The First Discriminant Theory of Linearly Separable Data

This book deals with the first discriminant theory of linearly separable data (LSD), Theory3, based on the four ordinary LSD of Theory1 and 169 microarrays (LSD) of Theory2. Furthermore, you can quickly analyze the medical data with the misclassified patients which is the true purpose of diagnoses. Author developed RIP (Optimal-linear discriminant function finding the combinatorial optimal solution) as Theory1 in decades ago, that found the minimum misclassifications. RIP discriminated 63 (=2 6 1) models of Swiss banknote (200*6) and found the minimum LSD: basic gene set (BGS).

In Theory2, RIP discriminated Shipp microarray (77*7129) which was LSD and had only 32 nonzero coefficients (first Small Matryoshka; SM1). Because RIP discriminated another 7,097 genes and found SM2, the author developed the Matryoshka feature selection Method 2 (Program 3), that splits microarray into many SMs. Program4 can split microarray into many BGSs. Then, the wide columnLSD (Revolution-0), such as microarray (n5 ) models, including BGS, become LSD among (2 19 1) models. Because Program2 confirms BGS has the minimum average error rate, BGS is the most compact and best model satisfying Occam's Razor.

With this book, physicians obtain complete diagnostic results for disease, and engineers can become a true data scientist, by obtaining integral knowledge ofstatistics and mathematical programming with simple programs.

Helps physicians obtain complete diagnostic results for cancer Helps teachers and engineers evaluate and solve pass/fail determinants Integrates knowledge of statistics and mathematical programming with simple programs

Autorentext
Shuichi Shinmura is Emeritus Professor in Seikei University, Tokyo. His publication includes "High-dimensional Microarray Data Analysis: Cancer Gene Diagnosis and Malignancy Indexes by Microarray" (Springer Nature 2019) and "New Theory of Discriminant Analysis After R. Fisher: Advanced Research by the Feature Selection Method for Microarray Data" (Springer 2017).

Inhalt

The most important knowledge by 27 Revolutionary Findings and the Outlook of this book.- LINGO Programs Usage and New Facts by Iris Data.- Swiss banknote data and CPD data.- Test Pass/Fail Judgment and Japanese Compact Cars and Regular Cars.- First Theory of Cancer Gene Data Analysis by 169 Microarrays: Four Universal Data Structures of Discriminant Data.- Three Important Studies for Cancer Gene Diagnosis.- Two-Step Practical Screening Method for Cancer Gene Diagnoses: Multivariate Oncogenes among 169 Microarrays.