Gaussianization of Earth Observation data - Invertible Transformations for Multidimensional Data Analysis

Abstract:

Remote sensing data often exhibit characteristics that are difficult to tackle with machine learning including heterogeneity, multivariate and multi-source. One of the biggest challenges of all is dealing with the curse of dimensionality; a common characteristic of Earth Observation (EO) data. This is especially problematic when trying to incorporate spatial, temporal and/or spectral information as input data streams. Gaussianization is a class of machine learning approaches that is effective in computing density estimates of your data. This framework uses a sequence of composite invertible transformations which transform data from its original domain to a base Gaussian domain.

In addition to this transformation via Gaussianization, we can also compute information theory measures (ITMs), which are particularly relevant for the analysis of Earth system data. The mean, variance and correlation provide first and second order measures and are typically used in analysis but ITMs can give higher order measures capturing more complexity and hence providing more insight on the problem at hand. In our work, we show that ITMs computed from (Rotation-Based Iterative Gaussianization) RBIG are very convenient as many ITMs can easily be computed from the actual transformation without any additional steps required.

We showcase how Gaussianization is useful in a selection of Earth observation data analysis problems including: synthesizing new data from Earth observation data, quantifying the information content across various Earth observation data, and computing similarity metrics on key land surface variables relevant for drought detection.