  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.
