  With the recent surge in big data analytics for hyper-dimensional data there
is a renewed interest in dimensionality reduction techniques for machine
learning applications. In order for these methods to improve performance gains
and understanding of the underlying data, a proper metric needs to be
identified. This step is often overlooked and metrics are typically chosen
without consideration of the underlying geometry of the data. In this paper, we
present a method for incorporating elastic metrics into the t-distributed
Stochastic Neighbor Embedding (t-SNE) and Uniform Manifold Approximation and
Projection (UMAP). We apply our method to functional data, which is uniquely
characterized by rotations, parameterization, and scale. If these properties
are ignored, they can lead to incorrect analysis and poor classification
performance. Through our method we demonstrate improved performance on shape
identification tasks for three benchmark data sets (MPEG-7, Car data set, and
Plane data set of Thankoor), where we achieve 0.77, 0.95, and 1.00 F1 score,
respectively.
