Sensitivity analysis of Gaussian process machine learning for chlorophyll prediction from optical remote sensing

Abstract

The machine learning method, Gaussian Process Regression (GPR), has lately been introduced for chlorophyll content mapping from remotely sensed data. It has been shown that GPR has outperformed other machine learning and empirical methods in accuracy, speed and stability. Moreover, GPR not only estimates the chlorophyll content, it also provides the certainty level of the prediction, allowing the assessment of additional certainty maps. However, since GPR is a non-linear kernel based regression method, the relevance of the features are not accessible directly from the weights. The main contribution of this thesis is to develop a procedure for feature sensitivity analysis in order to assign relative importance to the features. The sensitivity analysis was introduced for the predictive mean function and for the predictive variance function of the Gaussian process. Then the empirical estimates for the derived sensitivity functions were applied to a land chlorophyll dataset and to two ocean chlorophyll datasets. The sensitivity analysis revealed the most important spectral bands for land chlorophyll and for ocean chlorophyll prediction. Applying the proposed methodology to the land chlorophyll dataset discovered that bands outside the chlorophyll absorption spectrum also contribute to the prediction of chlorophyll. The results of the sensitivity analysis of the ocean chlorophyll datasets open the possibility of discriminating between Case-1 water and Case-2 water condition. The method also provides additional information through the sensitivity of the predictive variance. Thus, not only the most relevant spectral bands can be revealed, but also the stability of the variance for the feature in interest can be accessed.