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New Theory of Discriminant Analysis After R. Fisher - Advanced Research by the Feature Selection Method for Microarray Data (Hardcover, 1st ed. 2016)
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New Theory of Discriminant Analysis After R. Fisher - Advanced Research by the Feature Selection Method for Microarray Data (Hardcover, 1st ed. 2016)
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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.
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