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{{short description|Statistical method}}
'''Ordination''' or '''gradient analysis''', in [[multivariate analysis]], is a method complementary to [[data clustering]], and used mainly in [[exploratory data analysis]] (rather than in [[hypothesis testing]]). Ordination [[partially ordered set|orders]] objects that are characterized by values on multiple variables (multivariate objects) so that similar objects are near each other and dissimilar objects are farther from each other. Such relationships between the objects, on each of several axes (one for each variable), are then characterized numerically and/or graphically. Many ordination techniques exist, including [[principal components analysis]] (PCA), non-metric [[multidimensional scaling]] (NMDS), [[correspondence analysis]] (CA) and its derivatives ([[detrended correspondence analysis|detrended CA (DCA)]], canonical CA (CCA)), [[Bray–Curtis ordination]], and [[redundancy analysis]] (RDA), among others.
'''Ordination''' or '''gradient analysis''', in [[multivariate analysis]], is a method complementary to [[data clustering]], and used mainly in [[exploratory data analysis]] (rather than in [[hypothesis testing]]). In contrast to cluster analysis, ordination [[partially ordered set|orders]] quantities in a (usually lower-dimensional) latent space. In the ordination space, quantities that are near each other share attributes (i.e., are similar to some degree), and dissimilar objects are farther from each other. Such relationships between the objects, on each of several axes or [[Latent and observable variables|latent variables]], are then characterized numerically and/or graphically in a [[biplot]].

The first ordination method, [[principal components analysis]], was suggested by Karl Pearson in 1901.

== Methods ==
Ordination methods can broadly be categorized in eigenvector-, algorithm-, or model-based methods. Many classical ordination techniques, including principal components analysis, [[correspondence analysis]] (CA) and its derivatives ([[detrended correspondence analysis]], canonical correspondence analysis, and [[redundancy analysis]], belong to the first group).

The second group includes some distance-based methods such as non-metric [[multidimensional scaling]], and machine learning methods such as [[T-distributed stochastic neighbor embedding]] and [[nonlinear dimensionality reduction]].

The third group includes model-based ordination methods, which can be considered as multivariate extensions of [[Generalized linear model|Generalized Linear Models]].<ref>{{Cite journal |last1=Hui |first1=Francis K.C. |last2=Taskinen |first2=Sara |last3=Pledger |first3=Shirley |last4=Foster |first4=Scott D. |last5=Warton |first5=David I. |date=2015 |editor-last=O'Hara |editor-first=Robert B. |title=Model‐based approaches to unconstrained ordination |journal=Methods in Ecology and Evolution |language=en |volume=6 |issue=4 |pages=399–411 |doi=10.1111/2041-210X.12236 |issn=2041-210X |doi-access=free |s2cid=62624917}}</ref><ref>{{Cite journal |last1=Warton |first1=David I. |last2=Blanchet |first2=F. Guillaume |last3=O’Hara |first3=Robert B. |last4=Ovaskainen |first4=Otso |last5=Taskinen |first5=Sara |last6=Walker |first6=Steven C. |last7=Hui |first7=Francis K. C. |date=2015-12-01 |title=So Many Variables: Joint Modeling in Community Ecology |url=https://www.sciencedirect.com/science/article/pii/S0169534715002402 |journal=Trends in Ecology & Evolution |language=en |volume=30 |issue=12 |pages=766–779 |doi=10.1016/j.tree.2015.09.007 |issn=0169-5347 |pmid=26519235}}</ref><ref>{{Cite journal |last=Yee |first=Thomas W. |date=2004 |title=A New Technique for Maximum-Likelihood Canonical Gaussian Ordination |url=http://doi.wiley.com/10.1890/03-0078 |journal=Ecological Monographs |language=en |volume=74 |issue=4 |pages=685–701 |doi=10.1890/03-0078 |issn=0012-9615}}</ref><ref>{{Cite journal |last1=Hawinkel |first1=Stijn |last2=Kerckhof |first2=Frederiek-Maarten |last3=Bijnens |first3=Luc |last4=Thas |first4=Olivier |date=2019-02-13 |title=A unified framework for unconstrained and constrained ordination of microbiome read count data |journal=PLOS ONE |language=en |volume=14 |issue=2 |pages=e0205474 |doi=10.1371/journal.pone.0205474 |issn=1932-6203 |pmc=6373939 |pmid=30759084 |doi-access=free }}</ref> Model-based ordination methods are more flexible in their application than classical ordination methods, so that it is for example possible to include random-effects.<ref>{{Cite journal |last1=van der Veen |first1=Bert |last2=Hui |first2=Francis K. C. |last3=Hovstad |first3=Knut A. |last4=O'Hara |first4=Robert B. |date=2023 |title=Concurrent ordination: Simultaneous unconstrained and constrained latent variable modelling |journal=Methods in Ecology and Evolution |language=en |volume=14 |issue=2 |pages=683–695 |doi=10.1111/2041-210X.14035 |issn=2041-210X|doi-access=free |hdl=11250/3050891 |hdl-access=free }}</ref> Unlike in the aforementioned two groups, there is no (implicit or explicit) distance measure in the ordination. Instead, a distribution needs to be specified for the responses as is typical for statistical models. These and other assumptions, such as the assumed mean-variance relationship, can be validated with the use of residual diagnostics, unlike in other ordination methods.


