Noisy Data Visualization using Functional Data Analysis

TL;DR

This paper introduces Functional Information Geometry (FIG), a novel visualization method that improves noise handling and dimensionality reduction in high-dimensional dynamical data, outperforming previous approaches like EIG.

Contribution

The paper adapts the Empirical Intrinsic Geometry framework using functional data analysis to effectively visualize noisy high-dimensional data.

Findings

Outperforms EIG in capturing true data structure

More robust to hyperparameter variations

Faster computational performance

Abstract

Data visualization via dimensionality reduction is an important tool in exploratory data analysis. However, when the data are noisy, many existing methods fail to capture the underlying structure of the data. The method called Empirical Intrinsic Geometry (EIG) was previously proposed for performing dimensionality reduction on high dimensional dynamical processes while theoretically eliminating all noise. However, implementing EIG in practice requires the construction of high-dimensional histograms, which suffer from the curse of dimensionality. Here we propose a new data visualization method called Functional Information Geometry (FIG) for dynamical processes that adapts the EIG framework while using approaches from functional data analysis to mitigate the curse of dimensionality. We experimentally demonstrate that the resulting method outperforms a variant of EIG designed for visualization in terms of capturing the true structure, hyperparameter robustness, and computational speed. We then use our method to visualize EEG brain measurements of sleep activity.