Neural Ordinary Differential Equations for Hyperspectral Image Classification

Advances in deep learning (DL) have allowed for the development of more complex and powerful neural architectures. The adoption of deep convolutional-based architectures with residual learning [residual networks (ResNets)] has reached the state-of-the-art performance in hyperspectral image (HSI) classification. Traditionally, ResNets have been considered as stacks of discrete layers, where each one obtains a hidden state of the input data. This formulation must deal with very deep networks, which suffer from an important data degradation as they become deeper. Moreover, these complex models exhibit significant requirements in terms of memory due to the amount of parameters that need to be fine tuned. This leads to inadequate generalization and loss of accuracy. In order to address these issues, this article redesigns the ResNet as a continuous-time evolving model, where hidden representations (or states) are obtained with respect to time (understood as the depth of the network) through the evaluation of an ordinary differential equation (ODE), which is combined with a deep neural architecture. Our experimental results, conducted with four well-known HSI data sets, indicate that redefining deep networks as continuous systems through ODEs offers flexibility when processing and classifying these kinds of remotely sensed data, achieving significant performance even when a very few training samples are available.