==Applications==
==Applications==
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*[[Detrended correspondence analysis]]
*[[Detrended correspondence analysis]]
*[[Intrinsic dimension]]
*[[Intrinsic dimension]]
*[[Latent space]]
*{{cite journal | url = https://link.springer.com/article/10.1007/s11192-015-1744-x | doi=10.1007/s11192-015-1744-x | volume=105 | title=Methodi Ordinatio: a proposed methodology to select and rank relevant scientific papers encompassing the impact factor, number of citation, and year of publication | journal=Scientometrics | pages=2109–2135}}
*[[Latent variable model]]


== References ==
== References ==
{{Reflist}}
⚫
==Further reading==
* {{aut|Birks, H.J.B.}}, 1998. ''An Annotated Bibliography Of Canonical Correspondence Analysis And Related Constrained Ordination Methods'' 1986&ndash;1996. Botanical Institute, University of Bergen. World Wide Web: http://www.bio.umontreal.ca/Casgrain/cca_bib/index.html
* {{aut|Birks, H.J.B.}}, 1998. ''An Annotated Bibliography Of Canonical Correspondence Analysis And Related Constrained Ordination Methods'' 1986&ndash;1996. Botanical Institute, University of Bergen. World Wide Web: http://www.bio.umontreal.ca/Casgrain/cca_bib/index.html
* {{aut|Braak, C.J.F. ter & I.C. Prentice}} 1988 ''A theory of gradient analysis.'' Adv. Ecol. Res. 18:271-313.
* {{aut|Braak, C.J.F. ter & I.C. Prentice}} 1988 ''A theory of gradient analysis.'' Adv. Ecol. Res. 18:271-313.
* {{aut|Gauch, H.G.}}, Jr. 1982. ''Multivariate Analysis in Community Ecology.'' Cambridge University Press, Cambridge.
* {{aut|Gauch, H.G.}}, Jr. 1982. ''Multivariate Analysis in Community Ecology.'' Cambridge University Press, Cambridge.
* {{aut|Jongman et al.}}, 1995. ''Data Analysis in Community and Landscape Ecology.'' Cambridge University Press, Cambridge.
* {{aut|Jongman et al.}}, 1995. ''Data Analysis in Community and Landscape Ecology.'' Cambridge University Press, Cambridge.
* {{aut|Pagani et al.}}, 2015. ''Methodi Ordinatio: a proposed methodology to select and rank relevant scientific papers encompassing the impact factor, number of citation, and year of publication.'' Scientometrics, December 2015, Volume 105, Issue 3, pp 2109-2135.
* {{aut|Pagani et al.}}, 2015. ''Methodi Ordinatio: a proposed methodology to select and rank relevant scientific papers encompassing the impact factor, number of citation, and year of publication.'' Scientometrics, December 2015, Volume 105, Issue 3, pp 2109–2135.

