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| discriminant analysis in r: New Theory of Discriminant Analysis After R. Fisher Shuichi Shinmura, 2016-12-27 This is the first book to compare eight LDFs by different types of datasets, such as Fisher’s iris data, medical data with collinearities, Swiss banknote data that is a linearly separable data (LSD), student pass/fail determination using student attributes, 18 pass/fail determinations using exam scores, Japanese automobile data, and six microarray datasets (the datasets) that are LSD. We developed the 100-fold cross-validation for the small sample method (Method 1) instead of the LOO method. We proposed a simple model selection procedure to choose the best model having minimum M2 and Revised IP-OLDF based on MNM criterion was found to be better than other M2s in the above datasets. We compared two statistical LDFs and six MP-based LDFs. Those were Fisher’s LDF, logistic regression, three SVMs, Revised IP-OLDF, and another two OLDFs. Only a hard-margin SVM (H-SVM) and Revised IP-OLDF could discriminate LSD theoretically (Problem 2). We solved the defect of the generalized inverse matrices (Problem 3). For more than 10 years, many researchers have struggled to analyze the microarray dataset that is LSD (Problem 5). If we call the linearly separable model Matroska, the dataset consists of numerous smaller Matroskas in it. We develop the Matroska feature selection method (Method 2). It finds the surprising structure of the dataset that is the disjoint union of several small Matroskas. Our theory and methods reveal new facts of gene analysis. |
| discriminant analysis in r: An Introduction to Applied Multivariate Analysis with R Brian Everitt, Torsten Hothorn, 2011-04-23 The majority of data sets collected by researchers in all disciplines are multivariate, meaning that several measurements, observations, or recordings are taken on each of the units in the data set. These units might be human subjects, archaeological artifacts, countries, or a vast variety of other things. In a few cases, it may be sensible to isolate each variable and study it separately, but in most instances all the variables need to be examined simultaneously in order to fully grasp the structure and key features of the data. For this purpose, one or another method of multivariate analysis might be helpful, and it is with such methods that this book is largely concerned. Multivariate analysis includes methods both for describing and exploring such data and for making formal inferences about them. The aim of all the techniques is, in general sense, to display or extract the signal in the data in the presence of noise and to find out what the data show us in the midst of their apparent chaos. An Introduction to Applied Multivariate Analysis with R explores the correct application of these methods so as to extract as much information as possible from the data at hand, particularly as some type of graphical representation, via the R software. Throughout the book, the authors give many examples of R code used to apply the multivariate techniques to multivariate data. |
| discriminant analysis in r: Discriminant Analysis William R. Klecka, 1980-08 Background. Deriving the canonical discriminant functions. Interpreting the canonical discriminant functions. Classification procedures. Stepwise inclusion of variables. Concluding remarks. |
| discriminant analysis in r: Modern Multivariate Statistical Techniques Alan J. Izenman, 2009-03-02 This is the first book on multivariate analysis to look at large data sets which describes the state of the art in analyzing such data. Material such as database management systems is included that has never appeared in statistics books before. |
| discriminant analysis in r: R for Statistics Pierre-Andre Cornillon, Arnaud Guyader, Francois Husson, Nicolas Jegou, Julie Josse, Maela Kloareg, Eric Matzner-Lober, Laurent Rouvière, 2012-03-21 Although there are currently a wide variety of software packages suitable for the modern statistician, R has the triple advantage of being comprehensive, widespread, and free. Published in 2008, the second edition of Statistiques avec R enjoyed great success as an R guidebook in the French-speaking world. Translated and updated, R for Statistics includes a number of expanded and additional worked examples. Organized into two sections, the book focuses first on the R software, then on the implementation of traditional statistical methods with R. Focusing on the R software, the first section covers: Basic elements of the R software and data processing Clear, concise visualization of results, using simple and complex graphs Programming basics: pre-defined and user-created functions The second section of the book presents R methods for a wide range of traditional statistical data processing techniques, including: Regression methods Analyses of variance and covariance Classification methods Exploratory multivariate analysis Clustering methods Hypothesis tests After a short presentation of the method, the book explicitly details the R command lines and gives commented results. Accessible to novices and experts alike, R for Statistics is a clear and enjoyable resource for any scientist. Datasets and all the results described in this book are available on the book’s webpage at http://www.agrocampus-ouest.fr/math/RforStat |
| discriminant analysis in r: Discriminant Analysis and Applications T. Cacoullos, 2014-05-10 Discriminant Analysis and Applications comprises the proceedings of the NATO Advanced Study Institute on Discriminant Analysis and Applications held in Kifissia, Athens, Greece in June 1972. The book presents the theory and applications of Discriminant analysis, one of the most important areas of multivariate statistical analysis. This volume contains chapters that cover the historical development of discriminant analysis methods; logistic and quasi-linear discrimination; and distance functions. Medical and biological applications, and computer graphical analysis and graphical techniques for multidimensional data are likewise discussed. Statisticians, mathematicians, and biomathematicians will find the book very interesting. |
