SEN en A A RATS ME
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The SCG is a learning algorithm for ANN developed from the
general conjugate gradient methods for optimization problems,
which are well suited to handle large-scale problems in an
effective way (Fletcher 1975). The SCG method makes use of
both first- and second-order information to determine the
parameters in the learning process, but Moeller uses an
approximation for the 2nd-order information.
(Pearlmutter 1994) solved the problem concerning the
computation and storage of the Hessian matrix, which is
responsible for the 2nd-order information, in a surprisingly
efficient way, resulting in a SCG learning algorithm that
presents a final convergence much quicker than the standard
backpropagation.
4. EXPERIMENTAL RESULTS
A TM/LANDSAT image composed by bands 7, 4 and 5,
respectively associated to the colors red, green and blue, was
used to test the efficiency of the proposed neural architecture
(figure 7). The image has 512x512 pixels, and it corresponds
to the crossing region of rivers Pardo and Mogi (Sao Paulo
state, Brazil, longitude 48 west and 21 south) and was taken
on August 8th of 1990 .
The SOM used in the first phase was composed of 600
neurons, geometrically distributed over a rectangular grid of 20
rows by 30 columns. The KCM obtained after the SOM
training is shown in fig.8.
The table bellow shows the training time (in seconds) for the
sequential and for the PVM parallel implementation for three
grid sizes of. SOM. The machines used for the training were
IBM POWERstation 360 workstations.
SOM sequential parallel
dimension (6 machines)
20x30 6110 2458
40x60 27300 10707
80x100 75632 26280
Table 4: SOM training time performance.
After the SOM training, 5 land cover classes were easily
identified from the generated KCM with the assistance of an
expert: nude soil, water, humid soil, growing crop and
vegetation. The samples correspondent to these classes were
selected near the corners and in the center of the KCM. Each
sample for the neural classification was composed by a 3x3
pixel window.
error backpropagation advanced
SCG
le-2 989 169
le-3 1606 239
le-4 8029 343
le-5 60625 364
le-6 542720 439
Table 5: MLP training time performance.
These samples were presented in the training of the MLP
network. The network has 12 neurons in the hidden layer and 5
neurons in the output layer, correspondent to the land cover
classes chosen for this test classification. The table 5 shows
the performance in terms of number of epochs in the training
process between the standard backpropagation learning
algorithm and the SCG algorithm with the exact computation
of second order information.
To evaluate now the classification performance of the proposed
architecture its results were compared to those obtained by the
Maximum Likelihood algorithm, a statistical classification
method widely used. The samples used for classification by
the Maximum Likelihood algorithm were 5x5 pixel windows
taken directly from the original image as is conventionally
done.
The performance classification results between both methods
are shown on table 6.
neural maximum
network likelihood
total of pixels from training 81 425
samples
nonclassified pixels 37641 48862
relative variance 0.5214 0.3747
kappa coefficient 30
Table 6: Classification performance.
First it’s shown the total of pixels from the samples that were
needed for both methods. Then two measures for evaluating
the classification performance for each method were given: the
number of nonclassified pixels and the Relative Variance
(Johnson et al. 1982). The Relative Variance describes the
percentage of variability from the original data which are
explained by the classification. In this way the bigger the
Relative Variance the better the classification.
Finally the table shows the kappa coefficient, which is a
measure of the concordance between two data sets, it’s another
commonly used parameter to evaluate the classification
accuracy of sattelite images (Rocha 1992). In this case the
kappa coefficient is used to compare two classified images,
where one image’s pixels are used as the set of reference
patterns while the other image’s pixels are the set of testing
patterns.
Figures 10 and 11 show the classified test image by the neural
architecture and by the Maximum Likelihood algorithm
respectively with the 5 land cover classes chosen.
5. CONCLUSIONS AND FUTURE WORK
The advantages of the proposed system may be better
understood taking into account that ANN classification is
commonly done by a single MLP network, where the feature
extraction task, i.e., the selection of classes and samples is
done directly from the original image by an expert. With the
modularization of the architecture, the feature extraction task
was performed by SOM, generating an auxiliary visual tool,
the Kohonen Clusters Map (KCM), which provides useful
information regarding the representativity, the distribution and
the similarity of spectral classes. It makes possible the
identification and selection by visual inspection of the spectral
classes and its respective training samples, which will be used
in the classification phase. These advantages are emphasized
120
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996
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