New theory of discriminant analysis after R. Fisher : advanced research by the feature selection method for microarray data / Shuichi Shinmura.

Preface; Acknowledgments; Contents; Symbols; 1 New Theory of Discriminant Analysis; 1.1 Introduction; 1.1.1 Theory Theme; 1.1.2 Five Problems; 1.1.2.1 Problem 1; 1.1.2.2 Problem 2; 1.1.2.3 Problem 3; 1.1.2.4 Problem 4; 1.1.2.5 Problem 5; 1.1.2.6 Summary; 1.2 Motivation for Our Research; 1.2.1 Contribution by Fisher; 1.2.2 Defect of Fisher's Assumption for Medical Diagnosis; 1.2.3 Research Outlook; 1.2.4 Method 1 and Problem 4; 1.3 Discriminant Functions; 1.3.1 Statistical Discriminant Functions; 1.3.2 Before and After SVM; 1.3.3 IP-OLDF and Four New Facts of Discriminant Analysis

1.3.4 Revised IP-OLDF, Revised LP-OLDF, and Revised IPLP-OLDF1.4 Unresolved Problem (Problem 1); 1.4.1 Perception Gap of Problem 1; 1.4.2 Student Data; 1.5 LSD Discrimination (Problem 2); 1.5.1 Importance of This Problem; 1.5.2 Pass/Fail Determination; 1.5.3 Discrimination by Four Testlets; 1.6 Generalized Inverse Matrices (Problem 3); 1.7 K-Fold Cross-Validation (Problem 4); 1.7.1 100-Fold Cross-Validation; 1.7.2 LOO and K-Fold Cross-Validation; 1.8 Matroska Feature-Selection Method (Problem 5); 1.9 Summary; References; 2 Iris Data and Fisher's Assumption; 2.1 Introduction

2.1.1 Evaluation of Iris Data2.1.2 100-Fold Cross-Validation for Small Sample (Method 1); 2.2 Iris Data; 2.2.1 Data Outlook; 2.2.2 Model Selection by Regression Analysis; 2.3 Comparison of Seven LDFs; 2.3.1 Comparison of MNM and Eight NMs; 2.3.2 Comparison of Seven Discriminant Coefficient; 2.3.3 LINGO Program 1: Six MP-Based LDFs for Original Data; 2.4 100-Fold Cross-Validation for Small Sample Method (Method 1); 2.4.1 Four Trials to Obtain Validation Sample; 2.4.1.1 Generate Training and Validation Samples by Random Number; 2.4.1.2 20,000 Normal Random Sampling

2.4.1.3 20,000 Resampling Samples2.4.1.4 K-Fold Cross-Validation for Small Sample Method; 2.4.2 Best Model Comparison; 2.4.3 Comparison of Discriminant Coefficient; 2.5 Summary; References; 3 Cephalo-Pelvic Disproportion Data with Collinearities; 3.1 Introduction; 3.2 CPD Data; 3.2.1 Collinearities; 3.2.2 How to Find Linear Relationships in Collinearities; 3.2.3 Comparison Between MNM and Eight NMs; 3.2.4 Comparison of 95 % CI of Discriminant Coefficient; 3.3 100-Fold Cross-Validation; 3.3.1 Best Model; 3.3.2 95 % CI of Discriminant Coefficient; 3.4 Trial to Remove Collinearity

3.4.1 Examination by PCA (Alternative 2)3.4.2 Third Alternative Approach; 3.5 Summary; References; 4 Student Data and Problem 1; 4.1 Introduction; 4.2 Student Data; 4.2.1 Data Outlook; 4.2.2 Different LDFs; 4.2.3 Comparison of Seven LDFs; 4.2.4 K-Best Option; 4.2.5 Evaluation by Regression Analysis; 4.3 100-Fold Cross-Validation of Student Data; 4.3.1 Best Model; 4.3.2 Comparison of Coefficients by LINGO Program 1 and Program 2; 4.4 Student Linearly Separable Data; 4.4.1 Comparison of MNM and Nine "Diff1s"; 4.4.2 Best Model; 4.4.3 95 % CI of Discriminant Coefficient; 4.5 Summary; References