Optimal discriminant analysis and classification tree analysis: Difference between revisions

Revision as of 21:16, 1 September 2015

Latest revision as of 15:38, 19 April 2025

(26 intermediate revisions by 11 users not shown)

Line 1:

{{No footnotes|date=September 2009}}

'''Optimal Discriminant Analysis''' ('''ODA''')<ref>Provider: John Wiley & Sons, Ltd

'''Optimal Discriminant Analysis (ODA)''' 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 >&nbsp;0 dimensions, with the one-dimensional case being referred to as UniODA and the multidimensional case being referred to as MultiODA. Classification tree analysis is a generalization of optimal discriminant analysis to non-orthogonal trees. Classification tree analysis has more recently been called "hierarchical optimal discriminant analysis". Optimal discriminant analysis and classification tree analysis may be used to find the combination of variables and cut points that best separate classes of objects or events. These variables and cut points may then be used to reduce dimensions and to then build a statistical model that optimally describes the data.

Content:text/plain; charset="UTF-8"

TY - JOUR

Optimal discriminant analysis may be thought of as a generalization of Fisher's [[linear discriminant analysis]]. Optimal discriminant analysis is an alternative to [[analysis of variance|ANOVA]] (analysis of variance) and [[regression analysis]], which attempt to express one [[dependent variable]] as a linear combination of other features or measurements. However, ANOVA and regression analysis give a dependent variable that is a numerical variable, while optimal discriminant analysis gives a dependent variable that is a class variable.

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

'''OptimalER Discriminant Analysis (ODA)'''-1.tb00362.x</ref> 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 >&nbsp;0 dimensions, with the one-dimensional case being referred to as UniODA and the multidimensional case being referred to as MultiODA. ClassificationOptimal treediscriminant analysis is aan generalization of optimal discriminant analysisalternative to non-orthogonal trees. Classification tree [[analysis hasof more recently been called "hierarchical optimal discriminantvariance|ANOVA]] (analysis". of Optimal discriminant analysisvariance) and classification tree[[regression analysis may be used to find the combination of variables and cut points that best separate classes of objects or events. These variables and cut points may then be used to reduce dimensions and to then build a statistical model that optimally describes the data]].

==See also==

Line 21 ⟶ 40:

== References ==

<references/>

== Notes ==

* {{cite book

| title=Optimal Data Analysis

|first1=Paul R.
|last1=Yarnold

|first2=Robert C.
|last2=Soltysik

|publisher=American Psychological Association

|isbn=978-1-55798-981-89

|year=2004

|url=http://books.apa.org/books.cfm?id=4316000

|access-date=2009-09-11

}}

|archive-url=https://web.archive.org/web/20081123105843/http://books.apa.org/books.cfm?id=4316000

|archive-date=2008-11-23

|url-status=dead

}}

* {{cite journal

|last=Fisher |first=R. A. |authorlink=Ronald Fisher

Line 37 ⟶ 64:

|pages=179–188

|year=1936

|id={{hdl|=2440/15227}}|doi=10.1111/j.1469-1809.1936.tb02137.x

|issue=2

|hdl-access=free

}}

* {{cite journal

* {{cite journal |last1=Martinez |first1=A. M. |last2=Kak |first2=A. C. |title=PCA versus LDA |journal=[[IEEE Transactions on Pattern Analysis and Machine Intelligence]] |volume=23 |issue=2 |pages=228&ndash;233 |year=2001 |url=http://www.ece.osu.edu/~aleix/pami01f.pdf |doi=10.1109/34.908974 }}{{Dead link|date=April 2020 |bot=InternetArchiveBot |fix-attempted=yes }}

|last1=Martinez |first1=A. M. |last2=Kak |first2=A. C.

* {{cite journalbook

|title=PCA versus LDA

|author=Mika, S.

|journal=[[IEEE Transactions on Pattern Analysis and Machine Intelligence]]

|chapter=Fisher discriminant analysis with kernels

|volume=23 |issue=2 |pages=228&ndash;233

|title=Neural Networks for Signal Processing IX: Proceedings of the 1999 IEEE Signal Processing Society Workshop (Cat. No.98TH8468)

|year=2001

|url=http://www.ece.osu.edu/~aleix/pami01f.pdf

|doi=10.1109/34.908974

}}

* {{cite journal

|author=Mika, S.|title=Fisher Discriminant Analysis with Kernels

|journal=IEEE Conference on Neural Networks for Signal Processing IX

|year=1999

|pages=41&ndash;48

|doi=10.1109/NNSP.1999.788121

|display-authors=etal}}|isbn=978-0-7803-5673-3

|url=http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.9904

|citeseerx=10.1.1.35.9904

|display-authors=etal}}

|s2cid=8473401

}}

== External links ==

*[http://people.revoledu.com/kardi/tutorial/LDA/index.html LDA tutorial using MS Excel]

*[https://web.archive.org/web/20140526130544/http://www.roguewave.com/Portalsportals/0/products/imsl-numerical-libraries/fortran-library/docs/7.0/stat/stat.htm IMSL discriminant analysis function DSCRM], which has many useful mathematical definitions.

[[Category:Multivariate statistics]]

[[Category:Statistical classification]]

[[Category:Classification algorithms]]

[[Category:Psychometrics]]

[[Category:Market research]]

[[Category:Marketing]]

[[Category:Consumer behaviour]]

[[de:Diskriminanzanalyse]]