Topic

# Linear discriminant analysis

About: Linear discriminant analysis is a(n) research topic. Over the lifetime, 18361 publication(s) have been published within this topic receiving 603195 citation(s). The topic is also known as: Linear discriminant analysis & LDA.

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01 Jan 1983

TL;DR: In this Section: 1. Multivariate Statistics: Why? and 2. A Guide to Statistical Techniques: Using the Book Research Questions and Associated Techniques.

Abstract: In this Section: 1. Brief Table of Contents 2. Full Table of Contents 1. BRIEF TABLE OF CONTENTS Chapter 1 Introduction Chapter 2 A Guide to Statistical Techniques: Using the Book Chapter 3 Review of Univariate and Bivariate Statistics Chapter 4 Cleaning Up Your Act: Screening Data Prior to Analysis Chapter 5 Multiple Regression Chapter 6 Analysis of Covariance Chapter 7 Multivariate Analysis of Variance and Covariance Chapter 8 Profile Analysis: The Multivariate Approach to Repeated Measures Chapter 9 Discriminant Analysis Chapter 10 Logistic Regression Chapter 11 Survival/Failure Analysis Chapter 12 Canonical Correlation Chapter 13 Principal Components and Factor Analysis Chapter 14 Structural Equation Modeling Chapter 15 Multilevel Linear Modeling Chapter 16 Multiway Frequency Analysis 2. FULL TABLE OF CONTENTS Chapter 1: Introduction Multivariate Statistics: Why? Some Useful Definitions Linear Combinations of Variables Number and Nature of Variables to Include Statistical Power Data Appropriate for Multivariate Statistics Organization of the Book Chapter 2: A Guide to Statistical Techniques: Using the Book Research Questions and Associated Techniques Some Further Comparisons A Decision Tree Technique Chapters Preliminary Check of the Data Chapter 3: Review of Univariate and Bivariate Statistics Hypothesis Testing Analysis of Variance Parameter Estimation Effect Size Bivariate Statistics: Correlation and Regression. Chi-Square Analysis Chapter 4: Cleaning Up Your Act: Screening Data Prior to Analysis Important Issues in Data Screening Complete Examples of Data Screening Chapter 5: Multiple Regression General Purpose and Description Kinds of Research Questions Limitations to Regression Analyses Fundamental Equations for Multiple Regression Major Types of Multiple Regression Some Important Issues. Complete Examples of Regression Analysis Comparison of Programs Chapter 6: Analysis of Covariance General Purpose and Description Kinds of Research Questions Limitations to Analysis of Covariance Fundamental Equations for Analysis of Covariance Some Important Issues Complete Example of Analysis of Covariance Comparison of Programs Chapter 7: Multivariate Analysis of Variance and Covariance General Purpose and Description Kinds of Research Questions Limitations to Multivariate Analysis of Variance and Covariance Fundamental Equations for Multivariate Analysis of Variance and Covariance Some Important Issues Complete Examples of Multivariate Analysis of Variance and Covariance Comparison of Programs Chapter 8: Profile Analysis: The Multivariate Approach to Repeated Measures General Purpose and Description Kinds of Research Questions Limitations to Profile Analysis Fundamental Equations for Profile Analysis Some Important Issues Complete Examples of Profile Analysis Comparison of Programs Chapter 9: Discriminant Analysis General Purpose and Description Kinds of Research Questions Limitations to Discriminant Analysis Fundamental Equations for Discriminant Analysis Types of Discriminant Analysis Some Important Issues Comparison of Programs Chapter 10: Logistic Regression General Purpose and Description Kinds of Research Questions Limitations to Logistic Regression Analysis Fundamental Equations for Logistic Regression Types of Logistic Regression Some Important Issues Complete Examples of Logistic Regression Comparison of Programs Chapter 11: Survival/Failure Analysis General Purpose and Description Kinds of Research Questions Limitations to Survival Analysis Fundamental Equations for Survival Analysis Types of Survival Analysis Some Important Issues Complete Example of Survival Analysis Comparison of Programs Chapter 12: Canonical Correlation General Purpose and Description Kinds of Research Questions Limitations Fundamental Equations for Canonical Correlation Some Important Issues Complete Example of Canonical Correlation Comparison of Programs Chapter 13: Principal Components and Factor Analysis General Purpose and Description Kinds of Research Questions Limitations Fundamental Equations for Factor Analysis Major Types of Factor Analysis Some Important Issues Complete Example of FA Comparison of Programs Chapter 14: Structural Equation Modeling General Purpose and Description Kinds of Research Questions Limitations to Structural Equation Modeling Fundamental Equations for Structural Equations Modeling Some Important Issues Complete Examples of Structural Equation Modeling Analysis. Comparison of Programs Chapter 15: Multilevel Linear Modeling General Purpose and Description Kinds of Research Questions Limitations to Multilevel Linear Modeling Fundamental Equations Types of MLM Some Important Issues Complete Example of MLM Comparison of Programs Chapter 16: Multiway Frequency Analysis General Purpose and Description Kinds of Research Questions Limitations to Multiway Frequency Analysis Fundamental Equations for Multiway Frequency Analysis Some Important Issues Complete Example of Multiway Frequency Analysis Comparison of Programs

53,012 citations

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01 Jan 1973

TL;DR: In this article, a unified, comprehensive and up-to-date treatment of both statistical and descriptive methods for pattern recognition is provided, including Bayesian decision theory, supervised and unsupervised learning, nonparametric techniques, discriminant analysis, clustering, preprosessing of pictorial data, spatial filtering, shape description techniques, perspective transformations, projective invariants, linguistic procedures, and artificial intelligence techniques for scene analysis.