| discriminant analysis in r: Discriminant Analysis and Statistical Pattern Recognition Geoffrey J. McLachlan, 2005-02-25 The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. For both applied and theoretical statisticians as well as investigators working in the many areas in which relevant use can be made of discriminant techniques, this monograph provides a modern, comprehensive, and systematic account of discriminant analysis, with the focus on the more recent advances in the field. –SciTech Book News . . . a very useful source of information for any researcher working in discriminant analysis and pattern recognition. –Computational Statistics Discriminant Analysis and Statistical Pattern Recognition provides a systematic account of the subject. While the focus is on practical considerations, both theoretical and practical issues are explored. Among the advances covered are regularized discriminant analysis and bootstrap-based assessment of the performance of a sample-based discriminant rule, and extensions of discriminant analysis motivated by problems in statistical image analysis. The accompanying bibliography contains over 1,200 references. |
| discriminant analysis in r: Methods of Multivariate Analysis Alvin C. Rencher, 2003-04-14 Amstat News asked three review editors to rate their top five favorite books in the September 2003 issue. Methods of Multivariate Analysis was among those chosen. When measuring several variables on a complex experimental unit, it is often necessary to analyze the variables simultaneously, rather than isolate them and consider them individually. Multivariate analysis enables researchers to explore the joint performance of such variables and to determine the effect of each variable in the presence of the others. The Second Edition of Alvin Rencher's Methods of Multivariate Analysis provides students of all statistical backgrounds with both the fundamental and more sophisticated skills necessary to master the discipline. To illustrate multivariate applications, the author provides examples and exercises based on fifty-nine real data sets from a wide variety of scientific fields. Rencher takes a methods approach to his subject, with an emphasis on how students and practitioners can employ multivariate analysis in real-life situations. The Second Edition contains revised and updated chapters from the critically acclaimed First Edition as well as brand-new chapters on: Cluster analysis Multidimensional scaling Correspondence analysis Biplots Each chapter contains exercises, with corresponding answers and hints in the appendix, providing students the opportunity to test and extend their understanding of the subject. Methods of Multivariate Analysis provides an authoritative reference for statistics students as well as for practicing scientists and clinicians. |
| discriminant analysis in r: Applied MANOVA and Discriminant Analysis Carl J. Huberty, Stephen Olejnik, 2006-05-12 A complete introduction to discriminant analysis--extensively revised, expanded, and updated This Second Edition of the classic book, Applied Discriminant Analysis, reflects and references current usage with its new title, Applied MANOVA and Discriminant Analysis. Thoroughly updated and revised, this book continues to be essential for any researcher or student needing to learn to speak, read, and write about discriminant analysis as well as develop a philosophy of empirical research and data analysis. Its thorough introduction to the application of discriminant analysis is unparalleled. Offering the most up-to-date computer applications, references, terms, and real-life research examples, the Second Edition also includes new discussions of MANOVA, descriptive discriminant analysis, and predictive discriminant analysis. Newer SAS macros are included, and graphical software with data sets and programs are provided on the book's related Web site. The book features: Detailed discussions of multivariate analysis of variance and covariance An increased number of chapter exercises along with selected answers Analyses of data obtained via a repeated measures design A new chapter on analyses related to predictive discriminant analysis Basic SPSS(r) and SAS(r) computer syntax and output integrated throughout the book Applied MANOVA and Discriminant Analysis enables the reader to become aware of various types of research questions using MANOVA and discriminant analysis; to learn the meaning of this field's concepts and terms; and to be able to design a study that uses discriminant analysis through topics such as one-factor MANOVA/DDA, assessing and describing MANOVA effects, and deleting and ordering variables. |
| discriminant analysis in r: Statistical Prediction by Discriminant Analysis Robert Miller, 2016-06-27 The objects of the American Meteorological Society are the development and dissemination of knowledge of meteorology in all its phases and applications, and the advancement of its professional ideals. The organization of the Society took place in affiliation with the American Association for the Advancement of Science at Saint Louis, Missouri, December 29, 1919, and its incorporation, at Washington, D. C., January 21, 1920. The work of the Society is carried on by the Bulletin, the Journal, and Meteorological Monographs, by papers and discussions at meetings of the Society, through the offices of the Secretary and the Executive Secretary, and by correspondence. All of the Americas are represented in the membership of the Society as well as many foreign countries. |
| discriminant analysis in r: Multiple Discriminant Analysis: Marketing Research Applications Richard Johnson, 2011-06-30 |
| discriminant analysis in r: Easy Statistics for Food Science with R Abbas F.M. Alkarkhi, Wasin A. A. Alqaraghuli, 2018-09-18 Easy Statistics for Food Science with R presents the application of statistical techniques to assist students and researchers who work in food science and food engineering in choosing the appropriate statistical technique. The book focuses on the use of univariate and multivariate statistical methods in the field of food science. The techniques are presented in a simplified form without relying on complex mathematical proofs. This book was written to help researchers from different fields to analyze their data and make valid decisions. The development of modern statistical packages makes the analysis of data easier than before. The book focuses on the application of statistics and correct methods for the analysis and interpretation of data. R statistical software is used throughout the book to analyze the data. - Contains numerous step-by-step tutorials help the reader to learn quickly - Covers the theory and application of the statistical techniques - Shows how to analyze data using R software - Provides R scripts for all examples and figures |
