Dimensionality Reduction using Elastic Measures
This addresses the issue of incorrect analysis and poor classification in machine learning for functional data, though it is incremental as it builds on existing methods.
The paper tackled the problem of dimensionality reduction for functional data by incorporating elastic metrics into t-SNE and UMAP to account for rotations, parameterization, and scale, resulting in improved F1 scores of 0.77, 0.95, and 1.00 on three benchmark shape identification datasets.
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.