Abstract: Provides a unified, comprehensive and up-to-date treatment of both statistical and descriptive methods for pattern recognition. The topics treated include Bayesian decision theory, supervised and unsupervised learning, nonparametric techniques, discriminant analysis, clustering, preprosessing of pictorial data, spatial filtering, shape description techniques, perspective transformations, projective invariants, linguistic procedures, and artificial intelligence techniques for scene analysis.

13,634 citations

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Yale University

^{1}TL;DR: A face recognition algorithm which is insensitive to large variation in lighting direction and facial expression is developed, based on Fisher's linear discriminant and produces well separated classes in a low-dimensional subspace, even under severe variations in lighting and facial expressions.

Abstract: We develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression. Taking a pattern classification approach, we consider each pixel in an image as a coordinate in a high-dimensional space. We take advantage of the observation that the images of a particular face, under varying illumination but fixed pose, lie in a 3D linear subspace of the high dimensional image space-if the face is a Lambertian surface without shadowing. However, since faces are not truly Lambertian surfaces and do indeed produce self-shadowing, images will deviate from this linear subspace. Rather than explicitly modeling this deviation, we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation. Our projection method is based on Fisher's linear discriminant and produces well separated classes in a low-dimensional subspace, even under severe variation in lighting and facial expressions. The eigenface technique, another method based on linearly projecting the image space to a low dimensional subspace, has similar computational requirements. Yet, extensive experimental results demonstrate that the proposed "Fisherface" method has error rates that are lower than those of the eigenface technique for tests on the Harvard and Yale face databases.

11,674 citations

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TL;DR: In this paper, a set of financial and economic ratios are investigated in a bankruptcy prediction context wherein a multiple discriminant statistical methodology is employed, and the data used in the study are limited to manufacturing corporations, where an initial sample of sixty-six firms is utilized to establish a function which best discriminates between companies in two mutually exclusive groups: bankrupt and nonbankrupt firms.

Abstract: ACADEMICIANS SEEM to be moving toward the elimination of ratio analysis as an analytical technique in assessing the performance of the business enterprise. Theorists downgrade arbitrary rules of thumb, such as company ratio comparisons, widely used by practitioners. Since attacks on the relevance of ratio analysis emanate from many esteemed members of the scholarly world, does this mean that ratio analysis is limited to the world of \"nuts and bolts\"? Or, has the significance of such an approach been unattractively garbed and therefore unfairly handicapped? Can we bridge the gap, rather than sever the link, between traditional ratio \"analysis\" and the more rigorous statistical techniques which have become popular among academicians in recent years? The purpose of this paper is to attempt an assessment of this issue-the quality of ratio analysis as an analytical technique. The prediction of corporate bankruptcy is used as an illustrative case.' Specifically, a set of financial and economic ratios will be investigated in a bankruptcy prediction context wherein a multiple discriminant statistical methodology is employed. The data used in the study are limited to manufacturing corporations. A brief review of the development of traditional ratio analysis as a technique for investigating corporate performance is presented in section I. In section II the shortcomings of this approach are discussed and multiple discriminant analysis is introduced with the emphasis centering on its compatibility with ratio analysis in a bankruptcy prediction context. The discriminant model is developed in section III, where an initial sample of sixty-six firms is utilized to establish a function which best discriminates between companies in two mutually exclusive groups: bankrupt and non-bankrupt firms. Section IV reviews empirical results obtained from the initial sample and several secondary samples, the latter being selected to examine the reliability of the discriminant

9,776 citations

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01 Jan 1973

TL;DR: Kerlinger and Pedhazur as discussed by the authors present the three main applied analytical models which derive from the general linear hypothesis-analysis of variance, regression, and analysis of covariance.

Abstract: One of the dilemmas facing those who teach sociological methods and statistics these days is how to present the three main applied analytical models which derive from the general linear hypothesis-analysis of variance, regression, and analysis of covariance. The reason for this dilemma is that whereas there now exist in the sociological literature a number of theoretical expositions integrating these various models, nowhere has there existed a reference or, for that matter, a set of references which provided the computational integration in sufficient clarity that the teacher could assign them to his class and be assured that the student would obtain a clear picture of how the three models were computationally interrelated and interchangeable. Kerlinger and Pedhazur have painstakingly provided such a resource. For those looking for such a text (or reference book), it is a teacher's delight! The authors provide one with a consistency of framework which opens in Part 1 (five chapters). Those chapters are a review of the foundations of multiple regression and can be easily read by students who have had an introductory course in statistics. The review is, however, more than just a rehash of regression theory and procedures, as the authors are also developing a framework for the later integration of analysis of variance, analysis of covariance, time series analysis, path analysis and multivariate analysis (multivariate analysis of variance, canonical regression, and discriminant analysis). Part 2, which consists of six chapters, is the focal point of the book. For example, chapters 5, 6, and 7 give an introduction to the use of dummy coding to achieve the same results as one gets in one-way analysis of variance. Chapter 8 extends the procedures to multiple categorical variables and how they can be handled in the multiple regression framework to achieve the same results one would obtain via ANOV computational procedures in factorial designs. Chapter 9 departs from this theme to open considerations of testing for linear and curvilinear regression when working with continu'ous variables. Chapter 10 weaves these considerations into those developed earlier regarding categorical variables and discusses regression procedures for handling both continuous and categorical regressors in the same equation. (I have found this to be a topic of great interest among sociology students who wonder how to use

4,992 citations