Lagrange constrained neural network-based approach to hyperspectral remote sensing image classification

Lagrange constrained neural network (LCNN) was an unsupervised technique that can simultaneously estimate the endmembers and their abundance fractions in a remotely sensed image without any prior information. The network outputs corresponded to the estimated abundance fraction images (AFI), which displayed the distribution of the endmember materials in an image scene. Two constraints were universally imposed to the network outputs, one was the sum-to-one constraint and the other was the non-negativity constraint. One more data-specific constraint was to minimize the Lagrange linear estimation error vector E = /spl lambda/(As - x). Together they described the thermodynamics equilibrium of the Earth open system in the incoming and outgoing radiation fields. Thus, we adopted the thermodynamic Helmholtz free energy and seek the maximum value of a contrast function for the most likelihood solution. When such an LCNN was applied to hyperspectral remotely sensed images, the number of AFIs was equal to the number of bands because of its unbiased and unsupervised structure. So the resulting AFIs might be highly correlated and visually similar. A two-stage post-processing approach could be followed to facilitate the data assessment.