Joint Characterization of Spatiotemporal Data Manifolds
This work addresses the problem of analyzing high-dimensional spatiotemporal data for researchers in fields like climate science or imaging, but it is incremental as it combines existing methods without introducing new algorithms.
The paper tackled the challenge of characterizing spatiotemporal data manifolds by comparing linear (PCs/EOFs) and nonlinear (LE, t-SNE) dimensionality reduction methods, showing that joint use yields complementary insights into manifold topology with nonlinear methods providing more compact manifolds and reduced ambiguity.
Spatiotemporal (ST) image data are increasingly common and often high-dimensional (high-D). Modeling ST data can be a challenge due to the plethora of independent and interacting processes which may or may not contribute to the measurements. Characterization can be considered the complement to modeling by helping guide assumptions about generative processes and their representation in the data. Dimensionality reduction (DR) is a frequently implemented type of characterization designed to mitigate the "curse of dimensionality" on high-D signals. For decades, Principal Component (PC) and Empirical Orthogonal Function (EOF) analysis has been used as a linear, invertible approach to DR and ST analysis. Recent years have seen the additional development of a suite of nonlinear DR algorithms, frequently categorized as "manifold learning". Here, we explore the idea of joint characterization of ST data manifolds using PCs/EOFs alongside two nonlinear DR approaches: Laplacian Eigenmaps (LE) and t-distributed stochastic neighbor embedding (t-SNE). Starting with a synthetic example and progressing to global, regional, and field scale ST datasets spanning roughly 5 orders of magnitude in space and 2 in time, we show these three DR approaches can yield complementary information about ST manifold topology. Compared to the relatively diffuse TFS produced by PCs/EOFs, the nonlinear approaches yield more compact manifolds with decreased ambiguity in temporal endmembers (LE) and/or in spatiotemporal clustering (t-SNE). These properties are compensated by the greater interpretability, significantly lower computational demand and diminished sensitivity to spatial aliasing for PCs/EOFs than LE or t-SNE. Taken together, we find joint characterization using the three complementary DR approaches capable of greater insight into generative ST processes than possible using any single approach alone.