Authors:
- Shows how a new theory of discriminant analysis was used to solve unresolved cancer gene analysis for the first time
- Explains how high-dimensional data such as microarrays can be decomposed for genetic cancer diagnosis
- Describes how cancer gene sets included in small Matryoshkas can be separated into cancer and healthy classes
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Table of contents (10 chapters)
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Front Matter
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Back Matter
About this book
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 ratioof 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.
Many studies point out that it is difficult to separate signal and noise in a high-dimensional gene space. However, the definition of the signal is not clear. Convincing evidence is presented that LSD is a signal. Statistical analysis of the genes contained in the SM cannot provide useful information, but it shows that the discriminant score (DS) discriminated by RIP or H-SVM is easily LSD. For example, the Alon microarray has 2,000 genes which can be divided into 66 SMs. If 66 DSs are used as variables, the result is a 66-dimensional data. These signal data can be analyzed to find malignancy indicators by principal component analysis and cluster analysis.Authors and Affiliations
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Seikei University, Musashino, Japan
Shuichi Shinmura
Bibliographic Information
Book Title: High-dimensional Microarray Data Analysis
Book Subtitle: Cancer Gene Diagnosis and Malignancy Indexes by Microarray
Authors: Shuichi Shinmura
DOI: https://doi.org/10.1007/978-981-13-5998-9
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Singapore Pte Ltd. 2019
Hardcover ISBN: 978-981-13-5997-2Published: 24 May 2019
eBook ISBN: 978-981-13-5998-9Published: 14 May 2019
Edition Number: 1
Number of Pages: XXV, 419
Number of Illustrations: 131 b/w illustrations, 130 illustrations in colour
Topics: Statistics for Life Sciences, Medicine, Health Sciences, Statistical Theory and Methods, Biostatistics, Statistics for Social Sciences, Humanities, Law