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Books > Science & Mathematics > Biology, life sciences > Life sciences: general issues
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High-dimensional Microarray Data Analysis - Cancer Gene Diagnosis and Malignancy Indexes by Microarray (Hardcover, 1st ed. 2019)
Loot Price: R3,401
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High-dimensional Microarray Data Analysis - Cancer Gene Diagnosis and Malignancy Indexes by Microarray (Hardcover, 1st ed. 2019)
Expected to ship within 18 - 22 working days
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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.
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