| discriminant analysis in r: Face Recognition Harry Wechsler, Jonathon P. Phillips, Vicki Bruce, Francoise Fogelman Soulie, Thomas S. Huang, 2012-12-06 The NATO Advanced Study Institute (ASI) on Face Recognition: From Theory to Applications took place in Stirling, Scotland, UK, from June 23 through July 4, 1997. The meeting brought together 95 participants (including 18 invited lecturers) from 22 countries. The lecturers are leading researchers from academia, govemment, and industry from allover the world. The lecturers presented an encompassing view of face recognition, and identified trends for future developments and the means for implementing robust face recognition systems. The scientific programme consisted of invited lectures, three panels, and (oral and poster) presentations from students attending the AS!. As a result of lively interactions between the participants, the following topics emerged as major themes of the meeting: (i) human processing of face recognition and its relevance to forensic systems, (ii) face coding, (iii) connectionist methods and support vector machines (SVM), (iv) hybrid methods for face recognition, and (v) predictive learning and performance evaluation. The goals of the panels were to provide links among the lectures and to emphasis the themes of the meeting. The topics of the panels were: (i) How the human visual system processes faces, (ii) Issues in applying face recognition: data bases, evaluation and systems, and (iii) Classification issues involved in face recognition. The presentations made by students gave them an opportunity to receive feedback from the invited lecturers and suggestions for future work. |
| discriminant analysis in r: Biplots in Practice Michael J. Greenacre, 2010 Este libro explica las aplicaciones específicas y las interpretaciones del biplot en muchas áreas del análisis multivariante. regresión, modelos lineales generalizados, análisis de componentes principales, análisis de correspondencias y análisis discriminante. |
| discriminant analysis in r: Predictive Analytics Ajit C. Tamhane, 2020-10-13 Provides a foundation in classical parametric methods of regression and classification essential for pursuing advanced topics in predictive analytics and statistical learning This book covers a broad range of topics in parametric regression and classification including multiple regression, logistic regression (binary and multinomial), discriminant analysis, Bayesian classification, generalized linear models and Cox regression for survival data. The book also gives brief introductions to some modern computer-intensive methods such as classification and regression trees (CART), neural networks and support vector machines. The book is organized so that it can be used by both advanced undergraduate or masters students with applied interests and by doctoral students who also want to learn the underlying theory. This is done by devoting the main body of the text of each chapter with basic statistical methodology illustrated by real data examples. Derivations, proofs and extensions are relegated to the Technical Notes section of each chapter, Exercises are also divided into theoretical and applied. Answers to selected exercises are provided. A solution manual is available to instructors who adopt the text. Data sets of moderate to large sizes are used in examples and exercises. They come from a variety of disciplines including business (finance, marketing and sales), economics, education, engineering and sciences (biological, health, physical and social). All data sets are available at the book’s web site. Open source software R is used for all data analyses. R codes and outputs are provided for most examples. R codes are also available at the book’s web site. Predictive Analytics: Parametric Models for Regression and Classification Using R is ideal for a one-semester upper-level undergraduate and/or beginning level graduate course in regression for students in business, economics, finance, marketing, engineering, and computer science. It is also an excellent resource for practitioners in these fields. |
| discriminant analysis in r: An R and S-Plus® Companion to Multivariate Analysis Brian S. Everitt, 2006-03-30 Applied statisticians often need to perform analyses of multivariate data; for these they will typically use one of the statistical software packages, S-Plus or R. This book sets out how to use these packages for these analyses in a concise and easy-to-use way, and will save users having to buy two books for the job. The author is well-known for this kind of book, and so buyers will trust that he’s got it right. |
| discriminant analysis in r: R in Action Robert Kabacoff, 2015-03-03 R is a powerful language for statistical computing and graphics that can handle virtually any data-crunching task. It runs on all important platforms and provides thousands of useful specialized modules and utilities. This makes R a great way to get meaningful information from mountains of raw data. R in Action, Second Edition is a language tutorial focused on practical problems. Written by a research methodologist, it takes a direct and modular approach to quickly give readers the information they need to produce useful results. Focusing on realistic data analyses and a comprehensive integration of graphics, it follows the steps that real data analysts use to acquire their data, get it into shape, analyze it, and produce meaningful results that they can provide to clients. Purchase of the print book comes with an offer of a free PDF eBook from Manning. Also available is all code from the book. |
| discriminant analysis in r: Biometric Image Discrimination Technologies David Zhang, Xiaoyuan Jing, Jian Yang, 2006-01-01 The book gives an introduction to basic biometric image discrimination technologies including theories that are the foundations of those technologies and new algorithms for biometrics authentication--Provided by publisher. |
