Consequences of the Hughes Phenomenon on Some Classification Techniques

In supervised classification, each pixel of the image is labeled as representing a particular ground cover or class, taking information provided by the training samples, since the parameters of the classifier are estimated from the training samples. This training can be established using maps, site visits, or aerial photography. As the number of spectral bands or dimensions increases, the separability of classes also increases, but so does the number of statistical parameters defining the classes. Since there are only a fixed number of training samples for deriving the statistical parameters, at some point the accuracy of the estimation must begin to decrease. An optimal value of dimensions and training samples is shown to exist in any given practical circumstance and, in general, more dimensions do not necessarily lead to better results. This paper’s aim is to evaluate the behavior of two classifiers, Mahalanobis and SVM, as the number of dimensions increase. It is done using a heuristic analysis combining different numbers of training and dimensions on both synthetic and real hyperspectral data. It shows the relationship between training and dimensionality. Several tables are presented to show the superiority of SVM over Mahalanobis classifiers based on both synthetic and real hyperspectral data. These findings demonstrate that the curse of dimensionality occurs for as few as ten dimensions for Mahalanobis; however, this phenomenon has no effect on SVM.