Multi-class Support Vector Machine Classification for Hyperspectral Data

A progressive two-class decision classifier (pTCDC) was developed for hyperspectral data mapping to achieve maximum class separations between each class pair. In this paper, pTCDC is tested further by comparing it with other possible ways of converting multiclass to two-class classification including one-against-all and one-to-one methods used in implementing the newly developed support vector machine classifier for remote sensing data. Experiments carried out using an AVIRIS data set are presented and the results demonstrate that pTCDC is more efficient than that of one-to-one structure and more reliable than one-again-all method. INTRODUCTION Parametric supervised classification techniques, such as Gaussian maximum likelihood, have been widely adopted for multispectral remotes sensing image classification (1). However, when the number of spectral bands is high, class data modeling presents great challenges in order to reflect the class data’s real distribution in a high dimensional feature space with a limited number of training samples. Band selection and feature extraction can be introduced as preprocessing to solve the problem. However, the selected subset of data may not be optimal for each class pair in terms of their class separability. Multistage classification has been suggested which provides flexibility in features to use and a decision rule to use at each stage. Binary decision tree is preferred structure among all the mutlistage classification due to its regularity. On the other hand, nonparametric classification method is an alternative to avoid the difficulties in estimate of class data’s statistical parameters. One of the non-parametric pixel labeling algorithm is k nearest neighbors (k-NN), which bypasses density function estimation and goes directly to a decision rule (2). In recent years, support vector machines (SVM) (3) have been introduced to remote sensing image classification (4). It is a non-parametric approach aiming at finding a decision hyperplane by maximizing the margin between the separating plane and the data. The training is performed on two classes at a time. A direct multiclass SVM training (all-together) was proposed, however, it was found low performance than converting multiclass problem to two-class classification (5). Two methods for applying Bi-SVM to M-class classification are commonly adopted. They are Oneagainst-All, which constructs SVM decision boundary to separate each class from the rest in turn, and One–to–One, which constructs SVM for each class pair. In this paper, a progressive two-class decision classifier (pTCDC, (6)) (or a Directed Acyclic Graph (DAG) (7)) developed earlier is tested and compared to One-against-All and One-to-One methods. The next section SVM classification scheme and pTCDC will be presented, followed by experiments and discussions. METHODS Figure 1 illustrates the idea of SVM classifier. It shows a scatter plot of a two-dimensional training data for two classes. SVMs aim at finding an optimal decision hyperplane that makes the distance to the closest vectors support vectors, in each side maximum. © EARSeL and Warsaw University, Warsaw 2005. Proceedings of 4th EARSeL Workshop on Imaging Spectroscopy. New quality in environmental studies. Zagajewski B., Sobczak M., Wrzesień M., (eds)