Overview
- Compares eight LDFs by seven different kinds of data sets from the points of view of M2 and 95% CI of the coefficient
- Presents solutions for five serious problems of discriminant analysis and finds important facts of discriminant coefficient and error rate with a new method of discriminant analysis
- Makes feature selection naturally and reveals the structure of the microarray data by the Matroska feature selection method
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: New Theory of Discriminant Analysis After R. Fisher
Book Subtitle: Advanced Research by the Feature Selection Method for Microarray Data
Authors: Shuichi Shinmura
DOI: https://doi.org/10.1007/978-981-10-2164-0
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media Singapore 2016
Hardcover ISBN: 978-981-10-2163-3Published: 06 January 2017
Softcover ISBN: 978-981-10-9546-7Published: 07 July 2018
eBook ISBN: 978-981-10-2164-0Published: 27 December 2016
Edition Number: 1
Number of Pages: XX, 208
Number of Illustrations: 3 b/w illustrations, 25 illustrations in colour
Topics: Statistical Theory and Methods, Statistics for Life Sciences, Medicine, Health Sciences, Biostatistics, Statistics for Social Sciences, Humanities, Law