies topological structures

### The Value of Visualization 2

The Value of Visualization 2 G Janacek -0.69 1.11-3.1 4.0 GJJ () Visualization 1 / 21 Parallel coordinates Parallel coordinates is a common way of visualising high-dimensional geometry and analysing multivariate

### CS 2750 Machine Learning. Lecture 1. Machine Learning. http://www.cs.pitt.edu/~milos/courses/cs2750/ CS 2750 Machine Learning.

Lecture Machine Learning Milos Hauskrecht milos@cs.pitt.edu 539 Sennott Square, x5 http://www.cs.pitt.edu/~milos/courses/cs75/ Administration Instructor: Milos Hauskrecht milos@cs.pitt.edu 539 Sennott

### Assessing Data Mining: The State of the Practice

Assessing Data Mining: The State of the Practice 2003 Herbert A. Edelstein Two Crows Corporation 10500 Falls Road Potomac, Maryland 20854 www.twocrows.com (301) 983-3555 Objectives Separate myth from reality

### Data Mining and Neural Networks in Stata

Data Mining and Neural Networks in Stata 2 nd Italian Stata Users Group Meeting Milano, 10 October 2005 Mario Lucchini e Maurizo Pisati Università di Milano-Bicocca mario.lucchini@unimib.it maurizio.pisati@unimib.it

### SPECIAL PERTURBATIONS UNCORRELATED TRACK PROCESSING

AAS 07-228 SPECIAL PERTURBATIONS UNCORRELATED TRACK PROCESSING INTRODUCTION James G. Miller * Two historical uncorrelated track (UCT) processing approaches have been employed using general perturbations

### An Interactive Visualization Tool for the Analysis of Multi-Objective Embedded Systems Design Space Exploration

An Interactive Visualization Tool for the Analysis of Multi-Objective Embedded Systems Design Space Exploration Toktam Taghavi, Andy D. Pimentel Computer Systems Architecture Group, Informatics Institute

### On the Role of Hierarchy for Neural Network Interpretation

On the Role of Hierarchy for Neural Network Interpretation Jurgen Rahmel +, Christian Blum +, Peter Hahn* * University of Kaiserslautern, Centre for Learning Systems and Applications PO Box 3049, 67653

### A fast multi-class SVM learning method for huge databases

www.ijcsi.org 544 A fast multi-class SVM learning method for huge databases Djeffal Abdelhamid 1, Babahenini Mohamed Chaouki 2 and Taleb-Ahmed Abdelmalik 3 1,2 Computer science department, LESIA Laboratory,

### CS 2750 Machine Learning. Lecture 1. Machine Learning. CS 2750 Machine Learning.

Lecture 1 Machine Learning Milos Hauskrecht milos@cs.pitt.edu 539 Sennott Square, x-5 http://www.cs.pitt.edu/~milos/courses/cs75/ Administration Instructor: Milos Hauskrecht milos@cs.pitt.edu 539 Sennott

### Data Mining + Business Intelligence. Integration, Design and Implementation

Data Mining + Business Intelligence Integration, Design and Implementation ABOUT ME Vijay Kotu Data, Business, Technology, Statistics BUSINESS INTELLIGENCE - Result Making data accessible Wider distribution

### Strictly Localized Construction of Planar Bounded-Degree Spanners of Unit Disk Graphs

Strictly Localized Construction of Planar Bounded-Degree Spanners of Unit Disk Graphs Iyad A. Kanj Ljubomir Perković Ge Xia Abstract We describe a new distributed and strictly-localized approach for constructing

### Meta-learning. Synonyms. Definition. Characteristics

Meta-learning Włodzisław Duch, Department of Informatics, Nicolaus Copernicus University, Poland, School of Computer Engineering, Nanyang Technological University, Singapore wduch@is.umk.pl (or search

### USING SELF-ORGANIZING MAPS FOR INFORMATION VISUALIZATION AND KNOWLEDGE DISCOVERY IN COMPLEX GEOSPATIAL DATASETS

USING SELF-ORGANIZING MAPS FOR INFORMATION VISUALIZATION AND KNOWLEDGE DISCOVERY IN COMPLEX GEOSPATIAL DATASETS Koua, E.L. International Institute for Geo-Information Science and Earth Observation (ITC).

### Extend Table Lens for High-Dimensional Data Visualization and Classification Mining

Extend Table Lens for High-Dimensional Data Visualization and Classification Mining CPSC 533c, Information Visualization Course Project, Term 2 2003 Fengdong Du fdu@cs.ubc.ca University of British Columbia

### Clustering. Data Mining. Abraham Otero. Data Mining. Agenda

Clustering 1/46 Agenda Introduction Distance K-nearest 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

### Classification algorithm in Data mining: An Overview

Classification algorithm in Data mining: An Overview S.Neelamegam #1, Dr.E.Ramaraj *2 #1 M.phil Scholar, Department of Computer Science and Engineering, Alagappa University, Karaikudi. *2 Professor, Department

### A Modified K-Means Clustering with a Density-Sensitive Distance Metric

A Modified K-Means Clustering with a Density-Sensitive Distance Metric Ling Wang, Liefeng Bo, Licheng Jiao Institute of Intelligent Information Processing, Xidian University Xi an 710071, China {wliiip,blf0218}@163.com,

### QUANTITATIVE MEASUREMENT OF TEAMWORK IN BALL GAMES USING DOMINANT REGION

QUANTITATIVE MEASUREMENT OF TEAMWORK IN BALL GAMES USING DOMINANT REGION Tsuyoshi TAKI and Jun-ichi HASEGAWA Chukyo University, Japan School of Computer and Cognitive Sciences {taki,hasegawa}@sccs.chukyo-u.ac.jp

### PRACTICAL DATA MINING IN A LARGE UTILITY COMPANY

QÜESTIIÓ, vol. 25, 3, p. 509-520, 2001 PRACTICAL DATA MINING IN A LARGE UTILITY COMPANY GEORGES HÉBRAIL We present in this paper the main applications of data mining techniques at Electricité de France,

### Modelling, Extraction and Description of Intrinsic Cues of High Resolution Satellite Images: Independent Component Analysis based approaches

Modelling, Extraction and Description of Intrinsic Cues of High Resolution Satellite Images: Independent Component Analysis based approaches PhD Thesis by Payam Birjandi Director: Prof. Mihai Datcu Problematic

### Impact of Boolean factorization as preprocessing methods for classification of Boolean data

Impact of Boolean factorization as preprocessing methods for classification of Boolean data Radim Belohlavek, Jan Outrata, Martin Trnecka Data Analysis and Modeling Lab (DAMOL) Dept. Computer Science,

### Chapter 12 Discovering New Knowledge Data Mining

Chapter 12 Discovering New Knowledge Data Mining Becerra-Fernandez, et al. -- Knowledge Management 1/e -- 2004 Prentice Hall Additional material 2007 Dekai Wu Chapter Objectives Introduce the student to

### Information Management course

Università degli Studi di Milano Master Degree in Computer Science Information Management course Teacher: Alberto Ceselli Lecture 01 : 06/10/2015 Practical informations: Teacher: Alberto Ceselli (alberto.ceselli@unimi.it)

### International Journal of Advanced Research in Computer Science and Software Engineering

Volume 2, Issue 9, September 2012 ISSN: 2277 128X International Journal of Advanced Research in Computer Science and Software Engineering Research Paper Available online at: www.ijarcsse.com An Experimental