IEEE Geoscience and Remote Sensing Magazine - June 2013 - 20

that maximizes the margin. If the data are not linearly separable, soft margin classification with slack variables can be
used to allow mis-classification of difficult or noisy cases.
However, the most widely used approach in hyperspectral
classification is to combine soft margin classification with a
kernel trick that allows separation of the classes in a higher
dimensional space by means of a nonlinear transformation.
In other words, the SVM used with a kernel function is a
nonlinear classifier, where the nonlinear ability is included
in the kernel and different kernels lead to different types
of SVMs. The extension of SVM to the multi-class cases is
usually done by combining several binary classifiers. Two
classical procedures are the one versus the rest and the one
versus one [87].
In the following, we illustrate the performance of SVMs
(implemented using the Gaussian radial basis function
kernel) by processing a widely used hyperspectral data set
collected by the Reflective Optics Imaging Spectrographic
System (ROSIS) optical sensor over the urban area of the
University of Pavia, Italy. The flight was operated by the
Deutschen Zentrum for Luftund Raumfahrt (DLR, the German Aerospace Agency) in the framework of the HySens project, managed and sponsored by the European Commission.
The image size in pixels is 610 # 340, with very high spatial
resolution of 1.3 meters per pixel. The number of data channels in the acquired image is 103 (with spectral range from
0.43 to 0.86 nm). Fig. 11(a) shows a false color composite of

Mutual information, Bhattacharyya), or more sophisticated
class separability measures in feature space [3]. In this regard,
methods have been proposed that implement an exhaustive
search of optimal features, such as the progressive two-class
decision classifier [82]. Other advanced feature selection
strategies (e.g., using kernels) are described in [83].
B. supeRviseD clAssiFicAtion
Several techniques have been used to perform supervised
classification of hyperspectral data. For instance, in discriminant classifiers several types of discriminant functions can be applied: nearest neighbor, decision trees, linear
functions, nonlinear functions, etc. In linear discriminant
analysis (LDA) [84], a linear function is used in order to
maximize the discriminatory power and separate the available classes effectively. However, such a linear function
may not be the best choice and nonlinear strategies such as
quadratic discriminant analysis (QDA) or logarithmic discriminant analysis (LogDA) have also been used. The main
problem of these classic supervised classifiers, however, is
their sensitivity to the Hughes effect.
In this context, kernel methods such as the support vector machine (SVM) have been widely used in order to deal
effectively with the Hughes phenomenon [85], [86]. The
SVM was first investigated as a binary classifier [87]. Given
a training set mapped into an Hilbert space by some mapping, the SVM separates the data by an optimal hyperplane

Asphalt
Meadows
Gravel
Trees
Metal Sheets
Bare Soil
Bitumen
Bricks
Shadows

(a)

(b)

(c)

FIGURE 11. (a) False color composition of the ROSIS University of Pavia scene. (b) Reference map containing 9 mutually exclusive landcover classes. (c) Training set used in experiments.

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Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - June 2013