| discriminant analysis in r: Machine Learning with R, the tidyverse, and mlr Hefin Rhys, 2020-03-20 Summary Machine learning (ML) is a collection of programming techniques for discovering relationships in data. With ML algorithms, you can cluster and classify data for tasks like making recommendations or fraud detection and make predictions for sales trends, risk analysis, and other forecasts. Once the domain of academic data scientists, machine learning has become a mainstream business process, and tools like the easy-to-learn R programming language put high-quality data analysis in the hands of any programmer. Machine Learning with R, the tidyverse, and mlr teaches you widely used ML techniques and how to apply them to your own datasets using the R programming language and its powerful ecosystem of tools. This book will get you started! Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the book Machine Learning with R, the tidyverse, and mlr gets you started in machine learning using R Studio and the awesome mlr machine learning package. This practical guide simplifies theory and avoids needlessly complicated statistics or math. All core ML techniques are clearly explained through graphics and easy-to-grasp examples. In each engaging chapter, you’ll put a new algorithm into action to solve a quirky predictive analysis problem, including Titanic survival odds, spam email filtering, and poisoned wine investigation. What's inside Using the tidyverse packages to process and plot your data Techniques for supervised and unsupervised learning Classification, regression, dimension reduction, and clustering algorithms Statistics primer to fill gaps in your knowledge About the reader For newcomers to machine learning with basic skills in R. About the author Hefin I. Rhys is a senior laboratory research scientist at the Francis Crick Institute. He runs his own YouTube channel of screencast tutorials for R and RStudio. Table of contents: PART 1 - INTRODUCTION 1.Introduction to machine learning 2. Tidying, manipulating, and plotting data with the tidyverse PART 2 - CLASSIFICATION 3. Classifying based on similarities with k-nearest neighbors 4. Classifying based on odds with logistic regression 5. Classifying by maximizing separation with discriminant analysis 6. Classifying with naive Bayes and support vector machines 7. Classifying with decision trees 8. Improving decision trees with random forests and boosting PART 3 - REGRESSION 9. Linear regression 10. Nonlinear regression with generalized additive models 11. Preventing overfitting with ridge regression, LASSO, and elastic net 12. Regression with kNN, random forest, and XGBoost PART 4 - DIMENSION REDUCTION 13. Maximizing variance with principal component analysis 14. Maximizing similarity with t-SNE and UMAP 15. Self-organizing maps and locally linear embedding PART 5 - CLUSTERING 16. Clustering by finding centers with k-means 17. Hierarchical clustering 18. Clustering based on density: DBSCAN and OPTICS 19. Clustering based on distributions with mixture modeling 20. Final notes and further reading |
| discriminant analysis in r: Monthly Weather Review , 1993 |
| discriminant analysis in r: Knowledge-Based Intelligent Information and Engineering Systems Ignac Lovrek, Robert J. Howlett, L. C. Jain, 2008-08-18 Annotation The three volume set LNAI 5177, LNAI 5178, and LNAI 5179, constitutes the refereed proceedings of the 12th International Conference on Knowledge-Based Intelligent Information and Engineering Systems, KES 2008, held in Zagreb, Croatia, in September 2008. The 316 revised papers presented were carefully reviewed and selected. The papers present a wealth of original research results from the field of intelligent information processing in the broadest sense; topics covered in the first volume are artificial neural networks and connectionists systems; fuzzy and neuro-fuzzy systems; evolutionary computation; machine learning and classical AI; agent systems; knowledge based and expert systems; intelligent vision and image processing; knowledge management, ontologies, and data mining; Web intelligence, text and multimedia mining and retrieval; and intelligent robotics and control. |
| discriminant analysis in r: Discrete Discriminant Analysis Matthew Goldstein, William R. Dillon, 1978 The linear discriminant function; Discrete classification models; Error rates and the problem of bias; The variable-selection problem; Special topics; Computer programs. |
| discriminant analysis in r: Machine Learning for Business Analytics Galit Shmueli, Peter C. Bruce, Peter Gedeck, Inbal Yahav, Nitin R. Patel, 2023-03-22 MACHINE LEARNING FOR BUSINESS ANALYTICS Machine learning —also known as data mining or data analytics— is a fundamental part of data science. It is used by organizations in a wide variety of arenas to turn raw data into actionable information. Machine Learning for Business Analytics: Concepts, Techniques, and Applications in R provides a comprehensive introduction and an overview of this methodology. This best-selling textbook covers both statistical and machine learning algorithms for prediction, classification, visualization, dimension reduction, rule mining, recommendations, clustering, text mining, experimentation, and network analytics. Along with hands-on exercises and real-life case studies, it also discusses managerial and ethical issues for responsible use of machine learning techniques. This is the second R edition of Machine Learning for Business Analytics. This edition also includes: A new co-author, Peter Gedeck, who brings over 20 years of experience in machine learning using R An expanded chapter focused on discussion of deep learning techniques A new chapter on experimental feedback techniques including A/B testing, uplift modeling, and reinforcement learning A new chapter on responsible data science Updates and new material based on feedback from instructors teaching MBA, Masters in Business Analytics and related programs, undergraduate, diploma and executive courses, and from their students A full chapter devoted to relevant case studies with more than a dozen cases demonstrating applications for the machine learning techniques End-of-chapter exercises that help readers gauge and expand their comprehension and competency of the material presented A companion website with more than two dozen data sets, and instructor materials including exercise solutions, slides, and case solutions This textbook is an ideal resource for upper-level undergraduate and graduate level courses in data science, predictive analytics, and business analytics. It is also an excellent reference for analysts, researchers, and data science practitioners working with quantitative data in management, finance, marketing, operations management, information systems, computer science, and information technology. |
