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order ∙
is greater than that of an algorithm of
order n
3
.
This variation significantly delay the process of
polynomial growth, reducing the cost of memory
and CPU time.
4 CASE STUDY. MODELING
ECOLOGICAL VARIABLES
USING REMOTE SENSING
DATA
Within the framework of a study of environmental
variables, the objective of the present study has been
to substitute a RBF network used as an approxima-
tion function for the ecological variables, by a RBF
structure that approximates these variables with
comparable precision, but with shorter training
times.
The study of ecological variables is a fundamen-
tal component of the environmental sciences, for
environmental impact analysis and for determining
ecological partitions in a geographical area. This
work is essentially carried out by means of costly
field surveys, which require heavy investment and
slow down the rate at which results can be obtained.
The use of satellite information to obtain the same
data comprises an effective tool that is quick and of
modest cost.
Nevertheless, there is a need to understand the
relationship between the satellite information and
the ecological variables. Studies undertaken until
now have determined the relationship between in-
formation collected by LANDSAT sensors using
RBFs, and have identified the geographical zones
that share the same values of the ecological varia-
bles. There are a good number of studies which
correlate LANDSAT information with vegetation
data; however, the correlation of this information
with ecological variables is more complex (Cruz et
al., 2010).
Two restrictions were imposed on the new meth-
od of approximation: It should yield a precision
similar to that obtained using a single RBF and
There should be an exact fit for all cases in the input
set.
One of the operative characteristics of these prob-
lems is that training sets are very large (order of tens
of thousands of vectors). In this case, training sets
containing 22000 vectors were used, each with 20
elements, obtained from LANDSAT information,
with 16000 used for training of the RBFs and 6000
for calibrating the results.
We experimented using the 25 test sets corre-
sponding to the 25 different ecological variables (out
of a total of 45 that were used in the environmental
study (Cruz et al., 2010)).
Applying the algorithm our experiment took the
following values:
1. The random partition contained 100 groups.
a) To each group, we applied the SOM, with the
following features: Topology: hexagonal,
Number of rows: 32, Number of columns: 1.
2. We obtained 32 centroids for each of the 100
SOM, yielding a total of 3, 200 centroids.
a) In the fourth step, we applied the SOM to the
3200 earlier centroids, with the following fea-
tures: Topology: hexagonal, Number of rows:
5, Number of columns: 5.
3. In this way, we obtained 25 centroids and,
therefore, 25 RBFs.
When we analize the results of the
experiment, we
can see that, while the average time of execution of
the classic training of an RBF is approximately 1
hour 30 minutes for each training, the proposed new
method gives better results, Table 1 show the result
of these experiments.
Of course, we checked that the improvement in
the training phase did not cause a deterioration of the
goodness of fit in the subsequent classification
Table 1: Results of experiments using as application field, the approximation of environmental variables 25 and the training
process described above.
Training file training1.csv training2.csv training3.csv training4.csv training5.csv
Training time 48 seconds 44 seconds 45 seconds 45 seconds 47 seconds
Training file training6.csv training7.csv training8.csv training9.csv training10.csv
Training time 43 seconds 45 seconds 45 seconds 47 seconds 46 seconds
Training file training11.csv training12.csv training13.csv training14.csv training15.csv
Training time 44 seconds 42 seconds 45 seconds 45 seconds 46 seconds
Training file training16.csv training17.csv training18.csv training19.csv training20.csv
Training time 42 seconds 45 seconds 44 seconds 44 seconds 45 seconds
Training file training21.csv training22.csv training23.csv training24.csv training25.csv
Training time 47 seconds 46 seconds 44 seconds 47 seconds 46 seconds
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