Shinmura S. High-dimensional Microarray Data Analysis: Cancer Gene Diagnosis and Malignancy Indexes by Microarray

Springer, 2019. — 437 p. — ISBN: 978-981-13-5997-2.This book shows how to decompose high-dimensional microarrays into small subspaces (Small Matryoshkas, SMs), statistically analyze them, and perform cancer gene diagnosis. The information is useful for genetic experts, anyone who analyzes genetic data, and students to use as practical textbooks.
Discriminant analysis is the best approach for microarray consisting of normal and cancer classes. Microarrays are linearly separable data (LSD, Fact 3). However, because most linear discriminant function (LDF) cannot discriminate LSD theoretically and error rates are high, no one had discovered Fact 3 until now. Hard-margin SVM (H-SVM) and Revised IP-OLDF (RIP) can find Fact3 easily. LSD has the Matryoshka structure and is easily decomposed into many SMs (Fact 4). Because all SMs are small samples and LSD, statistical methods analyze SMs easily. However, useful results cannot be obtained. On the other hand, H-SVM and RIP can discriminate two classes in SM entirely. RatioSV is the ratio of SV distance and discriminant range. The maximum RatioSVs of six microarrays is over 11.67%. This fact shows that SV separates two classes by window width (11.67%). Such easy discrimination has been unresolved since 1970. The reason is revealed by facts presented here, so this book can be read and enjoyed like a mystery novel.New Theory of Discriminant Analysis and Cancer Gene Analysis
Overview of Cancer Gene Diagnosis
Cancer Gene Diagnosis of Alon’s microarray by RIP and Revised LP-OLDF
Further Examinations of SMs — Defect of Revised LP-OLDF and Correlations of Genes
Cancer Gene Diagnosis of Golub et al. Microarray
Cancer Gene Diagnosis of Shipp et al. Microarray
Cancer Gene Diagnosis of Singh et al. Microarray
Cancer Gene Diagnosis of Tian et al. Microarray
Cancer Gene Diagnosis of Chiaretti et al. Microarray
LINGO Programs of Cancer Gene Analysis