| discriminant analysis in r: Contributions to linear discriminant analysis with applications to growth curves Edward Kanuti Ngailo, 2020-05-06 This thesis concerns contributions to linear discriminant analysis with applications to growth curves. Firstly, we present the linear discriminant function coefficients in a stochastic representation using random variables from the standard univariate distributions. We apply the characterized distribution in the classification function to approximate the classification error rate. The results are then extended to large dimension asymptotics under assumption that the dimension p of the parameter space increases together with the sample size n to infinity such that the ratio converges to a positive constant c (0, 1). Secondly, the thesis treats repeated measures data which correspond to multiple measurements that are taken on the same subject at different time points. We develop a linear classification function to classify an individual into one out of two populations on the basis of the repeated measures data that when the means follow a growth curve structure. The growth curve structure we first consider assumes that all treatments (groups) follows the same growth profile. However, this is not necessarily true in general and the problem is extended to linear classification where the means follow an extended growth curve structure, i.e., the treatments under the experimental design follow different growth profiles. At last, a function of the inverse Wishart matrix and a normal distribution finds its application in portfolio theory where the vector of optimal portfolio weights is proportional to the product of the inverse sample covariance matrix and a sample mean vector. Analytical expressions for higher order moments and non-central moments of the portfolio weights are derived when the returns are assumed to be independently multivariate normally distributed. Moreover, the expressions for the mean, variance, skewness and kurtosis of specific estimated weights are obtained. The results are complemented using a Monte Carlo simulation study, where data from the multivariate normal and t-distributions are discussed. Den här avhandlingen studerar diskriminantanalys, klassificering av tillväxtkurvor och portföljteori. Diskriminantanalys och klassificering är flerdimensionella tekniker som används för att separera olika mängder av objekt och för att tilldela nya objekt till redan definierade grupper (så kallade klasser). En klassisk metod är att använda Fishers linjära diskriminantfunktion och när alla parametrar är kända så kan man enkelt beräkna sannolikheterna för felklassificering. Tyvärr är så sällan fallet, utan parametrarna måste skattas från data, och då blir Fishers linjära diskriminantfunktion en funktion av en Wishartmatris och multivariat normalfördelade vektorer. I den här avhandlingen studerar vi hur man kan approximativt beräkna sannolikheten för felklassificering under antagande att dimensionen på parameterrummet ökar tillsammans med antalet observationer genom att använda en särskild stokastisk representation av diskriminantfunktionen. Upprepade mätningar över tiden på samma individ eller objekt går att modellera med så kallade tillväxtkurvor. Vid klassificering av tillväxtkurvor, eller rättare sagt av upprepade mätningar för en ny individ, bör man ta tillvara på både den spatiala- och temporala informationen som finns hos dessa observationer. Vi vidareutvecklar Fishers linjära diskriminantfunktion att passa för upprepade mätningar och beräknar asymptotiska sannolikheter för felklassificering. Till sist kan man notera att snarlika funktioner av Wishartmatriser och multivariat normalfördelade vektorer dyker upp när man vill beräkna de optimala vikterna i portföljteori. Genom en stokastisk representation studerar vi egenskaperna hos portföljvikterna och gör dessutom en simuleringsstudie för att förstå vad som händer när antagandet om normalfördelning inte är uppfyllt. |
| discriminant analysis in r: Food Security, Poverty and Nutrition Policy Analysis Suresh Babu, Shailendra Gajanan, 2021-09-21 Food Security, Poverty and Nutrition Policy Analysis: Statistical Methods and Applications, Third Edition combines statistical data analysis and computer literacy, applying the results to develop policy alternatives through a series of statistical methods for real world food insecurity, malnutrition and poverty problems. The book presents the latest uses of statistical methods for policy analysis using the open source statistical environment R, in addition to having the original Stata files and applications. A new chapter on obesity brings in new datasets for analysis to effectively demonstrate the use of such data for addressing policy issues. Finally, program evaluation methods which can be directly applied to the data on food security, nutrition, poverty indicators and causal factors are included. This unique, real-world data takes the reader through a hands-on approach toward econometric practice whereby they can also test the effects of policy and program interventions. Further, this is the first book to explore actual data with STATA and R statistical packages that also provides a line-by-line guide to the programming and interpretation of results. - Provides a fully revised and updated tome on the latest technology, assessment advances and policy insights surrounding food security - Combines case-studies with data-based analysis - Includes self-contained, downloadable datasets, statistical appendices, computer programs, and interpretations of the results for policy applications |
