MINING IMPERFECT DATA with Examples in R and Python Second Edition

Total Page:16

File Type:pdf, Size:1020Kb

MINING IMPERFECT DATA with Examples in R and Python Second Edition MINING IMPERFECT DATA With Examples in R and Python Second Edition MN04_PEARSON_FM_V3.indd 1 6/30/2020 2:37:27 PM • MATHEMATICS IN INDUSTRY • Editor-in-Chief Thomas A. Grandine, Boeing Company Editorial Board Douglas N. Arnold, University of Minnesota Amr El-Bakry, ExxonMobil Michael Epton, Boeing Company Susan E. Minkoff, University of Texas at Dallas Jeff Sachs, Merck Clayton Webster, Oak Ridge National Laboratory Series Volumes Eldad Haber, Computational Methods in Geophysical Electromagnetics Lyn Thomas, Jonathan Crook, David Edelman, Credit Scoring and Its Applications, Second Edition Luis Tenorio, An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems Ronald K. Pearson, Mining Imperfect Data: With Examples in R and Python, Second Edition MN04_PEARSON_FM_V3.indd 2 6/30/2020 2:37:27 PM MINING IMPERFECT DATA With Examples in R and Python Second Edition RONALD K. PEARSON GeoVera Holdings, Inc. Fairfield, California Society for Industrial and Applied Mathematics Philadelphia MN04_PEARSON_FM_V3.indd 3 6/30/2020 2:37:28 PM Copyright © 2020 by the Society for Industrial and Applied Mathematics 10 9 8 7 6 5 4 3 2 1 All rights reserved. Printed in the United States of America. No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the publisher. For information, write to the Society for Industrial and Applied Mathematics, 3600 Market Street, 6th Floor, Philadelphia, PA 19104-2688 USA. No warranties, express or implied, are made by the publisher, authors, and their employers that the programs contained in this volume are free of error. They should not be relied on as the sole basis to solve a problem whose incorrect solution could result in injury to person or property. If the programs are employed in such a manner, it is at the user’s own risk and the publisher, authors, and their employers disclaim all liability for such misuse. Trademarked names may be used in this book without the inclusion of a trademark symbol. These names are used in an editorial context only; no infringement of trademark is intended. Excel is a trademark of Microsoft Corporation in the United States and/or other countries. Python is a registered trademark of Python Software Foundation. SAS and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS Institute Inc. in the USA and other countries. Publications Director Kivmars H. Bowling Executive Editor Elizabeth Greenspan Acquisitions Editor Paula Callaghan Developmental Editor Mellisa Pascale Managing Editor Kelly Thomas Production Editor Ann Manning Allen Copy Editor Julia Cochrane Production Manager Donna Witzleben Production Coordinator Cally A. Shrader Compositor Cheryl Hufnagle Graphic Designer Doug Smock Library of Congress Cataloging-in-Publication Data Names: Pearson, Ronald K., 1952- author. Title: Mining imperfect data : with examples in R and Python / Ronald K. Pearson, GeoVera Holdings, Inc., Fairfield, California. Description: Second edition. | Philadelphia : Society for Industrial and Applied Mathematics, [2020] | Includes bibliographical references and index. | Summary: “This second edition of Mining Imperfect Data reflects changes in the size and nature of the datasets commonly encountered for analysis, and the evolution of the tools now available for this analysis”-- Provided by publisher. Identifiers: LCCN 2020022249 (print) | LCCN 2020022250 (ebook) | ISBN 9781611976267 (paperback) | ISBN 9781611976274 (ebook) Subjects: LCSH: Data mining. Classification: LCC QA76.9.D343 P43 2020 (print) | LCC QA76.9.D343 (ebook) | DDC 006.2/12--dc23 LC record available at https://lccn.loc.gov/2020022249 LC ebook record available at https://lccn.loc.gov/2020022250 is a registered trademark. MN04_PEARSON_FM_V3.indd 4 6/30/2020 2:37:28 PM Contents Preface vii 1 What Is Imperfect Data? 1 1.1 A working definition of perfect data . .1 1.2 Data and software for this book . .2 1.3 Data types and their key characteristics . 