15.3 Reducing Dimensionality

Ordinations are a popular tool in vegetation science to extract the main information, frequently corresponding to ecological gradients, from large species-plot matrices mostly filled with 0s. However, they are also used in remote sensing, the soil sciences, geomarketing and many other fields.

Resources:

Techniques:

  • Principal component analysis (PCA) is probably the most famous ordination technique. It is a great tool to reduce dimensionality if one can expect linear relationships between variables

  • However,

    • nonlinear distribution (i.e. ideal conditions for plants)
    • the joint absence of a species in two plots is hardly an indication for similarity (i.e. two species both avoiding desert conditions)

  • Non-metric multidimensional scaling (NMDS) is one popular dimension-reducing technique used in ecology (von Wehrden et al. 2009)

    • NMDS reduces the rank-based differences between the distances between objects in the original matrix and distances between the ordinated objects
    • The difference is expressed as stress
    • The lower the stress value, the better the ordination
    • Stress values lower than 10 represent an excellent fit, stress values of around 15 are still good, and values greater than 20 represent a poor fit (McCune, Grace, and Urban 2002)