The First Discriminant Theory of Linearly Separable Data

This book deals with the first discriminant theory of linearly separable data (LSD), Theory 3, based on the four ordinary LSD of Theory 1 and 169 microarrays (LSD) of Theory 2. Furthermore, you can quickly analyze the medical data with the misclassified patients which is the true purpose of diagnoses. The author developed RIP (Optimal-linear discriminant function finding the combinatorial optimal solution) as Theory1 decades ago, which found the minimum misclassifications. RIP discriminated 63 (=26−1) models of Swiss banknote (200*6) and found the minimum LSD: basic gene set (BGS).

In Theory 2, 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), which splits microarray into many SMs. Program4 can split microarray into many BGSs. Then, the wide column-LSD (Revolution-0), such as microarray (n<p), is found to have several Matryoshka dolls, including SM up to BGS.