14 1.4 Ten forms of data imperfection . 27 1.5 Sources of data imperfection . 39 1.6 The data exchange problem . 45 1.7 Dealing with data anomalies . 63 1.8 Organization of this book . 67 2 Dealing with Univariate Outliers 71 2.1 Example: Outliers and kurtosis . 72 2.2 Outlier models and assumptions . 74 2.3 Outlier influence and related ideas . 78 2.4 Outlier-resistant procedures . 82 2.5 Univariate outlier detection procedures . 90 2.6 Performance comparisons . 97 2.7 Asymmetrically distributed data . 108 2.8 Inward and outward extensions . 118 2.9 Some practical recommendations . 120 3 Dealing with Multivariate Outliers 123 3.1 Multivariate distributions . 124 3.2 Bivariate data . 126 3.3 Correlation and covariance . 130 3.4 Multivariate outlier detection . 143 3.5 Depth-based analysis . 148 3.6 Distance- and density-based procedures . 159 3.7 Brief summary of methods . 171 3.8 A very brief introduction to copulas . 174 4 Dealing with Time-Series Outliers 177 4.1 Four real data examples . 177 4.2 The nature of time-series outliers . 182 4.3 Data cleaning filters . 195 4.4 A simulation-based comparison study . 207 v vi Contents 5 Dealing with Missing Data 233 5.1 Missing data representations . 234 5.2 Two missing data examples . 239 5.3 Missing data sources, types, and patterns . 242 5.4 Simple treatment strategies . 246 5.5 The EM algorithm . 252 5.6 Multiple imputation . 253 5.7 Unmeasured and unmeasurable variables . 262 5.8 More complex cases . 263 6 Dealing with Other Data Anomalies 275 6.1 Inliers . 275 6.2 Heaping, “flinching,” and coarsening . 280 6.3 Thin levels in categorical data . 290 6.4 Metadata errors . 296 6.5 Misalignment errors . 297 6.6 Postdictors and target leakage . 299 6.7 Noninformative variables . 301 6.8 Duplicated records . 309 7 Generalized Sensitivity Analysis 315 7.1 The GSA metaheuristic . 315 7.2 Two simple examples . 317 7.3 The notion of exchangeability . 321 7.4 Choosing scenarios . 323 7.5 Sampling schemes: A brief overview . 333 7.6 Selecting a descriptor d(·) ........................... 335 7.7 Displaying and interpreting the results . 336 7.8 Case study: Time-series imputation . 341 7.9 Extensions of the basic GSA framework . 346 8 Sampling Schemes for a Fixed Dataset 349 8.1 Four general strategies . 349 8.2 Random selection examples . 375 8.3 Subset deletion examples . 381 8.4 Comparison-based examples . 387 8.5 Systematic selection examples . 398 9 What Is a “Good” Data Characterization? 409 9.1 A motivating example . 410 9.2 Characterization via functional equations . 411 9.3 Characterization via inequalities . 426 9.4 Coda: “Good” data characterizations . 438 10 Concluding Remarks and Open Questions 441 10.1 Updates to the first edition summary . 441 10.2 Seven new open questions . 448 10.3 Concluding remarks . 457 Bibliography 461 Index 479 Preface Since the first edition of Mining Imperfect Data appeared in 2005, much has happened in the world of data analysis. Some examples follow: • Netflix announced a $1 million prize in 2006 for any person or group who could improve the accuracy of their movie recommender system by 10%. The basis for this prize was a dataset of just over 100 million ratings given to almost 18,000 movies by approximately 480,000 users. The prize was ultimately awarded to a team of researchers in 2009, who achieved an improvement of 10.06%. • Kaggle, an organization that sponsors many similar competitions—although with smaller prizes—was founded in 2010, and, as of July, 2015, this organization claimed over 300,000 data scientists on its job boards. • The term zettabyte, designating one million petabytes, one billion terabytes, or one tril- lion gigabytes, was listed in a 2007 paper by John Gantz that estimated “the amount of digital information created, captured, and replicated” in 2006 