A Graph-Based Mathematical Model for More Efficient Dimensionality Reduction of Landmark Data in Geometric Morphometrics

Abstract

Geometric Morphometrics can be used to describe morphology as a series of coordinates after the effects of variation in translation, rotation, and scale have been removed. This can be further divided into the notion of shape and form, where the latter excludes the scaling procedure from analyses. Dimensionality reduction in Geometric Morphometrics is necessary for the representation of this data into a reduced, more manageable set of dimensions, while preserving as much of the original variation as possible. The purpose of this study is to explore a new means of performing dimensionality reduction on Procrustes landmark data. Here we present a new mathematical model that can be used to enhance dimensionality reduction techniques such as Principal Component Analyses. Integrated into a new R library, the GraphGMM framework uses elements of geometric learning and graph theory to aggregate and embed (project) morphological information from Procrustes coordinates into a new set of transformed coordinates. We validate this model through the use of theoretically constructed, as well as open source, datasets. We finally present a pilot case study using great ape radii to show how these transformed landmarks efficiently capture morphological information, prior to dimensionality reduction, leading to a more efficient construction of a final representation of a morphological coordinate space. Graph-based Geometric Morphometrics thus provides a new insight into the study of morphological patterns, that can be used as an additional source of information in bioanthropological studies.