Swiss Banknote Data and CPD Data: The Essence of Discriminant Theory

We show two results of Swiss banknote data (200 * 6) and CPD (Cephalo-pelvic Disproportion) data (19 * 240) explaining the important roles of Theory3. Banknote data has 100 genuine and 100 counterfeit bills with 6 variables. We found it was LSD, and (X4, X6) were the minimum LSD (BGS). We found that 16 models, including BGS, are LSD, and the other 47 are not LSD, by Fact2 (MNMk ≥  MNM(k+1)). Thus, we started the LSD study. Program2 (tenfold CV) evaluates 63 models. M2’s 16 and 47 models range from [0, 0.4] and [0.5, 21.55]. BGS is the most compact LSD and the best model with M2 = 0. This result shows the usefulness of Program2 and BGS. CPD data has two strong multicollinearities and two misclassified patients. We can create LSD (CPD238), omitting two patients unique for CPD found by RIP. Program1 finds SM1 (18 variables). Program4 finds BGS1 (13 variables). Both models naturally exclude the multicollinearities. Program2 evaluates BGS1, SM1, and 19 variables and shows M2 increases in this order. Analyzing CPD238 is a revolutionary idea of the “case selection and variable selection methods” that no one had proposed. This new idea becomes the gospel of every discriminant data, especially every medical diagnosis.