⚫
==Further reading==
* Mike Palmer, [http://ordination.okstate.edu/ Ordination Methods for Ecologists] Botany Department of Oklahoma State University. Retrieved 15 August 2010.


== External links ==
== External links ==
#General
#General
#*http://ordination.okstate.edu/ The Ordination Web Page - Ordination Methods for Ecologists
#*http://ordination.okstate.edu/ The Ordination Web Page - Ordination Methods for Ecologists
#*https://www.davidzeleny.net/anadat-r/doku.php/en:start
#*http://userwww.sfsu.edu/~efc/classes/biol710/ordination/ordination.htm
#*https://link.springer.com/article/10.1007/s11192-015-1744-x
#*https://link.springer.com/article/10.1007/s11192-015-1744-x
#Specific Techniques
#Specific Techniques
#*http://www.statsoft.com/textbook/stcoran.html
#*http://www.statsoft.com/textbook/stcoran.html
#*http://userwww.sfsu.edu/~efc/classes/biol710/ordination/CA.htm
#*http://www.statsoft.com/textbook/stmulsca.html
#*http://www.statsoft.com/textbook/stmulsca.html
#*http://www2.chass.ncsu.edu/garson/pa765/correspondence.htm
#*http://www.statsoft.com/textbook/glosfra.html
#*http://www.statsoft.com/textbook/glosfra.html
#*https://link.springer.com/article/10.1007/s11192-015-1744-x Ordination method for articles, using year of publication, impact factor and number of citations.
#*https://link.springer.com/article/10.1007/s11192-015-1744-x Ordination method for articles, using year of publication, impact factor and number of citations.
Line 40: Line 48:
#*http://www.brodgar.com
#*http://www.brodgar.com
#*http://www.VisuMap.com
#*http://www.VisuMap.com
#*https://cran.r-project.org/web/packages/vegan/vegan.pdf R package for classical ordination methods
#*http://cc.oulu.fi/~jarioksa/softhelp/ceprog.html DECORANA
#*http://cc.oulu.fi/~jarioksa/softhelp/casvd.html Correspondence Analysis with SVD
#*https://cran.r-project.org/package=seriation R package for ordering objects
#*https://cran.r-project.org/package=seriation R package for ordering objects
#*https://cran.r-project.org/web/packages/gllvm/index.html R package for model-based ordination
#*https://cran.r-project.org/web/packages/VGAM/index.html R package for model-based ordination
#*https://cran.r-project.org/web/packages/boral/index.html R package for model-based ordination


[[Category:Dimension reduction]]
[[Category:Dimension reduction]]

Latest revision as of 16:01, 31 July 2024

Ordination or gradient analysis, in multivariate analysis, is a method complementary to data clustering, and used mainly in exploratory data analysis (rather than in hypothesis testing). In contrast to cluster analysis, ordination orders quantities in a (usually lower-dimensional) latent space. In the ordination space, quantities that are near each other share attributes (i.e., are similar to some degree), and dissimilar objects are farther from each other. Such relationships between the objects, on each of several axes or latent variables, are then characterized numerically and/or graphically in a biplot.

The first ordination method, principal components analysis, was suggested by Karl Pearson in 1901.

Methods

[edit]

Ordination methods can broadly be categorized in eigenvector-, algorithm-, or model-based methods. Many classical ordination techniques, including principal components analysis, correspondence analysis (CA) and its derivatives (detrended correspondence analysis, canonical correspondence analysis, and redundancy analysis, belong to the first group).

