Abstract
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).
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References
Cox DR (1958) The regression analysis of binary sequences (with discussion). J Roy Stat Soc B 20:215–242
Firth D (1993) Bias reduction of maximum likelihood estimates. Biometrika 80:27–39
Golub TR, Slonim DK, Tamayo P, Huard C, Gaasenbeek M, Mesirov JP, Coller H, Loh ML, Downing JR, Caligiuri MA, Bloomfield CD, Lander ES (1999) Molecular classification of cancer: class discovery and class prediction by gene expression monitoring. Science 286(5439):531–537
Lachenbruch PA, Mickey MR (1968) Estimation of error rates in discriminant analysis. Technometrics 10(1):11
Sall JP, Creighton L, Lehman A (2004) JMP start statistics, 3rd edn. SAS Institute Inc. USA (Shinmura S. edits Japanese version)
Schrage L (2006) Optimization modeling with LINGO. LINDO Systems Inc. (Shinmura S translates Japanese version)
Shinmura S (2010) Saiteki senkei hanbetsu kansu (The optimal linearly discriminant function). JUSE Press, Tokyo, Japan. ISBN 978-4-8171-9364-3
Shinmura S (2016a) New theory of discriminant analysis after R. Fisher. Springer, Tokyo
Shinmura S (2016b) The 100-fold cross-validation for small sample. Data Anal 2016:1–8
Shinmura S (2017) Cancer gene analysis by Singh et al. Microarray data. ISI2017:1–6
Shinmura S (2018a) Cancer gene analysis of microarray data. In: 3rd IEEE/ACIS international conference on BCD’, vol 18, pp 1–6
Shinmura S (2018b) First success of cancer gene analysis by microarrays. Biocomp’, vol 18, pp 1–7
Shipp MA, Ross KN, Tamayo P, Weng AP, Kutok JL, Aguiar RC, Gaasenbeek M, Angelo M, Reich M, Pinkus GS, Ray TS, Koval MA, Last KW, Norton A, Lister TA, Mesirov J, Neuberg DS, Lander ES, Aster JC, Golub TR (2002) Diffuse large B-cell lymphoma outcome prediction by gene-expression profiling and supervised machine learning. Nat Med 8(1): 68–74. (https://doi.org/10.1038/nm0102-6)
Vapnik V (1995) The nature of statistical learning theory. Springer
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Shinmura, S. (2019). Cancer Gene Diagnosis of Golub et al. Microarray. In: High-dimensional Microarray Data Analysis. Springer, Singapore. https://doi.org/10.1007/978-981-13-5998-9_5
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DOI: https://doi.org/10.1007/978-981-13-5998-9_5
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