Improving the SVDD Approach to Hyperspectral Image Classification

Abstract

In recent studies, the support vector data description (SVDD) has been successfully applied to the classification of hyperspectral images. However, there is a major problem with this approach, namely, the precise setting of the Gaussian kernel width (i.e., the sigma), which is, in fact, the common limitation of kernel methods in achieving a reliable performance. Generally, the sigma is tuned for multiclass data sets through the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -fold cross validation ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> CV), a time-consuming method. To reduce the computation time in real-time applications, typically, the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> CV is used to constrain all the involved SVDD classifiers to share the same sigma. This letter presents a fast and straightforward method to estimate the sigma for each individual SVDD classifier based on statistical properties of the Gaussian kernel. To evaluate the performance of the proposed method, three frequently used hyperspectral data sets are employed. The results are then compared to the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> CV method for sigma selection, and, in addition, two direct sigma estimation methods. Preliminary results using incomplete training data suggest that the proposed method can achieve similar or better performance with faster processing times than the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> CV and also provide a significant superior performance in comparison with the direct methods.