A Novel Active Learning Method for Support Vector Regression to Estimate Biophysical Parameters from Remotely Sensed Images

This paper presents a novel active learning (AL) technique in the context of e-insensitive support vector regression (SVR) to estimate biophysical parameters from remotely sensed images. The proposed AL method aims at selecting the most informative and representative unlabeled samples which have maximum uncertainty, diversity and density assessed according to the SVR estimation rule. This is achieved on the basis of two consecutive steps that rely on the kernel k-means clustering. In the first step the most uncertain unlabeled samples are selected by removing the most certain ones from a pool of unlabeled samples. In SVR problems, the most uncertain samples are located outside or on the boundary of the e-tube of SVR, as their target values have the lowest confidence to be correctly estimated. In order to select these samples, the kernel k-means clustering is applied to all unlabeled samples together with the training samples that are not SVs, i.e., those that are inside the e-tube, (non-SVs). Then, clusters with non-SVs inside are rejected, whereas the unlabeled samples contained in the remained clusters are selected as the most uncertain samples. In the second step the samples located in the high density regions in the kernel space and as much diverse as possible to each other are chosen among the uncertain samples. The density and diversity of the unlabeled samples are evaluated on the basis of their clusters' information. To this end, initially the density of each cluster is measured by the ratio of the number of samples in the cluster to the distance of its two furthest samples. Then, the highest density clusters are chosen and the medoid samples closest to the centers of the selected clusters are chosen as the most informative ones. The diversity of samples is accomplished by selecting only one sample from each selected cluster. Experiments applied to the estimation of single-tree parameters, i.e., tree stem volume and tree stem diameter, show the effectiveness of the proposed technique.