5. Cancer Gene Diagnosis of Golub et al. Microarray

Golub microarray consists of 72 patients and 7,129 genes. They analyzed the microarray by various statistical methods. For example, they analyzed “marker” genes having the highest correlation with the target class-by-class separation statistics (signal-to-noise ratio), weighted votes, and SOM. Mainly, discriminant analysis is the most proper method to identify oncogenes. However, because the statistical discriminant analysis was useless at all, medical researchers had developed many methods. Our theory shows that six microarrays are LSD (MNM = 0). Method2 can decompose the microarray into many Small Matryoshka (SM) those are LSD. Then, by analyzing SM, we achieved cancer gene diagnosis by malignancy indexes. If Golub et al. validate our results, cancer gene diagnosis will be more improved. Method2 already obtained the different sets of SM in Chap. 2. In 2018, we change the number of iterations of RIP and Revised LP-OLDF in Method2 and decided the proper number of iterations as same as Alon's microarray in Chap. 4. We obtained SM by those iteration numbers. We examined the signal data made by RIP discriminant scores (RipDSs). We confirm the Revised LP-OLDF cannot find all SMs as same as Alon's microarray. Thus, we analyze only 179 SMs obtained by the RIP and examine the correlation coefficient of 179 RipDSs. We compare RatioSV of six MP-based LDFs and NM of statistical discriminant function. Then, the cluster analysis and PCA analyze signal data made by RIP and H-SVM. We propose the possibility of cancer gene diagnosis such as malignancy indexes. We propose how to find new subclasses of cancer pointed out by Golub et al. (Science 286(5439): 531–537, 1999).