Optimal discriminant analysis and classification tree analysis explained

Optimal Discriminant Analysis (ODA)^[1] and the related classification tree analysis (CTA) are exact statistical methods that maximize predictive accuracy. For any specific sample and exploratory or confirmatory hypothesis, optimal discriminant analysis (ODA) identifies the statistical model that yields maximum predictive accuracy, assesses the exact Type I error rate, and evaluates potential cross-generalizability. Optimal discriminant analysis may be applied to > 0 dimensions, with the one-dimensional case being referred to as UniODA and the multidimensional case being referred to as MultiODA. Optimal discriminant analysis is an alternative to ANOVA (analysis of variance) and regression analysis.

See also

• Data mining
• Decision tree
• Factor analysis
• Linear classifier
• Logit (for logistic regression)
• Machine learning
• Multidimensional scaling
• Perceptron
• Preference regression
• Quadratic classifier
• Statistics

References

1. Provider: John Wiley & Sons, LtdContent:text/plain; charset="UTF-8"

   TY - JOURAU - Yarnold, Paul R.AU - Soltysik, Robert C.TI - Theoretical Distributions of Optima for Univariate Discrimination of Random Data*JO - Decision SciencesVL - 22IS - 4PB - Blackwell Publishing LtdSN - 1540-5915UR - https://dx.doi.org/10.1111/j.1540-5915.1991.tb00362.xDO - 10.1111/j.1540-5915.1991.tb00362.xSP - 739EP - 752KW - Discrete ProgrammingKW - Linear Statistical ModelsKW - Mathematical ProgrammingKW - and Statistical TechniquesPY - 1991ER -1.tb00362.x

Notes

• Book: Optimal Data Analysis . Paul R. . Yarnold . Robert C. . Soltysik . American Psychological Association . 978-1-55798-981-9 . 2004 . 2009-09-11 . https://web.archive.org/web/20081123105843/http://books.apa.org/books.cfm?id=4316000 . 2008-11-23 . dead .
• Fisher . R. A. . Ronald Fisher . The Use of Multiple Measurements in Taxonomic Problems . . 7 . 179–188 . 1936 . 2440/15227. 10.1111/j.1469-1809.1936.tb02137.x . 2. free .
• Martinez . A. M. . Kak . A. C. . PCA versus LDA . . 23 . 2 . 228 - 233 . 2001 . 10.1109/34.908974 .
• Book: Mika, S.. 1999 . Fisher discriminant analysis with kernels . Neural Networks for Signal Processing IX: Proceedings of the 1999 IEEE Signal Processing Society Workshop (Cat. No.98TH8468) . 1999 . 41 - 48 . 10.1109/NNSP.1999.788121 . etal. 978-0-7803-5673-3 . 10.1.1.35.9904 . 8473401 .

External links

• LDA tutorial using MS Excel
• IMSL discriminant analysis function DSCRM, which has many useful mathematical definitions.