Joint Characterization of Spatiotemporal Data Manifolds

Abstract

Modeling spatiotemporal data can be a challenge due to the plethora of processes, both independent and interacting, which may or may not contribute to the measurements. Characterization can be considered a complement to modeling by helping guide assumptions about generative processes and their representation in the data. For high-D signals, Dimensionality Reduction (DR) is a frequently implemented type of characterization designed to mitigate the effects of the so-called “curse of dimensionality”. For decades, Principal Component (PC) and Empirical Orthogonal Function (EOF) analysis has been used as a linear, invertible approach to dimensionality reduction and spatiotemporal 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 spatiotemporal data manifolds using the PC/EOF approach 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 spatiotemporal datasets spanning roughly 5 orders of spatial magnitude and 2 orders of temporal magnitude, we show these three DR approaches can yield complementary information about the topology of spatiotemporal data manifolds. Compared to the PC/EOF projections, the nonlinear DR approaches yield more compact manifolds with decreased ambiguity in temporal endmembers (LE) and/or in spatiotemporal clustering (t-SNE), compared to the relatively diffuse temporal feature space produced by the PC/EOF approach. However, these properties are compensated by the greater interpretability of PCs and EOFs than of the LE or t-SNE dimensions, as well as significantly lower computational demand and diminished sensitivity to spatial aliasing for PCs/EOFs than LE or t-SNE. Taken together, we find the joint characterization using the three complementary DR approaches capable of providing substantially greater insight about the generative processes represented in spatiotemporal datasets than is possible using any single approach alone. This parsimonious, complementary characterization of both local manifold structure and global variance can advance remote sensing time series analysis by providing important context to constrain and guide design of effective spatiotemporal models.