By Shuichi Shinmura
This is the 1st booklet to check 8 LDFs through types of datasets, akin to Fisher’s iris facts, scientific info with collinearities, Swiss banknote information that could be a linearly separable information (LSD), pupil pass/fail choice utilizing pupil attributes, 18 pass/fail determinations utilizing examination ratings, jap vehicle info, and 6 microarray datasets (the datasets) which are LSD. We constructed the 100-fold cross-validation for the small pattern strategy (Method 1) rather than the john strategy. We proposed an easy version choice method to decide on the easiest version having minimal M2 and Revised IP-OLDF in line with MNM criterion used to be came across to be higher than different M2s within the above datasets.
We in comparison statistical LDFs and 6 MP-based LDFs. these have been Fisher’s LDF, logistic regression, 3 SVMs, Revised IP-OLDF, and one other OLDFs. just a hard-margin SVM (H-SVM) and Revised IP-OLDF may discriminate LSD theoretically (Problem 2). We solved the illness of the generalized inverse matrices (Problem 3).
For greater than 10 years, many researchers have struggled to research the microarray dataset that's LSD (Problem 5). If we name the linearly separable version "Matroska," the dataset comprises various smaller Matroskas in it. We enhance the Matroska characteristic choice approach (Method 2). It unearths the wonderful constitution of the dataset that's the disjoint union of a number of small Matroskas. Our thought and strategies display new proof of gene analysis.
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Extra info for New Theory of Discriminant Analysis After R. Fisher: Advanced Research by the Feature Selection Method for Microarray Data
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Jpn J Clin Oncol 36(9):570–577 Epub 2006 Aug 22 Nomura Y, Shinmura S (1978) Computer-assisted prognosis of acute myocardial infarction. MEDINFO 77, In: Shires W (ed) IFIP. North-Holland Publishing Company, The Netherland, pp 517–521 Rubin PA (1997) Solving mixed integer classification problems by decomposition. Ann Oper Res 74:51–64 Sall JP (1981) SAS regression applications. , USA. (Shinmura S. translate Japanese version) Sall JP, Creighton L, Lehman A (2004) JMP start statistics, third edition.
2. 3. 4. 6 % worse than Revised IP-OLDF. SVM1 is worse than another MP-based LDFs and logistic regression. The 95 % CI of the best discriminant coefficients is obtained. Furthermore, if we select the median of the coefficient of seven LDFs, with the exception of Fisher’s LDF, seven medians are almost the same as the trivial LDF for linearly separable models. Chapter 6: Best model of Swiss Banknote Data—Explanation 1 of Matroska Feature-selection Method (Method 2) Swiss banknote data are LSD. We find that the two-variable model, such as (X4, X6), is the minimum model that is linearly separable; we also find that 16 models, including these two variables, are linearly separable, whereas 47 other models are not linearly separable.
J Jpn Soc Comput Stat 20(1–2):59–94 Shinmura S (2010a) The optimal linearly discriminant function (Saiteki Senkei Hanbetu Kansuu). Union of Japanese Scientist and Engineer Publishing, Japan Shinmura S (2010b) Improvement of CPU time of Revised IP-OLDF using linear programming. J Jpn Soc Comput Stat 22(1):39–57 Shinmura S (2011a) Beyond Fisher’s linear discriminant analysis—new world of the discriminant analysis. ISI2011 CD-ROM, pp 1–6 Shinmura S (2011b) Problems of discriminant analysis by mark sense test data.