Multi-Objective Support Vector Regression Reduces Systematic Error in Moderate Resolution Maps of Tree Species Abundance

Kasey Legaard,Aaron Weiskittel,Erin Simons-Legaard

doi:10.3390/rs12111739

Abstract

When forest conditions are mapped from empirical models, uncertainty in remotely sensed predictor variables can cause the systematic overestimation of low values, underestimation of high values, and suppression of variability. This regression dilution or attenuation bias is a well-recognized problem in remote sensing applications, with few practical solutions. Attenuation is of particular concern for applications that are responsive to prediction patterns at the high end of observed data ranges, where systematic error is typically greatest. We addressed attenuation bias in models of tree species relative abundance (percent of total aboveground live biomass) based on multitemporal Landsat and topoclimatic predictor data. We developed a multi-objective support vector regression (MOSVR) algorithm that simultaneously minimizes total prediction error and systematic error caused by attenuation bias. Applied to 13 tree species in the Acadian Forest Region of the northeastern U.S., MOSVR performed well compared to other prediction methods including single-objective SVR (SOSVR) minimizing total error, Random Forest (RF), gradient nearest neighbor (GNN), and Random Forest nearest neighbor (RFNN) algorithms. SOSVR and RF yielded the lowest total prediction error but produced the greatest systematic error, consistent with strong attenuation bias. Underestimation at high relative abundance caused strong deviations between predicted patterns of species dominance/codominance and those observed at field plots. In contrast, GNN and RFNN produced dominance/codominance patterns that deviated little from observed patterns, but predicted species relative abundance with lower accuracy and substantial systematic error. MOSVR produced the least systematic error for all species with total error often comparable to SOSVR or RF. Predicted patterns of dominance/codominance matched observations well, though not quite as well as GNN or RFNN. Overall, MOSVR provides an effective machine learning approach to the reduction of systematic prediction error and should be fully generalizable to other remote sensing applications and prediction problems.

Highlights

As forest ecosystems are pushed toward novel conditions by anthropogenic disturbance and environmental change, there is an increasing need for information on the spatial distribution and condition of forest resources as a basis for quantifying ecosystem services, evaluating and forecasting change, and planning management actions
Rather than select models with minimal systematic error from one end of the front, where small decreases in RMSESYS were associated with large increases in RMSET, we selected models from the midsection where prediction error represented more of a compromise between systematic and total error (e.g., Model 2, Figure 4c)
Algorithms that yielded the lowest total prediction error (RF and single-objective SVR (SOSVR)) produced the greatest systematic error, consistent with a strong attenuation bias arising from predictor variable uncertainty

Summary

Introduction

As forest ecosystems are pushed toward novel conditions by anthropogenic disturbance and environmental change, there is an increasing need for information on the spatial distribution and condition of forest resources as a basis for quantifying ecosystem services, evaluating and forecasting change, and planning management actions. Field data and forest inventory measurements can provide great detail at high accuracy, but are collected from a sample of small plots. Forest conditions are mapped from empirical relationships between field measurements and remote sensing data, often using some form of regression algorithm (e.g., [1,2,3,4,5,6]). A prominent source of uncertainty in predictor variables may be physical differences in measurements between field plots and image pixels [7]. Image georeferencing or registration error coupled with GPS error in plot coordinates further interferes with the physical correspondence of pixels and plots [7] Compounding these problems are differences in timing between image acquisitions and plot measurements and additional sources of predictor uncertainty associated with remote sensing platforms, instrumentation, viewing conditions, and data handling

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