was 161 exabytes, or 0.161 zettabytes. A 2014 article in the online magazine Business Insider [37] describes the an- nouncement of a new computer from HP, claimed to be capable of processing brontobytes; although unofficial, one brontobyte is one million zettabytes. • Microsoft introduced its first 64-bit Windows operating system for personal computers in 2005 (the Windows XP Professional X64 Edition), and 64-bit personal computers have now become commonplace. • In 2005, a “large” flash drive had a capacity of 512 megabytes; today, a “large” flash drive holds 512 gigabytes, for about the same price. These and other developments since 2005 have had a number of important practical implications. First, both the Netflix prize and the advent of Kaggle have raised the profile of data analysis, contributing to the popularity of terms like “big data,” “data science,” and “predictive analytics.” (The October 2012 issue of Harvard Business Review was devoted to the subject of big data, including an article with the title “Data Scientist: The Sexiest Job of the 21st Century.”) As large businesses have increasingly decided that customer data and other data sources represent a valu- able resource to be mined for competitive advantage, the number of people engaged in analyzing large datasets has grown rapidly. Also, the size of the Netflix dataset described above—100 million records—is orders of magnitude larger than the examples discussed in traditional statis- tics and data analysis texts, and the need to analyze datasets this large has led to significant advances in both hardware and software. As a specific example, the original version of Hadoop was developed in 2005 as an internal Yahoo! project, leading to the open-source Apache Hadoop software framework released in 2011. The basic idea is to split very large data files into large blocks, process each block independently (as independently as possible), and combine the results. vii viii Preface Even at the low end of the computing spectrum—personal computers—the advances since 2005 have made many things possible and even routine that were unthinkable at that time.
Recommended publications
  • Robustbase: Basic Robust Statistics
    Package ‘robustbase’ June 2, 2021 Version 0.93-8 VersionNote Released 0.93-7 on 2021-01-04 to CRAN Date 2021-06-01 Title Basic Robust Statistics URL http://robustbase.r-forge.r-project.org/ Description ``Essential'' Robust Statistics. Tools allowing to analyze data with robust methods. This includes regression methodology including model selections and multivariate statistics where we strive to cover the book ``Robust Statistics, Theory and Methods'' by 'Maronna, Martin and Yohai'; Wiley 2006. Depends R (>= 3.5.0) Imports stats, graphics, utils, methods, DEoptimR Suggests grid, MASS, lattice, boot, cluster, Matrix, robust, fit.models, MPV, xtable, ggplot2, GGally, RColorBrewer, reshape2, sfsmisc, catdata, doParallel, foreach, skewt SuggestsNote mostly only because of vignette graphics and simulation Enhances robustX, rrcov, matrixStats, quantreg, Hmisc EnhancesNote linked to in man/*.Rd LazyData yes NeedsCompilation yes License GPL (>= 2) Author Martin Maechler [aut, cre] (<https://orcid.org/0000-0002-8685-9910>), Peter Rousseeuw [ctb] (Qn and Sn), Christophe Croux [ctb] (Qn and Sn), Valentin Todorov [aut] (most robust Cov), Andreas Ruckstuhl [aut] (nlrob, anova, glmrob), Matias Salibian-Barrera [aut] (lmrob orig.), Tobias Verbeke [ctb, fnd] (mc, adjbox), Manuel Koller [aut] (mc, lmrob, psi-func.), Eduardo L. T. Conceicao [aut] (MM-, tau-, CM-, and MTL- nlrob), Maria Anna di Palma [ctb] (initial version of Comedian) 1 2 R topics documented: Maintainer Martin Maechler <[email protected]> Repository CRAN Date/Publication 2021-06-02 10:20:02 UTC R topics documented: adjbox . .4 adjboxStats . .7 adjOutlyingness . .9 aircraft . 12 airmay . 13 alcohol . 14 ambientNOxCH . 15 Animals2 . 18 anova.glmrob . 19 anova.lmrob .
