High-Dimensional Density Estimation via SCA: An Example in the Modelling of Hurricane Tracks

TL;DR

This paper introduces a nonparametric, high-dimensional density estimation method using dimensionality reduction, inverse mapping, and verification, demonstrated on hurricane trajectory data to model tropical cyclone variability.

Contribution

It presents a novel three-part methodology combining dimensionality reduction, inverse mapping, and validation for high-dimensional density estimation, applicable to complex irregular data structures.

Findings

Effective density estimation of hurricane trajectories

Demonstrated approach captures spatial variability of tropical cyclones

Framework can be extended to include climatic variables

Abstract

We present nonparametric techniques for constructing and verifying density estimates from high-dimensional data whose irregular dependence structure cannot be modelled by parametric multivariate distributions. A low-dimensional representation of the data is critical in such situations because of the curse of dimensionality. Our proposed methodology consists of three main parts: (1) data reparameterization via dimensionality reduction, wherein the data are mapped into a space where standard techniques can be used for density estimation and simulation; (2) inverse mapping, in which simulated points are mapped back to the high-dimensional input space; and (3) verification, in which the quality of the estimate is assessed by comparing simulated samples with the observed data. These approaches are illustrated via an exploration of the spatial variability of tropical cyclones in the North Atlantic; each datum in this case is an entire hurricane trajectory. We conclude the paper with a discussion of extending the methods to model the relationship between TC variability and climatic variables.