Student Data and Problem 1

Student data consist of 40 students with six variables, which are the study hours per day (X1), spending money per month (X2), drinking days per week (X3), gender (X4), smoking (X5), and examination scores (X6). The amount of data is not large. We published four statistical books on SAS, SPSS, Statistica, and JMP using these data because the reader could easily understand the meaning of variables and data. Although we never believed the data would be helpful for our research, we discriminated the data after we completed analysis of the Iris, CPD, and random number data in 1999. When we discriminated these data using five variables with 70 points as the passing mark, we found a defect in IP-OLDF. Because four numerical variables are integer values and two variables are the binary integers 0/1, and there are many overlapping cases, the obtained vertex of convex polyhedron (CP)Convex polyhedron (CP) consists of over (p + 1) cases and the obtained solution is not true MNM. Although we recognized Problems 1 and 4 before 1980, we did not realize that Problem 1Problem 1 causes a defect in IP-OLDF. By the scatter plotScatter plot of two variables, as indicated in Table 1.1 , we found that the reason for the defect in IP-OLDF is the result of Problem 1. However, we could not revise this problem until 2006, when Revised IP-OLDF solved Problem 1Problem 1 completely. In 2004, IP-OLDF found that Swiss banknote data are LSD, and no LDFs, with the exception of Revised IP-OLDFRevised IP-OLDF and H-SVM, could discriminate LSD theoretically (Problem 2Problem 2 ). In 2005, we were able to validate the discrimination of original data (the training sample) by 20,000 resampling samples (the validation sample). After 2006, we could compare six MP-based LDFs and two statistical LDFs. After 2009, we developed the 100-fold cross-validation for small sample method (the Method 1). The Method 1 solves Problem 4Problem 4 , and the best model provides clear evaluation of eight LDFs. Although we could not explain the usefulUseful meaning of 95 % CI of the coefficient, we completed the basic research in 2010. After 2010, applied research started on LSD discrimination using the pass/fail determination that employs examination scores. We find Problem 3Problem 3 that was solved in 2013. In 2015, the applied research was completed because we could successfully explain the useful meaning of 95 % CI of the coefficient, and the TheoryThe theory Method 1 solved Problem 4 completely. In October 2015, a young researcher, Ishii, presented the challenging results of microarray datasets using principal component analysis (PCA). Because the researcher indicated six microarray datasets on HP ( http://www.bioinf.ucd.ie/people/ian/ ), we developed the Matroska feature-selection method (Method 2) within 41 days. For more than ten years, many researchers have struggled to analyze microarray datasets because the datasetsThe dataset consist of few cases with huge genes (Problem 5Problem 5 ). The TheoryThe theory is most suitable for Problem 5Problem 5 . Recently, many researchers have expected LASSO to solve Problem 5. Because Revised IP-OLDF selects features naturally, they should compare their results to ours through the Swiss banknote data, Japanese-automobile data, Student linearly separable data, and six microarray datasets. Such comparison should be helpful for LASSO research.