| discriminant analysis in r: Basics of Matrix Algebra for Statistics with R Nick Fieller, 2018-09-03 A Thorough Guide to Elementary Matrix Algebra and Implementation in R Basics of Matrix Algebra for Statistics with R provides a guide to elementary matrix algebra sufficient for undertaking specialized courses, such as multivariate data analysis and linear models. It also covers advanced topics, such as generalized inverses of singular and rectangular matrices and manipulation of partitioned matrices, for those who want to delve deeper into the subject. The book introduces the definition of a matrix and the basic rules of addition, subtraction, multiplication, and inversion. Later topics include determinants, calculation of eigenvectors and eigenvalues, and differentiation of linear and quadratic forms with respect to vectors. The text explores how these concepts arise in statistical techniques, including principal component analysis, canonical correlation analysis, and linear modeling. In addition to the algebraic manipulation of matrices, the book presents numerical examples that illustrate how to perform calculations by hand and using R. Many theoretical and numerical exercises of varying levels of difficulty aid readers in assessing their knowledge of the material. Outline solutions at the back of the book enable readers to verify the techniques required and obtain numerical answers. Avoiding vector spaces and other advanced mathematics, this book shows how to manipulate matrices and perform numerical calculations in R. It prepares readers for higher-level and specialized studies in statistics. |
| discriminant analysis in r: Statistical Pattern Recognition Andrew R. Webb, 2003-07-25 Statistical pattern recognition is a very active area of study andresearch, which has seen many advances in recent years. New andemerging applications - such as data mining, web searching,multimedia data retrieval, face recognition, and cursivehandwriting recognition - require robust and efficient patternrecognition techniques. Statistical decision making and estimationare regarded as fundamental to the study of pattern recognition. Statistical Pattern Recognition, Second Edition has been fullyupdated with new methods, applications and references. It providesa comprehensive introduction to this vibrant area - with materialdrawn from engineering, statistics, computer science and the socialsciences - and covers many application areas, such as databasedesign, artificial neural networks, and decision supportsystems. * Provides a self-contained introduction to statistical patternrecognition. * Each technique described is illustrated by real examples. * Covers Bayesian methods, neural networks, support vectormachines, and unsupervised classification. * Each section concludes with a description of the applicationsthat have been addressed and with further developments of thetheory. * Includes background material on dissimilarity, parameterestimation, data, linear algebra and probability. * Features a variety of exercises, from 'open-book' questions tomore lengthy projects. The book is aimed primarily at senior undergraduate and graduatestudents studying statistical pattern recognition, patternprocessing, neural networks, and data mining, in both statisticsand engineering departments. It is also an excellent source ofreference for technical professionals working in advancedinformation development environments. For further information on the techniques and applicationsdiscussed in this book please visit ahref=http://www.statistical-pattern-recognition.net/www.statistical-pattern-recognition.net/a |
| discriminant analysis in r: Chemometrics in Practical Applications Kurt Varmuza, 2012-03-23 In the book Chemometrics in practical applications, various practical applications of chemometric methods in chemistry, biochemistry and chemical technology are presented, and selected chemometric methods are described in tutorial style. The book contains 14 independent chapters and is devoted to filling the gap between textbooks on multivariate data analysis and research journals on chemometrics and chemoinformatics. |
| discriminant analysis in r: The R Book Michael J. Crawley, 2007-06-13 The high-level language of R is recognized as one of the mostpowerful and flexible statistical software environments, and israpidly becoming the standard setting for quantitative analysis,statistics and graphics. R provides free access to unrivalledcoverage and cutting-edge applications, enabling the user to applynumerous statistical methods ranging from simple regression to timeseries or multivariate analysis. Building on the success of the author’s bestsellingStatistics: An Introduction using R, The R Book ispacked with worked examples, providing an all inclusive guide to R,ideal for novice and more accomplished users alike. The bookassumes no background in statistics or computing and introduces theadvantages of the R environment, detailing its applications in awide range of disciplines. Provides the first comprehensive reference manual for the Rlanguage, including practical guidance and full coverage of thegraphics facilities. Introduces all the statistical models covered by R, beginningwith simple classical tests such as chi-square and t-test. Proceeds to examine more advance methods, from regression andanalysis of variance, through to generalized linear models,generalized mixed models, time series, spatial statistics,multivariate statistics and much more. The R Book is aimed at undergraduates, postgraduates andprofessionals in science, engineering and medicine. It is alsoideal for students and professionals in statistics, economics,geography and the social sciences. |
| discriminant analysis in r: Modern Regression Techniques Using R Daniel B Wright, Kamala London, 2009-02-19 Statistics is the language of modern empirical social and behavioural science and the varieties of regression form the basis of this language. Statistical and computing advances have led to new and exciting regressions that have become the necessary tools for any researcher in these fields. In a way that is refreshingly engaging and readable, Wright and London describe the most useful of these techniques and provide step-by-step instructions, using the freeware R, to analyze datasets that can be located on the books′ webpage: www.sagepub.co.uk/wrightandlondon. Techniques covered in this book include multilevel modeling, ANOVA and ANCOVA, path analysis, mediation and moderation, logistic regression (generalized linear models), generalized additive models, and robust methods. These are all tested out using a range of real research examples conducted by the authors in every chapter. Given the wide coverage of techniques, this book will be essential reading for any advanced undergraduate and graduate student (particularly in psychology) and for more experienced researchers wanting to learn how to apply some of the more recent statistical techniques to their datasets. The Authors are donating all royalties from the book to the American Partnership for Eosinophilic Disorders. |