    [Show full text]
  • A Practical Guide to Support Predictive Tasks in Data Science
    A Practical Guide to Support Predictive Tasks in Data Science Jose´ Augusto Camaraˆ Filho1, Jose´ Maria Monteiro1,Cesar´ Lincoln Mattos1 and Juvencioˆ Santos Nobre2 1Department of Computing, Federal University of Ceara,´ Fortaleza, Ceara,´ Brazil 2Department of Statistics and Applied Mathematics, Federal University of Ceara,´ Fortaleza, Ceara,´ Brazil Keywords: Practical Guide, Prediction, Data Science. Abstract: Currently, professionals from the most diverse areas of knowledge need to explore their data repositories in order to extract knowledge and create new products or services. Several tools have been proposed in order to facilitate the tasks involved in the Data Science lifecycle. However, such tools require their users to have specific (and deep) knowledge in different areas of Computing and Statistics, making their use practically unfeasible for non-specialist professionals in data science. In this paper, we propose a guideline to support predictive tasks in data science. In addition to being useful for non-experts in Data Science, the proposed guideline can support data scientists, data engineers or programmers which are starting to deal with predic- tive tasks. Besides, we present a tool, called DSAdvisor, which follows the stages of the proposed guideline. DSAdvisor aims to encourage non-expert users to build machine learning models to solve predictive tasks, ex- tracting knowledge from their own data repositories. More specifically, DSAdvisor guides these professionals in predictive tasks involving regression and classification. 1 INTRODUCTION dict the future, and create new services and prod- ucts (Ozdemir, 2016). Data science makes it pos- Due to a large amount of data currently available, sible to identifying patterns hidden and obtain new arises the need for professionals of different areas to insights hidden in these datasets, from complex ma- extract knowledge from their repositories to create chine learning algorithms.
    [Show full text]
  • Detecting Outliers in Weighted Univariate Survey Data
    Detecting outliers in weighted univariate survey data Anna Pauliina Sandqvist∗ October 27, 2015 Preliminary Version Abstract Outliers and influential observations are a frequent concern in all kind of statistics, data analysis and survey data. Especially, if the data is asymmetrically distributed or heavy- tailed, outlier detection turns out to be difficult as most of the already introduced methods are not optimal in this case. In this paper we examine various non-parametric outlier detec- tion approaches for (size-)weighted growth rates from quantitative surveys and propose new respectively modified methods which can account better for skewed and long-tailed data. We apply empirical influence functions to compare these methods under different data spec- ifications. JEL Classification: C14 Keywords: Outlier detection, influential observation, size-weight, periodic surveys 1 Introduction Outliers are usually considered to be extreme values which are far away from the other data points (see, e.g., Barnett and Lewis (1994)). Chambers (1986) was first to differentiate between representative and non-representative outliers. The former are observations with correct values and are not considered to be unique, whereas non-representative outliers are elements with incorrect values or are for some other reasons considered to be unique. Most of the outlier analysis focuses on the representative outliers as non-representatives values should be taken care of already in (survey) data editing. The main reason to be concerned about the possible outliers is, that whether or not they are included into the sample, the estimates might differ considerably. The data points with substantial influence on the estimates are called influential observations and they should be ∗Authors address: KOF Swiss Economic Institute, ETH Zurich, Leonhardstrasse 21 LEE, CH-8092 Zurich, Switzerland.
