New Theory of Discriminant Analysis After R. Fisher

1. Front Matter

   Pages i-xx

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2. New Theory of Discriminant Analysis

   • Shuichi Shinmura

   Pages 1-35

3. Iris Data and Fisher’s Assumption

   • Shuichi Shinmura

   Pages 37-55

4. Cephalo-Pelvic Disproportion Data with Collinearities

   • Shuichi Shinmura

   Pages 57-80

5. Student Data and Problem 1

   • Shuichi Shinmura

   Pages 81-98

6. Pass/Fail Determination Using Examination Scores

   • Shuichi Shinmura

   Pages 99-115

7. Best Model for Swiss Banknote Data

   • Shuichi Shinmura

   Pages 117-138

8. Japanese-Automobile Data

   • Shuichi Shinmura

   Pages 139-161

9. Matroska Feature-Selection Method for Microarray Dataset (Method 2)

   • Shuichi Shinmura

   Pages 163-189

10. LINGO Program 2 of Method 1

    • Shuichi Shinmura

    Pages 191-204

11. Back Matter

    Pages 205-208

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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.

• Comparison of Eight LDFs
• Model Selection by Best Model
• 100-fold Cross Validation for Small Sample Method
• Matroska Feature Selection Method for Microarray Data
• Simple Structure of Microarray Data

• Faculty of Economics, Seikei University, Musashinoshi, Japan

  Shuichi Shinmura

Shuichi Shinmura, Seikei University

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