Geoscience Reference
In-Depth Information
-nu|--nu
The parameter nu of nu_SVC, one_class SVM, and nu_SVR (default: 0.5).
-eloss|--eloss
The epsilon in loss function of epsilon_SVR (default: 0.1).
-cache|--cache
Cache memory size in MB (default: 100).
-etol|--etol
The tolerance of termination criterion (default: 0.001).
-shrink|--shrink
Whether to use the shrinking heuristics (default: false).
12.5.1 The SVM Classifier
A classifier based on a support vector machine is a non-parametric supervised clas-
sifier. This means that no
apriori
assumptions are made about the underlying prob-
ability density function for each class. Instead, a SVM is based on the concept of a
decision hyperplane
7
that defines the decision boundary. It tries to find the hyper-
plane that gives the largest minimum distance to the training examples. To do this, the
SVM maximizes the margin of separation, as shown in Fig.
12.6
. The small subset
of vectors that are on the margin of the hyperplane are referred to as
support vectors
.
Cortes and Vapnik suggested a modification to the original method, by introducing
a
soft margin
(Cortes and Vapnik 1995). The idea is that mis-classified vectors are
tolerated at the cost of a penalizing function in the optimization algorithm. This cost
is one of the parameters that can tune the SVM (set with the option
-cc|--ccost
).
Another important parameter is related to the
kernel function
. This function imple-
ments the transformation
that maps a feature vector into a higher dimensional space.
The assumptions is that a linear classifier can solve a non-linear classification prob-
lem in a higher dimensional space. A popular choice for the kernel function is the
Gaussian radial basis function (the default in
pksvm
). It contains a parameter
ˆ
ʳ
,set
ʳ
with the option
-g|--gamma
. The parameters cost and
can have a significant
impact on the classification accuracy. In Sect.
12.5.4
we briefly describe how these
parameters can be optimized. More information on the functioning of a SVM and its
parameters can be found on the website of libsvm.
8
As an example, we show two examples of how to classify a raster dataset, using
a training sample in Spatialite vector format. The first example is based on the IEEE
data fusion contest of 2013. The input raster file contains both a digital surface model
and a hyperspectral image, stacked as a singlemultiband image (seeAppendixA.2.3).
The training sample, prepared with
pkextract
, contains both the class labels and
7
A hyperplane is a flat subspace of dimension n-1 within an n-dimensional space. It separates the
n-dimensional space into two half spaces (From Wikipedia).
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