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Optimal Discriminant Analysis (ODA)Provider: John Wiley & Sons, Ltd Content:text/plain; charset="UTF-8" TY - JOUR AU - Yarnold, Paul R. AU - Soltysik, Robert C. TI - Theoretical Distributions of Optima for Univariate Discrimination of Random Data* JO - Decision Sciences VL - 22 IS - 4 PB - Blackwell Publishing Ltd SN - 1540-5915 UR - https://dx.doi.org/10.1111/j.1540-5915.1991.tb00362.x DO - 10.1111/j.1540-5915.1991.tb00362.x SP - 739 EP - 752 KW - Discrete Programming KW - Linear Statistical Models KW - Mathematical Programming KW - and Statistical Techniques PY - 1991 ER -1.tb00362.x 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 In statistical hypothesis testing, a type I error is the mistaken rejection of an actually true null hypothesis (also known as a "false positive" finding or conclusion; example: "an innocent person is convicted"), while a type II error is the fa ...
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 (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among means. ANOVA was developed by the statistician ...
(analysis of variance) and
regression analysis In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one ...
.


See also

* Data mining *
Decision tree A decision tree is a decision support tool that uses a tree-like model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. It is one way to display an algorithm that only contains condit ...
*
Factor analysis Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors. For example, it is possible that variations in six observed ...
*
Linear classifier In the field of machine learning, the goal of statistical classification is to use an object's characteristics to identify which class (or group) it belongs to. A linear classifier achieves this by making a classification decision based on the val ...
*
Logit In statistics, the logit ( ) function is the quantile function associated with the standard logistic distribution. It has many uses in data analysis and machine learning, especially in data transformations. Mathematically, the logit is the ...
(for
logistic regression In statistics, the logistic model (or logit model) is a statistical model that models the probability of an event taking place by having the log-odds for the event be a linear function (calculus), linear combination of one or more independent var ...
) *
Machine learning Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence. Machine ...
*
Multidimensional scaling Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a dataset. MDS is used to translate "information about the pairwise 'distances' among a set of n objects or individuals" into a configurati ...
*
Perceptron In machine learning, the perceptron (or McCulloch-Pitts neuron) is an algorithm for supervised learning of binary classifiers. A binary classifier is a function which can decide whether or not an input, represented by a vector of numbers, belon ...
*
Preference regression Preference regression is a statistical technique used by marketers to determine consumers’ preferred core benefits. It usually supplements product positioning techniques like multi dimensional scaling or factor analysis and is used to create ...
*
Quadratic classifier In statistics, a quadratic classifier is a statistical classifier that uses a quadratic decision surface to separate measurements of two or more classes of objects or events. It is a more general version of the linear classifier. The classific ...
*
Statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...


References


Notes

* * * * {{cite book , author=Mika, S., date=1999 , chapter=Fisher discriminant analysis with kernels , title=Neural Networks for Signal Processing IX: Proceedings of the 1999 IEEE Signal Processing Society Workshop (Cat. No.98TH8468) , year=1999 , pages=41–48 , doi=10.1109/NNSP.1999.788121 , display-authors=etal, isbn=978-0-7803-5673-3 , citeseerx=10.1.1.35.9904 , s2cid=8473401


External links


LDA tutorial using MS Excel
which has many useful mathematical definitions. Classification algorithms de:Diskriminanzanalyse eo:Vikipedio:Projekto matematiko/Lineara diskriminanta analitiko fr:Analyse discriminante linéaire hr:Linearna analiza različitih it:Analisi discriminante nl:Discriminantanalyse ja:判別分析 pl:Liniowa analiza dyskryminacyjna ru:Дискриминантный анализ sl:Diskriminantna analiza zh:線性判別分析