Curves are complex data. Tools for visualizing, exploring, and discovering the structure
of a data set of curves are valuable. In this paper, we propose a scalable methodology to
solve this challenge. On the one hand, we consider two distances in the shape and size
space, one well-known distance and another recently proposed, which differentiate the
contribution in shape and in size of the elements considered to compute the distance.
On the other hand, we use archetypoid analysis (ADA) for the first time in elastic
shape analysis. ADA is a recent technique in unsupervised statistical learning, whose
objective is to find a set of archetypal observations (curves in this case), in such a way
that we can describe the data set as convex combinations of these archetypal curves.
This makes interpretation easy, even for non-experts. Archetypal curves or pure types
are extreme cases, which also facilitates human understanding. The methodology is
illustrated with a simulated data set and applied to a real problem. It is important to
know the distribution of foot shapes to design suitable footwear that accommodates
the population. For this purpose, we apply our proposed methodology to a real data
set composed of foot contours from the adult Spanish population.Funding for open access charge: CRUE-Universitat Jaume