Fuzzy ARTMAP Based Neurocomputational Spatial Uncertainty Measures

This paper proposes non-parametric measures for the fuzzy ARTMAP computational neural network to handle spatial uncertainty in remotely sensed imagery classification, i.e., ART Commitment (ART-C) and ART Typicality (ART-T), expressing in the first case the degree of commitment a classifier has for each class for a specific pixel, and in the second case, how typical that pixel’s reflectances are of the ones upon which the classifier was trained for each class. Results from case studies were compared against the previously developed SOM Commitment (SOM-C) and SOM Typicality (SOM-T) classifiers as well as conventional Bayesian posterior probability and Mahalanobis typicality soft classifiers. Principal Components Analysis (PCA) was used to explore the relationship between these different measures. Results indicate that ART-C and SOM-C measures express values similar to Bayesian posterior probabilies, and ART-T and SOM-T are closely related to Mahalanobis typicalities. However, the proposed neural approaches outperform the traditional methods due to their non-parametric advantage. Introduction Recently, soft classification has become an attractive means of land-cover classification from remotely-sensed imagery (Bernard et al., 1997). Conventional hard classification, which assumes that each pixel represents a homogeneous land-cover, has been widely used for land-cover mapping. In reality, a pixel may represent mixed classes or unknown patterns. The “one-pixel-one-class” method no doubt causes information loss (Wang, 1990) and fails to depict heterogeneity and variability within the pixel. Rather than forcing allocation to one class, in contrast, soft classification yields a set of images expressing information of the membership, probability, or sub-pixel mixture proportion of each land-cover class (Eastman and Laney, 2002; Foody, 1996). Soft classifiers are used not only for the potential of uncovering the proportional constituents of mixed pixels (Foody, 1999), but also for the examination of classification uncertainty (Eastman and Laney, 2002). Much effort has been directed in the last two decades to develop soft classification algorithms for remotely sensed data, which include soft outputs based on Bayesian posterior probabilities (Foody, 1992; Eastman and Laney, 2002), Mahalanobis typicalities (Foody et al., 1992), Fuzzy Set membership grades (Eastman, 2003), Linear Mixture fractions (Settle and Drake, 1993), Dempster-Shafer beliefs Fuzzy ARTMAP Based Neurocomputational Spatial Uncertainty Measures