The second group includes some distance-based methods such as non-metric multidimensional scaling, and machine learning methods such as T-distributed stochastic neighbor embedding and nonlinear dimensionality reduction.

The third group includes model-based ordination methods, which can be considered as multivariate extensions of Generalized Linear Models.[1][2][3][4] Model-based ordination methods are more flexible in their application than classical ordination methods, so that it is for example possible to include random-effects.[5] Unlike in the aforementioned two groups, there is no (implicit or explicit) distance measure in the ordination. Instead, a distribution needs to be specified for the responses as is typical for statistical models. These and other assumptions, such as the assumed mean-variance relationship, can be validated with the use of residual diagnostics, unlike in other ordination methods.

Applications

[edit]

Ordination can be used on the analysis of any set of multivariate objects. It is frequently used in several environmental or ecological sciences, particularly plant community ecology. It is also used in genetics and systems biology for microarray data analysis and in psychometrics.

See also

[edit]

References

[edit]
  1. ^ Hui, Francis K.C.; Taskinen, Sara; Pledger, Shirley; Foster, Scott D.; Warton, David I. (2015). O'Hara, Robert B. (ed.). "Model‐based approaches to unconstrained ordination". Methods in Ecology and Evolution. 6 (4): 399–411. doi:10.1111/2041-210X.12236. ISSN 2041-210X. S2CID 62624917.
  2. ^ Warton, David I.; Blanchet, F. Guillaume; O’Hara, Robert B.; Ovaskainen, Otso; Taskinen, Sara; Walker, Steven C.; Hui, Francis K. C. (2015-12-01). "So Many Variables: Joint Modeling in Community Ecology". Trends in Ecology & Evolution. 30 (12): 766–779. doi:10.1016/j.tree.2015.09.007. ISSN 0169-5347. PMID 26519235.
  3. ^ Yee, Thomas W. (2004). "A New Technique for Maximum-Likelihood Canonical Gaussian Ordination". Ecological Monographs. 74 (4): 685–701. doi:10.1890/03-0078. ISSN 0012-9615.
  4. ^ Hawinkel, Stijn; Kerckhof, Frederiek-Maarten; Bijnens, Luc; Thas, Olivier (2019-02-13). "A unified framework for unconstrained and constrained ordination of microbiome read count data". PLOS ONE. 14 (2): e0205474. doi:10.1371/journal.pone.0205474. ISSN 1932-6203. PMC 6373939. PMID 30759084.
  5. ^ van der Veen, Bert; Hui, Francis K. C.; Hovstad, Knut A.; O'Hara, Robert B. (2023). "Concurrent ordination: Simultaneous unconstrained and constrained latent variable modelling". Methods in Ecology and Evolution. 14 (2): 683–695. doi:10.1111/2041-210X.14035. hdl:11250/3050891. ISSN 2041-210X.

Further reading

[edit]
  • Birks, H.J.B., 1998. An Annotated Bibliography Of Canonical Correspondence Analysis And Related Constrained Ordination Methods 1986–1996. Botanical Institute, University of Bergen. World Wide Web: http://www.bio.umontreal.ca/Casgrain/cca_bib/index.html
  • Braak, C.J.F. ter & I.C. Prentice 1988 A theory of gradient analysis. Adv. Ecol. Res. 18:271-313.
  • Gauch, H.G., Jr. 1982. Multivariate Analysis in Community Ecology. Cambridge University Press, Cambridge.
  • Jongman et al., 1995. Data Analysis in Community and Landscape Ecology. Cambridge University Press, Cambridge.
  • Pagani et al., 2015. Methodi Ordinatio: a proposed methodology to select and rank relevant scientific papers encompassing the impact factor, number of citation, and year of publication. Scientometrics, December 2015, Volume 105, Issue 3, pp 2109–2135.
[edit]
  1. General
  2. Specific Techniques
  3. Software
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