| discriminant analysis in r: Inference and Learning from Data Ali H. Sayed, 2022-11-30 Discover data-driven learning methods with the third volume of this extraordinary three-volume set. |
| discriminant analysis in r: RMS Lg Studies of Underground Nuclear Explosions in the U.S.S.R. and the U.S. P. G. Richards, 1993 |
| discriminant analysis in r: Linear Models with R Julian J. Faraway, 2016-04-19 A Hands-On Way to Learning Data AnalysisPart of the core of statistics, linear models are used to make predictions and explain the relationship between the response and the predictors. Understanding linear models is crucial to a broader competence in the practice of statistics. Linear Models with R, Second Edition explains how to use linear models |
| discriminant analysis in r: Handbook of Applied Multivariate Statistics and Mathematical Modeling Howard E.A. Tinsley, Steven D. Brown, 2000-05-22 Multivariate statistics and mathematical models provide flexible and powerful tools essential in most disciplines. Nevertheless, many practicing researchers lack an adequate knowledge of these techniques, or did once know the techniques, but have not been able to keep abreast of new developments. The Handbook of Applied Multivariate Statistics and Mathematical Modeling explains the appropriate uses of multivariate procedures and mathematical modeling techniques, and prescribe practices that enable applied researchers to use these procedures effectively without needing to concern themselves with the mathematical basis. The Handbook emphasizes using models and statistics as tools. The objective of the book is to inform readers about which tool to use to accomplish which task. Each chapter begins with a discussion of what kinds of questions a particular technique can and cannot answer. As multivariate statistics and modeling techniques are useful across disciplines, these examples include issues of concern in biological and social sciences as well as the humanities. |
| discriminant analysis in r: Using R for Data Management, Statistical Analysis, and Graphics Nicholas J. Horton, Ken Kleinman, 2010-07-28 Quick and Easy Access to Key Elements of Documentation Includes worked examples across a wide variety of applications, tasks, and graphicsUsing R for Data Management, Statistical Analysis, and Graphics presents an easy way to learn how to perform an analytical task in R, without having to navigate through the extensive, idiosyncratic, and sometimes |
| discriminant analysis in r: Introduction to Data Science Rafael A. Irizarry, 2019-11-20 Introduction to Data Science: Data Analysis and Prediction Algorithms with R introduces concepts and skills that can help you tackle real-world data analysis challenges. It covers concepts from probability, statistical inference, linear regression, and machine learning. It also helps you develop skills such as R programming, data wrangling, data visualization, predictive algorithm building, file organization with UNIX/Linux shell, version control with Git and GitHub, and reproducible document preparation. This book is a textbook for a first course in data science. No previous knowledge of R is necessary, although some experience with programming may be helpful. The book is divided into six parts: R, data visualization, statistics with R, data wrangling, machine learning, and productivity tools. Each part has several chapters meant to be presented as one lecture. The author uses motivating case studies that realistically mimic a data scientist’s experience. He starts by asking specific questions and answers these through data analysis so concepts are learned as a means to answering the questions. Examples of the case studies included are: US murder rates by state, self-reported student heights, trends in world health and economics, the impact of vaccines on infectious disease rates, the financial crisis of 2007-2008, election forecasting, building a baseball team, image processing of hand-written digits, and movie recommendation systems. The statistical concepts used to answer the case study questions are only briefly introduced, so complementing with a probability and statistics textbook is highly recommended for in-depth understanding of these concepts. If you read and understand the chapters and complete the exercises, you will be prepared to learn the more advanced concepts and skills needed to become an expert. |
| discriminant analysis in r: Discriminant Analysis and Statistical Pattern Recognition Geoffrey McLachlan, 1992-04-10 Reflecting also the increasingly image-based nature of data, especially in remote sensing, the book outlines extensions of discriminant analysis motivated by problems in statistical image analysis. The sequence of chapters is clearly and logically developed, beginning with a general introduction to discriminant analysis in Chapter 1. |
| discriminant analysis in r: Multilinear Subspace Learning Haiping Lu, Konstantinos N. Plataniotis, Anastasios Venetsanopoulos, 2013-12-11 Due to advances in sensor, storage, and networking technologies, data is being generated on a daily basis at an ever-increasing pace in a wide range of applications, including cloud computing, mobile Internet, and medical imaging. This large multidimensional data requires more efficient dimensionality reduction schemes than the traditional techniqu |