    [Show full text]
  • Outlier Detection
    OUTLIER DETECTION Short Course Session 1 Nedret BILLOR Auburn University Department of Mathematics & Statistics, USA Statistics Conference, Colombia, Aug 8‐12, 2016 OUTLINE Motivation and Introduction Approaches to Outlier Detection Sensitivity of Statistical Methods to Outliers Statistical Methods for Outlier Detection Outliers in Univariate data Outliers in Multivariate Classical and Robust Statistical Distance‐ based Methods PCA based Outlier Detection Outliers in Functional Data MOTIVATION & INTRODUCTION Hadlum vs. Hadlum (1949) [Barnett 1978] Ozone Hole Case I: Hadlum vs. Hadlum (1949) [Barnett 1978] The birth of a child to Mrs. Hadlum happened 349 days after Mr. Hadlum left for military service. Average human gestation period is 280 days (40 weeks). Statistically, 349 days is an outlier. Case I: Hadlum vs. Hadlum (1949) [Barnett 1978] − blue: statistical basis (13634 observations of gestation periods) − green: assumed underlying Gaussian process − Very low probability for the birth of Mrs. Hadlums child for being generated by this process − red: assumption of Mr. Hadlum (another Gaussian process responsible for the observed birth, where the gestation period responsible) − Under this assumption the gestation period has an average duration and highest‐possible probability Case II: The Antarctic Ozone Hole The History behind the Ozone Hole • The Earth's ozone layer protects all life from the sun's harmful radiation. Case II: The Antarctic Ozone Hole (cont.) . Human activities (e.g. CFS's in aerosols) have damaged this shield. Less protection from ultraviolet light will, over time, lead to higher skin cancer and cataract rates and crop damage. Case II: The Antarctic Ozone Hole (cont.) Molina and Rowland in 1974 (lab study) and many studies after this, demonstrated the ability of CFC's (Chlorofluorocarbons) to breakdown Ozone in the presence of high frequency UV light .
    [Show full text]
  • Mining Software Engineering Data for Useful Knowledge Boris Baldassari
    Mining Software Engineering Data for Useful Knowledge Boris Baldassari To cite this version: Boris Baldassari. Mining Software Engineering Data for Useful Knowledge. Machine Learning [stat.ML]. Université de Lille, 2014. English. tel-01297400 HAL Id: tel-01297400 https://tel.archives-ouvertes.fr/tel-01297400 Submitted on 4 Apr 2016 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. École doctorale Sciences Pour l’Ingénieur THÈSE présentée en vue d’obtenir le grade de Docteur, spécialité Informatique par Boris Baldassari Mining Software Engineering Data for Useful Knowledge preparée dans l’équipe-projet SequeL commune Soutenue publiquement le 1er Juillet 2014 devant le jury composé de : Philippe Preux, Professeur des universités - Université de Lille 3 - Directeur Benoit Baudry, Chargé de recherche INRIA - INRIA Rennes - Rapporteur Laurence Duchien, Professeur des universités - Université de Lille 1 - Examinateur Flavien Huynh, Ingénieur Docteur - Squoring Technologies - Examinateur Pascale Kuntz, Professeur des universités - Polytech’ Nantes - Rapporteur Martin Monperrus, Maître de conférences - Université de Lille 1 - Examinateur 2 Preface Maisqual is a recursive acronym standing for “Maisqual Automagically Improves Software QUALity”. It may sound naive or pedantic at first sight, but it clearly stated at one time the expectations of Maisqual.
    [Show full text]
  • Robust Statistics Part 1: Introduction and Univariate Data General References
    Robust Statistics Part 1: Introduction and univariate data Peter Rousseeuw LARS-IASC School, May 2019 Peter Rousseeuw Robust Statistics, Part 1: Univariate data LARS-IASC School, May 2019 p. 1 General references General references Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., Stahel, W.A. Robust Statistics: the Approach based on Influence Functions. Wiley Series in Probability and Mathematical Statistics. Wiley, John Wiley and Sons, New York, 1986. Rousseeuw, P.J., Leroy, A. Robust Regression and Outlier Detection. Wiley Series in Probability and Mathematical Statistics. John Wiley and Sons, New York, 1987. Maronna, R.A., Martin, R.D., Yohai, V.J. Robust Statistics: Theory and Methods. Wiley Series in Probability and Statistics. John Wiley and Sons, Chichester, 2006. Hubert, M., Rousseeuw, P.J., Van Aelst, S. (2008), High-breakdown robust multivariate methods, Statistical Science, 23, 92–119. wis.kuleuven.be/stat/robust Peter Rousseeuw Robust Statistics, Part 1: Univariate data LARS-IASC School, May 2019 p. 2 General references Outline of the course General notions of robustness Robustness for univariate data Multivariate location and scatter Linear regression Principal component analysis Advanced topics Peter Rousseeuw Robust Statistics, Part 1: Univariate data LARS-IASC School, May 2019 p. 3 General notions of robustness General notions of robustness: Outline 1 Introduction: outliers and their effect on classical estimators 2 Measures of robustness: breakdown value, sensitivity curve, influence function, gross-error sensitivity, maxbias curve. Peter Rousseeuw Robust Statistics, Part 1: Univariate data LARS-IASC School, May 2019 p. 4 General notions of robustness Introduction What is robust statistics? Real data often contain outliers.
