The Most Important Knowledge by 27 Revolutionary Findings and the Outlook of This Book

Shuichi Shinmura ()

Chapter Chapter 1 in The First Discriminant Theory of Linearly Separable Data, 2024, pp 1-65 from Springer

Abstract: Abstract The author completed a new discriminant theory (Theory1) that solved four discriminant problems by RIP (Revised Optimal LDF) and two Facts in 2015. RIP finds the minimum number of misclassifications (MNM) instead of NM. MNM=0 means LSD. Fact1 explains the relationship between the LDF discriminant coefficient and NM. Fact2 explains the monotonicity of MNM. In 2015, RIP discriminated against 6 1st-generation old microarrays. Then, I found four universal data structures (Fact3) of microarrays that consisted of many small LSD, Small Matryoshka (SM), and the minimum-dimensional LSD, Basic Gene Set (BGS). In Theory2, Fact1 indicates that the discriminant theory is combinatorial, and almost all genes of microarrays became many SMs and BGSs. Fact2 explains Fact3 in Theory2. In 2022, I completed Theory2 and confirmed Fact3 by 169 microarrays. I review these results, and the six ordinary data analyzed in Theory1 from the perspective of LSD research and find surprising results in addition to Theory2. This book explains the necessary knowledge from 27 innovative revolutions about the relationship between three Facts, three Methods, and four Validations of Theory3. In this book, if you understand the usage of four Programs in Chap. 2 , you can quickly discriminate all discriminant data in addition to four ordinary LSD and 169 microarrays. Theory3 opens the new world of discriminant analyses.

Keywords: Theory1 (New Discriminant Theory after R. Fisher); RIP (Revised Optimal LDF by IP); MNM (the minimum number of misclassifications; Minimum NM); ER (Error Rate); LSD (Linearly Separable Data) defined by MNM = 0; Fact1 (the relationship between the LDF discriminant coefficient and NM); Fact2 (the monotonicity of MNM); Theory2 (High-dimensional gene data analysis); Fact3 (Four Universal Data Structures of LSD); SM (Small Matryoshka Decompositions); BGS (Basic Gene Set Decompositions); Yamanaka’s four Factors; DF Decompositions; Theory3 (Theory of LSD); CPD (Cephalo-pelvic Disproportion) with two misclassifications and two multicollinearities (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-99-9420-5_1

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DOI: 10.1007/978-981-99-9420-5_1

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