Fisher Discriminant Analysis for Extracting Interpretable Phenological Information From Multivariate Time Series Data

This article explores the use of Fisher discriminant analysis (FDA) as a method for extracting time-resolved information from multivariate environmental time series data. FDA is useful because it can be applied to multivariate input data and produces a transformation that is physically interpretable. This article contains both theoretical and applied components. First, we use FDA to demonstrate the time dependence of information contained in remotely sensed data. Where curve-fitting and other commonly used data transformations are sensitive to variation throughout a full time series, we show how FDA identifies application-relevant variation in specific variables at specific points in time. Next, we apply FDA to estimate county-average corn planting dates in the U.S. corn belt. We find that using multivariate data inputs can reduce prediction root mean squared error (RMSE, in days) by 20% relative to models using only univariate inputs. We also compare FDA (which is linear) to nonlinear planting date estimation models based on curve-fitting and random forest (RF) estimators. We find that multivariate FDA models significantly improve on univariate curve-fitting and have comparable performance when using the same univariate inputs despite the linearity of FDA. We also find that FDA-based approaches have lower RMSE than RF in all configurations. Finally, we interpret FDA coefficients for individual measurements sensitive to vegetation density, land surface temperature, and soil moisture by relating them to physical mechanisms indicative of earlier or later planting.