    [Show full text]
  • Unsupervised Anomaly Detection in Receipt Data
    DEGREE PROJECT IN COMPUTER SCIENCE AND ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2017 Unsupervised Anomaly Detection in Receipt Data ANDREAS FORSTÉN KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF COMPUTER SCIENCE AND COMMUNICATION Unsupervised anomaly detection in receipt data ANDREAS FORSTÉN Master in Computer Science Date: September 17, 2017 Supervisor: Professor Örjan Ekeberg Examiner: Associate Professor Mårten Björkman Swedish title: Oövervakad anomalidetektion i kvittodata School of Computer Science and Communication iii Abstract With the progress of data handling methods and computing power comes the possibility of automating tasks that are not necessarily han- dled by humans. This study was done in cooperation with a company that digitalizes receipts for companies. We investigate the possibility of automating the task of finding anomalous receipt data, which could automate the work of receipt auditors. We study both anomalous user behaviour and individual receipts. The results indicate that automa- tion is possible, which may reduce the necessity of human inspection of receipts. Keywords: Anomaly detection, receipt, receipt digitalization, au- tomatization iv Sammanfattning Med de framsteg inom datahantering och datorkraft som gjorts så kommer också möjligheten att automatisera uppgifter som ej nödvän- digtvis utförs av människor. Denna studie gjordes i samarbete med ett företag som digitaliserar företags kvitton. Vi undersöker möjligheten att automatisera sökandet av avvikande kvittodata, vilket kan avlas- ta revisorer. Vti studerar både avvikande användarbeteenden och in- dividuella kvitton. Resultaten indikerar att automatisering är möjligt, vilket kan reducera behovet av mänsklig inspektion av kvitton. Nyckelord: Anomalidetektion, kvitto, kvittodigitalisering, automa- tisering Contents 1 Introduction 1 1.1 Problem description . .1 1.2 Ethical considerations .
    [Show full text]
  • Package 'Robustbase'
    Package ‘robustbase’ March 6, 2013 Version 0.9-7 Date 2012-03-06 Title Basic Robust Statistics Author Original code by many authors, notably Peter Rousseeuw and Christophe Croux, see file ’Copyrights’; Valentin Todorov <[email protected]>, Andreas Ruckstuhl <[email protected]>, Matias Salibian-Barrera <[email protected]>, Tobias Verbeke <[email protected]>, Manuel Koller <[email protected]>, Martin Maechler Maintainer Martin Maechler <[email protected]> URL http://robustbase.r-forge.r-project.org/ Description ‘‘Essential’’ Robust Statistics. The goal is to provide tools allowing to analyze data with robust methods. This includes regression methodology including model selections and multivariate statistics where we strive to cover the book ‘‘Robust Statistics, Theory and Methods’’ by Maronna, Martin and Yohai; Wiley 2006. Depends R (>= 2.15.1), stats, graphics, methods Imports stats, graphics, utils Suggests grid, MASS, lattice, boot, cluster, Matrix, MPV, xtable,ggplot2, RColorBrewer, reshape2, sfsmisc LazyData yes License GPL (>= 2) NeedsCompilation yes Repository CRAN Date/Publication 2013-03-06 15:19:29 1 2 R topics documented: R topics documented: adjbox . .4 adjboxStats . .7 adjOutlyingness . .8 aircraft . 10 airmay . 11 alcohol . 12 ambientNOxCH . 13 Animals2 . 16 anova.glmrob . 17 anova.lmrob . 19 bushfire . 21 carrots . 22 chgDefaults-methods . 23 cloud . 23 coleman . 24 condroz . 25 covMcd . 26 covOGK . 28 CrohnD . 31 cushny . 32 delivery . 33 education . 34 epilepsy . 35 exAM............................................ 36 functionX-class . 37 functionXal-class . 38 glmrob . 38 glmrobMqle.control . 43 h.alpha.n . 44 hbk ............................................. 45 heart . 46 huberM . 47 kootenay . 48 lactic . 50 lmrob . 50 lmrob..D..fit . 54 lmrob..M..fit .
