The effect of imposing 'fractional abundance constraints' onto the multilayer perceptron for sub-pixel land cover classification

To be physically interpretable, sub-pixel land cover fractions or abundances should fulfill two constraints, the Abundance Non-negativity Constraint (ANC) and the Abundance Sum-to-one Constraint (ASC). This paper focuses on the effect of imposing these constraints onto the MultiLayer Perceptron (MLP) for a multi-class sub-pixel land cover classification of a time series of low resolution MODIS-images covering the northern part of Belgium. Two constraining modes were compared, (i) an in-training approach that uses 'softmax' as the transfer function in the MLP's output layer and (ii) a post-training approach that linearly rescales the outputs of the unconstrained MLP. Our results demonstrate that the pixel-level prediction accuracy is markedly increased by the explicit enforcement, both in-training and post-training, of the ANC and the ASC. For aggregations of pixels (municipalities), the constrained perceptrons perform at least as well as their unconstrained counterparts. Although the difference in performance between the in-training and post-training approach is small, we recommend the former for integrating the fractional abundance constraints into MLPs meant for sub-pixel land cover estimation, regardless of the targeted level of spatial aggregation.