Ordination with any dissimilarity measure: a weighted Euclidean solution

Area of Science:

• Ecology
• Multivariate Statistics
• Bioinformatics

Background:

• Classical ordination methods rely on Euclidean distance variants for sample comparison.
• Techniques like principal component analysis and correspondence analysis use specific distance measures.
• Extending these methods to non-Euclidean dissimilarities presents a challenge.

Purpose of the Study:

• To propose a method for extending Euclidean-based ordination to non-Euclidean or nonmetric dissimilarities.
• To preserve the advantages of classical ordination while accommodating broader dissimilarity measures.
• To introduce a novel approach for ecological data analysis.

Main Methods:

• Estimation of a weighted Euclidean distance to approximate given dissimilarities.
• Application of this weighted distance within existing ordination frameworks.
• Utilizing species weights derived from the estimation process.

Main Results:

• The proposed method successfully extends Euclidean ordination to non-Euclidean dissimilarities.
• Estimated species weights provide insights into species contributions to dissimilarity.
• Weights close to zero can facilitate variable selection in ordination.
• The method maintains species-based dimensionality, avoiding sample-size dependent increases.

Conclusions:

• The weighted Euclidean distance offers a flexible extension to classical ordination techniques.
• This approach enhances interpretability by providing species weights.
• It offers a robust solution for analyzing ecological community data with diverse dissimilarity structures.