Dimensionality Reduction using Elastic Measures

TL;DR

This paper introduces a novel approach to dimensionality reduction by integrating elastic metrics into t-SNE and UMAP, improving shape classification in functional data by considering geometric properties.

Contribution

The paper presents a new method that incorporates elastic metrics into existing dimensionality reduction techniques, enhancing analysis of functional data with geometric considerations.

Findings

Improved shape identification accuracy on benchmark datasets

Achieved high F1 scores of 0.77, 0.95, and 1.00

Demonstrated the importance of geometric-aware metrics in data analysis

Abstract

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.