Gaussian mixture discriminant analysis and sub-pixel land cover characterization in remote sensing

Mixture analysis is a necessary component for capturing sub-pixel heterogeneity in the characterization of land cover from remotely sensed images. Mixture analysis approaches in remote sensing vary from conventional linear mixture models to nonlinear neural network mixture models. Linear mixture models are fairly simple and generally result in poor mixture analysis accuracy. Neural network models can achieve much higher accuracy, but typically lack interpretability. In this paper we present a mixture discriminant analysis (MDA) model for inferring land cover fractions within forest stands from Landsat Thematic Mapper images. Specifically, individual class distributions are modeled as mixtures of subclasses of Gaussian distributions, and land cover fractions are estimated using the corresponding posterior probabilities. Compared to a benchmark study on accuracy of mixture models with Plumas National Forest data, this MDA model easily outperforms traditional linear mixture models and parallels the performance of the ARTMAP neural network mixture model. In other words, the MDA model is observed to successfully combine the performance characteristics of more complex neural network models (due to the nonlinear nature of its classification rules), with the ease of interpretation associated with linear mixture models (due to its relatively simple structure). MDA models therefore offer an attractive alternative for addressing the mixture modeling problem in remote sensing.