    [Show full text]
  • Exploring Ways of Identifying Outliers in Spatial Point Patterns Jie Liu East Tennessee State University
    East Tennessee State University Digital Commons @ East Tennessee State University Electronic Theses and Dissertations Student Works 5-2015 Exploring Ways of Identifying Outliers in Spatial Point Patterns Jie Liu East Tennessee State University Follow this and additional works at: https://dc.etsu.edu/etd Part of the Mathematics Commons Recommended Citation Liu, Jie, "Exploring Ways of Identifying Outliers in Spatial Point Patterns" (2015). Electronic Theses and Dissertations. Paper 2528. https://dc.etsu.edu/etd/2528 This Thesis - Open Access is brought to you for free and open access by the Student Works at Digital Commons @ East Tennessee State University. It has been accepted for inclusion in Electronic Theses and Dissertations by an authorized administrator of Digital Commons @ East Tennessee State University. For more information, please contact [email protected]. Exploring Ways of Identifying Outliers in Spatial Point Patterns A thesis presented to the faculty of the Department of Mathematics and Statistics East Tennessee State University In partial fulfillment of the requirements for the degree Master of Science in Mathematical Sciences by Jie Liu May 2015 Edith Seier, Ph.D., Chair Michele Joyner, Ph.D. Yali Liu, Ph.D. Keywords: spatial data, outlier, distance method, statistics. ABSTRACT Exploring Ways of Identifying Outliers in Spatial Point Patterns by Jie Liu This work discusses alternative methods to detect outliers in spatial point patterns. Outliers are defined based on location only and also with respect to associated vari- ables. Throughout the thesis we discuss five case studies, three of them come from experiments with spiders and bees, and the other two are data from earthquakes in a certain region.
    [Show full text]
  • Research Article a Robust Skewed Boxplot for Detecting Outliers in Rainfall Observations in Real-Time Flood Forecasting
    Hindawi Advances in Meteorology Volume 2019, Article ID 1795673, 7 pages https://doi.org/10.1155/2019/1795673 Research Article A Robust Skewed Boxplot for Detecting Outliers in Rainfall Observations in Real-Time Flood Forecasting Chao Zhao 1 and Jinyan Yang 2 1School of Environmental Science and Engineering, Xiamen University of Technology, 361024 Xiamen, China 2Suzhou Branch of Hydrology and Water Resources Investigation Bureau of Jiangsu Province, 215000 Suzhou, China Correspondence should be addressed to Chao Zhao; [email protected] Received 17 September 2018; Accepted 30 January 2019; Published 28 February 2019 Academic Editor: Harry D. Kambezidis Copyright © 2019 Chao Zhao and Jinyan Yang. /is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. /e standard boxplot is one of the most popular nonparametric tools for detecting outliers in univariate datasets. For Gaussian or symmetric distributions, the chance of data occurring outside of the standard boxplot fence is only 0.7%. However, for skewed data, such as telemetric rain observations in a real-time flood forecasting system, the probability is significantly higher. To overcome this problem, a medcouple (MC) that is robust to resisting outliers and sensitive to detecting skewness was introduced to construct a new robust skewed boxplot fence. /ree types of boxplot fences related to MC were analyzed and compared, and the exponential function boxplot fence was selected. Operating on uncontaminated as well as simulated contaminated data, the results showed that the proposed method could produce a lower swamping rate and higher accuracy than the standard boxplot and semi- interquartile range boxplot.
