Combining Support Vector Machines With a Pairwise Decision Tree

Abstract

To address the multiclass classification problem of hyperspectral data, a new method called pairwise decision tree of support vector machines (PDTSVM) is proposed. For an <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> -class problem, after training <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> - 1)/2 binary support vector machines (SVMs) for each pair of information class, PDTSVM only requires <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> - 1 binary SVMs for one classification. Based on the separability estimated by the geometric margin between two classes, binary SVMs are recursively selected by using a fast sequential forward selection. Each binary SVM is used to exclude the less-similar class. PDTSVM eliminates the wrong votes of the one-against-one method. It also has much fewer layers than other tree-based methods, which decreases accumulated errors. Tested with an 11-class problem, the results demonstrate the effectiveness of our method.