Multi-Objective Parameter Optimization in Support Vector Regression: General Formulation and Application to the Retrieval of Soil Moisture From Remote Sensing Data

This paper deals with the tuning of the free parameters of the Support Vector Regression technique used for the retrieval of geo/bio-physical variables from remotely sensed data. We propose to address this task in the framework of the multi-objective optimization. A multi-objective function is defined based on a set of two (or more) metrics (e.g., mean squared error MSE and determination coefficient R² ) that quantify from different (and sometimes competing) perspectives the goodness of a given parameter configuration. Then the metrics are jointly optimized according to the concept of Pareto optimality. This allows preserving the meaning of each metric and deriving multiple optimal solutions to the tuning problem. Each solution leads to a different optimal trade-off among the considered metrics. The main advantages of the proposed multi-objective parameter optimization approach with respect to traditional mono-objective strategies are: (1) the intrinsic improved robustness and efficiency, since multiple metrics are jointly exploited in the tuning of the free parameters of the considered regression method; and (2) the possibility to select the parameter configuration that leads to the desired trade-off among different criteria and thus best meets both the application constraints and the requirements of the specific estimation problem. The experimental analysis was focused on the challenging application domain of soil moisture retrieval from microwave remotely sensed data. The results obtained on data sets associated with two different operative conditions are very promising and show the effectiveness of the proposed approach in comparison with more traditional tuning strategies based on a single metric and its usefulness in defining estimation systems for real application domains.