    [Show full text]
  • Robust Normality Test and Robust Power Transformation with Application to State Change Detection in Non Normal Processes
    Robust normality test and robust power transformation with application to state change detection in non normal processes Dissertation zur Erlangung des akademischen Grades Doktor der Naturwissenschaften der Fakultät Statistik der Technische Universität Dortmund vorgelegt von Arsene Ntiwa Foudjo Gutachter Prof. Dr. Roland Fried Prof. Dr. Walter Krämer Vorsitzenderin Prof. Dr. Christine Müller Tag der mündlichen Prüfung 04. Juni 2013 Contents Motivation 8 1RobustShapiro-Wilktestfornormality 10 1.1 Introduction . 10 1.2 Tests of normality . 11 1.2.1 TheShapiro-Wilktest . 11 1.2.2 TheJarque-Beratest . 12 1.3 Robust tests of normality in the literature . 13 1.3.1 Robustification of the Jarque-Bera test . 13 1.3.2 Robust test of normality against heavy-tailed alternatives . 15 1.3.3 A robust modification of the Jarque-Bera test . 16 1.3.4 Assessingwhenasampleismostlynormal . 17 1.4 New robust Shapiro-Wilk test . 18 1.4.1 Theadjustedboxplot. 18 1.4.2 Outlier detection for skewed data . 19 1.4.3 New robust tests of normality . 20 1.4.3.1 Symmetrical trimming . 21 1.4.3.2 Asymmetrical trimming . 22 1.5 Asymptotic theory for the new test . 23 1.5.1 Notations . 23 1.5.2 Asymptotic distribution of the modified sequence . 25 1.5.2.1 Properties........................... 25 1 1.5.2.2 ProofofTheorem1. 31 1.5.3 Asymptotic distribution of the new robust test statistic . 34 1.5.3.1 Definition and auxiliary results to prove Theorem 3 . 35 1.5.3.2 Proofoftheorem3 . 43 1.5.3.3 Auxiliary results to prove Theorem 4 . 46 1.5.3.4 ProofofTheorem4.
    [Show full text]
  • Package 'Mrfdepth'
    Package ‘mrfDepth’ August 26, 2020 Type Package Version 1.0.13 Date 2020-08-24 Title Depth Measures in Multivariate, Regression and Functional Settings Description Tools to compute depth measures and implementations of related tasks such as outlier detection, data exploration and classification of multivariate, regression and functional data. Depends R (>= 3.6.0), ggplot2 Imports abind, geometry, grid, matrixStats, reshape2, Suggests robustbase LinkingTo RcppEigen (>= 0.3.2.9.0), Rcpp (>= 0.12.6), RcppArmadillo (>= 0.7.600.1.0) License GPL (>= 2) LazyLoad yes URL https://github.com/PSegaert/mrfDepth BugReports https://github.com/PSegaert/mrfDepth/issues RoxygenNote 6.1.0 NeedsCompilation yes Author Pieter Segaert [aut], Mia Hubert [aut], Peter Rousseeuw [aut], Jakob Raymaekers [aut, cre], Kaveh Vakili [ctb] Maintainer Jakob Raymaekers <[email protected]> Repository CRAN Date/Publication 2020-08-26 16:10:33 UTC 1 2 R topics documented: R topics documented: adjOutl . .3 bagdistance . .6 bagplot . .9 bloodfat . 11 cardata90 . 12 characterA . 13 characterI . 14 cmltest . 15 compBagplot . 16 depthContour . 19 dirOutl . 22 distSpace . 25 dprojdepth . 28 dprojmedian . 30 fheatmap . 31 fom ............................................. 32 fOutl . 34 geological . 37 glass . 37 hdepth . 38 hdepthmedian . 42 medcouple . 43 mfd ............................................. 45 mfdmedian . 47 mrainbowplot . 49 mri.............................................. 50 octane . 52 outlyingness . 52 plane . 56 plotContours . 58 projdepth . 59 projmedian . 61 rdepth . 63 rdepthmedian . 65 sdepth . 66 sprojdepth . 68 sprojmedian . 70 stars . 72 symtest . 73 tablets . 74 wine............................................. 75 Index 76 adjOutl 3 adjOutl Adjusted outlyingness of points relative to a dataset Description Computes the skew-adjusted outlyingness of p-dimensional points z relative to a p-dimensional dataset x.
    [Show full text]