Semi-supervised learning with constrained virtual support vector machines for classification of remote sensing image data

We introduce two semi-supervised models for the classification of remote sensing image data. The models are built upon the framework of Virtual Support Vector Machines (VSVM). Generally, VSVM follow a two-step learning procedure: A Support Vector Machines (SVM) model is learned to determine and extract labeled sam-ples that constitute the decision boundary with the maximum margin between thematic classes, i.e., the Support Vectors (SVs). The SVs govern the creation of so-called virtual samples. This is done by modifying, i.e., per-turbing, the image features to which a decision boundary needs to be invariant. Subsequently, the classification model is learned for a second time by using the newly created virtual samples in addition to the SVs to eventually find a new optimal decision boundary. Here, we extend this concept by (i) integrating a constrained set of semi -labeled samples when establishing the final model. Thereby, the model constrainment, i.e., the selection mechanism for including solely informative semi-labeled samples, is built upon a self-learning procedure composed of two active learning heuristics. Additionally, (ii) we consecutively deploy semi-labeled samples for the creation of semi-labeled virtual samples by modifying the image features of semi-labeled samples that have become semi-labeled SVs after an initial model run. We present experimental results from classifying two multispectral data sets with a sub-meter geometric resolution. The proposed semi-supervised VSVM models exhibit the most favorable performance compared to related SVM and VSVM-based approaches, as well as (semi-) supervised CNNs, in situations with a very limited amount of available prior knowledge, i.e., labeled samples.