Cite as:
Mahecha, M.D.; Martinez, A.; Lischeid, G. &amp; 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
Individual: Alfredo Martinez
Individual: Gunnar Lischeid
Individual: Erwin Beck
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 &#946;-<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:
Journal: Ecological Informatics
Volume: 2
Page Range: 138-149
Publisher: Elsevier
Metadata Provider:
Individual: Kristin Roos
Online Distribution:
Download File:

Quick search

  • Publications:
  • Datasets: