Dimensionality Reduction Techniques for Visualizing Morphometric Data: Comparing Principal Component Analysis to Nonlinear Methods

Principal component analysis (PCA) is the most widely used dimensionality reduction technique in the biological sciences, and is commonly employed to create 2D visualizations of geometric morphometric data. However, interesting biological information may be lost or misrepresented in these plots due to PCA's inability to summarize nonlinear dependencies between variables. Nonlinear alternative methods exist, but their effectiveness has never been tested on morphometric data. Here, the performance of PCA on the task of visualizing morphometric variation is compared to four nonlinear techniques: Sammon Mapping, Isomap, Locally Linear Embedding, and Laplacian Eigenmaps. The performance of methods is assessed on the basis of global and local preservation of pairwise distances for a variety of simulated and empirical datasets. The relative performance of PCA varies in function of the distribution of variation, complexity, and size of datasets. Overall, nonlinear methods show superior preservation of small differences between morphologies compared to PCA.