| discriminant analysis in r: Foodinformatics Karina Martinez-Mayorga, José Luis Medina-Franco, 2014-11-21 The explosion in the generation of information parallels the explosion of computational resources. The use of computers to collect, store and manipulate chemical information is at the heart of chemoinformatics. These methodologies, whose main target thus far has been the pharmaceutical field, are general and can be applied to other types of chemical data sets, such as those containing food chemicals. While the use of chemical information methodologies to address food-related challenges is still in its infancy, interest is growing and will continue to do so as the methods prove useful, particularly for providing practical solutions to food industry challenges. Foodinformatics gives an overview of basic concepts, applications, tools and perspectives of the emerging field of foodinformatics. The book is an important addition to the literature and will be of interest of food chemists, nutritionists, informaticians and scientists of related fields. About the Editors Karina Martínez-Mayorga, Instituto de Química, UNAM, Mexico City, México and Torrey Pines Institute for Molecular Studies, Port St. Lucie, FL, USA José Luis Medina-Franco, Instituto de Química, UNAM, México City, México, and Torrey Pines Institute for Molecular Studies, Port St. Lucie, FL, USA |
| discriminant analysis in r: Machine Learning Essentials Alboukadel Kassambara, 2018-03-10 Discovering knowledge from big multivariate data, recorded every days, requires specialized machine learning techniques. This book presents an easy to use practical guide in R to compute the most popular machine learning methods for exploring real word data sets, as well as, for building predictive models. The main parts of the book include: A) Unsupervised learning methods, to explore and discover knowledge from a large multivariate data set using clustering and principal component methods. You will learn hierarchical clustering, k-means, principal component analysis and correspondence analysis methods. B) Regression analysis, to predict a quantitative outcome value using linear regression and non-linear regression strategies. C) Classification techniques, to predict a qualitative outcome value using logistic regression, discriminant analysis, naive bayes classifier and support vector machines. D) Advanced machine learning methods, to build robust regression and classification models using k-nearest neighbors methods, decision tree models, ensemble methods (bagging, random forest and boosting). E) Model selection methods, to select automatically the best combination of predictor variables for building an optimal predictive model. These include, best subsets selection methods, stepwise regression and penalized regression (ridge, lasso and elastic net regression models). We also present principal component-based regression methods, which are useful when the data contain multiple correlated predictor variables. F) Model validation and evaluation techniques for measuring the performance of a predictive model. G) Model diagnostics for detecting and fixing a potential problems in a predictive model. The book presents the basic principles of these tasks and provide many examples in R. This book offers solid guidance in data mining for students and researchers. Key features: - Covers machine learning algorithm and implementation - Key mathematical concepts are presented - Short, self-contained chapters with practical examples. |
Formula, Rules, Discriminant of Quadratic Qquation - Cuemath
The discriminant in math is defined for polynomials and it is a function of coefficients of polynomials. The discriminant of quadratic equation ax^2+bx+c = 0 is b^2 - 4ac and it is …
Discriminant - Wikipedia
In mathematics, the discriminant of a polynomial is a quantity that depends on the coefficients and allows deducing some properties of the roots without computing them. More precisely, it is a …
A Complete Guide to the Discriminant of Quadratic - Maths at …
What is the Discriminant of a Quadratic Equation? The discriminant is the part of the quadratic formula found within the square root. For a quadratic of the form a𝑥 2 + b𝑥 + c, its discriminant is …
Discriminant | Definition, Examples, & Facts | Britannica
Discriminant, in mathematics, a parameter of an object or system calculated as an aid to its classification or solution. In the case of a quadratic equation, ax^2 + bx + c = 0, the …
Using the discriminant to determine the number of roots
The discriminant is \({b^2} - 4ac\), which comes from the quadratic formula and we can use this to find the nature of the roots. Roots can occur in a parabola in 3 different ways as shown in the...
Discriminant of a Quadratic Equation with Examples - Math Monks
Aug 3, 2023 · In a quadratic formula, the discriminant is only a part of the quadratic formula within the square root. For a quadratic equation ax 2 + bx + c = 0, b 2 – 4ac is the discriminant (D), as …
The Discriminant - A Level Maths Revision Notes - Save My Exams
Nov 29, 2024 · Learn about using the discriminant for your A level maths exam. This revision note covers what the discriminant is, and worked examples.
Formula, Rules, Discriminant of Quadratic Qquation - Cuemath
The discriminant in math is defined for polynomials and it is a function of coefficients of polynomials. The discriminant of quadratic equation ax^2+bx+c = 0 is b^2 - 4ac and it is …
Discriminant - Wikipedia
In mathematics, the discriminant of a polynomial is a quantity that depends on the coefficients and allows deducing some properties of the roots without computing them. More precisely, it is a …
A Complete Guide to the Discriminant of Quadratic - Maths at …
What is the Discriminant of a Quadratic Equation? The discriminant is the part of the quadratic formula found within the square root. For a quadratic of the form a𝑥 2 + b𝑥 + c, its discriminant is …
Discriminant | Definition, Examples, & Facts | Britannica
Discriminant, in mathematics, a parameter of an object or system calculated as an aid to its classification or solution. In the case of a quadratic equation, ax^2 + bx + c = 0, the …
Using the discriminant to determine the number of roots
The discriminant is \({b^2} - 4ac\), which comes from the quadratic formula and we can use this to find the nature of the roots. Roots can occur in a parabola in 3 different ways as shown in the...
Discriminant of a Quadratic Equation with Examples - Math Monks
Aug 3, 2023 · In a quadratic formula, the discriminant is only a part of the quadratic formula within the square root. For a quadratic equation ax 2 + bx + c = 0, b 2 – 4ac is the discriminant (D), …
The Discriminant - A Level Maths Revision Notes - Save My Exams
Nov 29, 2024 · Learn about using the discriminant for your A level maths exam. This revision note covers what the discriminant is, and worked examples.
