Mahecha, M.D.; Martinez, A.; Lischeid, G. & Beck, E. (2007): <b>Nonlinear dimensionality reduction: Alternative ordination approaches for extracting and visualizing biodiversity patterns in tropical montane forest vegetation data</b>. <i>Ecological Informatics</i> <b>2</b>, 138-149.
Resource Description
Title:
Nonlinear dimensionality reduction: Alternative ordination approaches for extracting and visualizing biodiversity patterns in tropical montane forest vegetation data
FOR816dw ID:
424
Publication Date:
2007-08-01
License and Usage Rights:
Resource Owner(s):
Individual:
Miguel D. Mahecha
Contact:
email:
webmaster <at> tropicalmountainforest.com
Individual:
Alfredo Martinez
Contact:
email:
webmaster <at> tropicalmountainforest.com
Individual:
Gunnar Lischeid
Contact:
email:
webmaster <at> tropicalmountainforest.com
Individual:
Erwin Beck
Contact:
email:
erwin.beck <at> uni-bayreuth.de
Universitätsstr. 30
Faculty of Biology, Chemistry and Geoscience
University of Bayreuth
95440 Bayreuth
Germany
Abstract:
Ecological patterns are difficult to extract directly from vegetation data. The respective<br/>
surveys provide a high number of interrelated species occurrence variables. Since often only<br/>
a limited number of ecological gradients determine species distributions, the data might be<br/>
represented by much fewer but effectively independent variables. This can be achieved by<br/>
reducing the dimensionality of the data. Conventional methods are either limited to linear<br/>
feature extraction (e.g., principal component analysis, and Classical Multidimensional<br/>
Scaling, CMDS) or require a priori assumptions on the intrinsic data dimensionality (e.g.,<br/>
Nonmetric Multidimensional Scaling, NMDS, and self organized maps, SOM).<br/>
In this studywe explored the potential of Isometric FeatureMapping (Isomap). This new method<br/>
of dimensionality reduction is a nonlinear generalization of CMDS. Isomap is based on a<br/>
nonlinear geodesic inter-point distance matrix. Estimating geodesic distances requires one free<br/>
threshold parameter, which defines linear geometry to be preserved in the global nonlinear<br/>
distance structure.We compared Isomap to its linear (CMDS) and nonmetric (NMDS) equivalents.<br/>
Furthermore, the use of geodesic distances allowed also extending NMDS to a version that we<br/>
calledNMDS-G. In additionwe investigated a supervised Isomap variant (S-Isomap) and showed<br/>
that all these techniques are interpretable within a single methodical framework.<br/>
As an example we investigated seven plots (subdivided in 456 subplots) in different secondary<br/>
tropical montane forests with 773 species of vascular plants. A key problem for the study of<br/>
tropical vegetation data is the heterogeneous small scale variability implying large ranges of β-<br/>
diversity. The CMDS and NMDSmethods did not reduce the data dimensionality reasonably. On<br/>
the contrary, Isomap explained 95% of the data variance in the first five dimensions and provided<br/>
ecologically interpretable visualizations; NMDS-G yielded similar results. The main shortcoming<br/>
of the latterwas the high computational cost and the requirement to predefine the dimension of<br/>
the embedding space.The S-Isomap learning scheme didnot improve the Isomap variant for an<br/>
optimal threshold parameter but substantially improved the nonoptimal solutions.<br/>
We conclude that Isomap as a new ordination method allows effective representations of<br/>
high dimensional vegetation data sets. The method is promising since it does not require a<br/>
priori assumptions, and is computationally highly effective.
Literature type specific fields:
ARTICLE
Journal:
Ecological Informatics
Volume:
2
Page Range:
138-149
Publisher:
Elsevier
Metadata Provider:
Individual:
Kristin Roos
Contact:
email:
biene.tomate <at> gmx.net
Faculty of Biology, Chemistry and Geoscience
Department of Plant Physiology
Universitätsstr. 30
95440 Bayreuth
Germany
