Basics of Multivariate Analysis III (Discriminant Analysis, 2nd Edition): Theory and Exercise using R

Many introductory books on Discriminant Analysis (DA) using R have been published. These books describe how to use the lda() function of R. Uniquely, this text book provides a step-by-step description of the background theory of the lda() function. It also presents examples ranging from simple to complex, which will help readers to identify discriminant planes.

Readers of this book should be familiar with the basics of differentiation, vectors (including their inner product) and matrix analysis (including their product, transpose, inverse, and eigenvalues).

The scripts used in this book can be downloaded from the website:

http://www.mybook-pub-site.sakura.ne.jp/multi_variate_analysis/DA/index.html

This book uses R 3.3.0 for Windows. The software is freely downloadable from http://cran.r-project.org/. This book uses the Windows versions of scripts. Mac users need only to change the file path to load the data files.

Table of Contents

1 Introduction

2 Bivariate Linear Discriminant Analysis

2.1 Basic Theory
2.2 Numerical Example 1
2.3 Matrix Expression
2.4 Matrix Calculation using R
2.5 Calculation using lda()

3 Determination of the constant c

3.1 Mahalanobis distance
3.2 Determination of constant c
3.3 Calculation using R
3.4 Classification of unknown data

4 Multi-Variate Linear Discriminant Analysis

4.1 Matrix Expression
4.2 Determination of constant a0
4.3 Calculation using R
4.4 Calculation using the lda() function
4.5 Classification of unknown data

5 Nonlinear Discriminant Analysis

5.1 Bivariate Normal Distribution
5.2 Mahalanobis distance
5.3 Calculation using R
5.4 Matrix expression of bivariate normal distribution
5.5 Calculation using R
5.6 Matrix expression of n-variate normal distribution
5.7 Classification of iris data using R
5.8 Calculation of iris data using R’s mahalanobis() function
5.9 Comparison of classified results of linear/nonlinear discriminant analyses
5.10 Comparison of classified results using predict() function
5.11 Theory of predict() function (Bayes rule)

6 Concluding Remarks