Relevance vector machines for sparse learning of biophysical parameters

Abstract

In this communication, we evaluate the performance of the relevance vector machine (RVM) (Tipping,2000) for the estimation of biophysical parameters from remote sensing images. For illustration purposes, we focus on the estimation of chlorophyll concentrations from multispectral imagery, whose measurements are subject to high levels of uncertainty, both regarding the difficulties in ground-truth data acquisition, and when comparing <i>in situ</i> measurements against satellite-derived data. Moreover, acquired data are commonly affected by noise in the acquisition phase, and time mismatch between the acquired image and the recorded measurements, which is critical for instance for coastal water monitoring. In this context, robust and stable regressors that provide inverse models are desirable. Lately, the use of the support vector regressor (SVR) has produced good results to this end. However, the SVR has many deficiencies, which could be theoretically alleviated by the RVM. In this paper, performance of the RVM is benchmarked with SVR in terms of accuracy and bias of the estimations, sparseness of the solutions, distribution of the residuals, robustness to low number of training samples, and computational burden. In addition, some theoretical issues are discussed, such as the sensitivity to hyperparameters setting, kernel selection, and confidence intervals on the predictions. Results suggest that RVM offer an excellent compromise between accuracy and sparsity of the solution, and reveal itself as less sensitive to selection of the free parameters. Some disadvantages are also pointed, such as the unintuitive confidence intervals provided and the computational cost.