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High-dimensional Microarray Data Analysis

Cancer Gene Diagnosis and Malignancy Indexes by Microarray

Authors: Shinmura, Shuichi

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  • 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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eBook $89.00
price for USA in USD (gross)
  • ISBN 978-981-13-5998-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
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  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
  • ISBN 978-981-13-5997-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

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.

About the authors

Shuichi Shinmura, Seikei University

Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook $89.00
price for USA in USD (gross)
  • ISBN 978-981-13-5998-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
  • ISBN 978-981-13-5997-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
High-dimensional Microarray Data Analysis
Book Subtitle
Cancer Gene Diagnosis and Malignancy Indexes by Microarray
Authors
Copyright
2019
Publisher
Springer Singapore
Copyright Holder
Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-13-5998-9
DOI
10.1007/978-981-13-5998-9
Hardcover ISBN
978-981-13-5997-2
Edition Number
1
Number of Pages
XXV, 419
Number of Illustrations
131 b/w illustrations, 130 illustrations in colour
Topics