  Natural numerical networks are introduced as a new classification algorithm
based on the numerical solution of nonlinear partial differential equations of
forward-backward diffusion type on complete graphs. The proposed natural
numerical network is applied to open important environmental and nature
conservation task, the automated identification of protected habitats by using
satellite images. In the natural numerical network, the forward diffusion
causes the movement of points in a feature space toward each other. The
opposite effect, keeping the points away from each other, is caused by backward
diffusion. This yields the desired classification. The natural numerical
network contains a few parameters that are optimized in the learning phase of
the method. After learning parameters and optimizing the topology of the
network graph, classification necessary for habitat identification is
performed. A relevancy map for each habitat is introduced as a tool for
validating the classification and finding new Natura 2000 habitat appearances.
