Cancer Gene Diagnosis of Alon’s microarray by RIP and Revised LP-OLDF

Abstract

This chapter discusses the following three points. (1) We have introduced only SMs obtained with the RIP in Chap. 2. RIP analyzed SMs by Program3’ arbitrary iteration number. In 2017, we increase the number of iterations successively from 1 and select the iteration number that the number of SM obtained is constant. Moreover, we compare two types of SMs obtained by the RIP and Revised LP-OLDF and evaluate the eight LDFs and QDF by RatioSV and the number of misclassifications (NMs). (2) The microarrays are linearly separable data (LSD). However, because the statistical discriminant functions cannot discriminate LSD theoretically, many researchers could not solve the cancer gene analysis completely from 1970 (Problem5). Moreover, the Matryoshka feature selection method (Method2) and LINGO Program3 can decompose the microarray into many SMs those are LSD. Although all SMs are small samples, many statistical methods cannot find the linear separable facts. However, RIP, Revised LP-OLDF, and H-SVM can discriminate all SMs correctly. We realized the three data made by three LDFs are signal data and reduce the high-dimensional microarray to low-dimensional signal data. (3) We propose the standard procedure for how to analyze all SMs. Specialists of gene analysis can solve the cancer gene analysis and approach the cancer gene diagnosis from the new aspect. On the other hand, statisticians recognize the difficulties of cancer gene analysis and understand the easiness of the cancer gene diagnosis by statistical methods. Statistical users can analyze many SMs those are a gift from high-dimensional data and skill-up their statistical ability to solve practical applications.