Chapter 2 . Unsupervised Artificial Neural Networks
31
of such techniques have been proposed with SOMs (Vesanto et al. 1998) and
could be tumed to good account with large ecological datasets.
With unsupervised training, the map quality cannot easily be estimated: the
SOM algorithm is not based on the minimization of a goal function. However,
several criteria have been suggested, for instance, average quantization error and
topologie al quantization error may be used to quantify topology preservation
(Hämäläinen 1994, Kraaijveld et al. 1995). For ecologieal data, the Euclidean
distance is not necessarily the only possibility, thus the use of the topographie
error • ·(Kiviluoto 1996) can be suggested. The topographie error • gives the
proportion of sampie units for whieh the first BMU and the second BMU are not
in adjacent hexagons on the map. On the forest upland dataset, • has been
computed equal to 0 - for all SUs, the first BMU and the second BMU are in two
adjacent hexagons - this is the proof of an excellent leaming process and the
achievement of a very smooth map.
.
Sometimes, in a few sites, some species abundances are not known. In such a
case, conventional clustering methods cannot be used. However, a SOM can be
computed in the following way: in step 3, if some components of SU j are missing,
the computation of the distances between S~ and each virtual unit has to be made
only with the available components. The BMU is worked out and updated with its
neighbors (eq. 2.1) using only the available components of SUj" If only a small
proportion of the components of the data vector is missing, better results are
obtained in this way than by discarding the sampie units from which components
are missing (Kaski 1997).
All the experiments have been carried out on a PC computer with an Intel
Pentium PIII-500 using MATLAB software with a pro gram file written by the
authors. Depending on the size of the input dataset, the training process can last
from a few minutes to several hours, but this process has to be carried out only
once. The U-matrix computation and the different displays last a very short time (a
few seconds).
2.5
Conclusion
We presented in this paper some ways to use SOMs for visualizing an abundance
dataset. Due to its extreme adaptability, the SOM can have a number of variants
that make it a very convenient tool for studying the ecological communities.
The SOM enhanced by the U-matrix method is an effective clustering method
including techniques to display the species abundance or abiotie variables.
The SOM is a promising approach and completes the results obtained by
classical methods of classification.
31
of such techniques have been proposed with SOMs (Vesanto et al. 1998) and
could be tumed to good account with large ecological datasets.
With unsupervised training, the map quality cannot easily be estimated: the
SOM algorithm is not based on the minimization of a goal function. However,
several criteria have been suggested, for instance, average quantization error and
topologie al quantization error may be used to quantify topology preservation
(Hämäläinen 1994, Kraaijveld et al. 1995). For ecologieal data, the Euclidean
distance is not necessarily the only possibility, thus the use of the topographie
error • ·(Kiviluoto 1996) can be suggested. The topographie error • gives the
proportion of sampie units for whieh the first BMU and the second BMU are not
in adjacent hexagons on the map. On the forest upland dataset, • has been
computed equal to 0 - for all SUs, the first BMU and the second BMU are in two
adjacent hexagons - this is the proof of an excellent leaming process and the
achievement of a very smooth map.
.
Sometimes, in a few sites, some species abundances are not known. In such a
case, conventional clustering methods cannot be used. However, a SOM can be
computed in the following way: in step 3, if some components of SU j are missing,
the computation of the distances between S~ and each virtual unit has to be made
only with the available components. The BMU is worked out and updated with its
neighbors (eq. 2.1) using only the available components of SUj" If only a small
proportion of the components of the data vector is missing, better results are
obtained in this way than by discarding the sampie units from which components
are missing (Kaski 1997).
All the experiments have been carried out on a PC computer with an Intel
Pentium PIII-500 using MATLAB software with a pro gram file written by the
authors. Depending on the size of the input dataset, the training process can last
from a few minutes to several hours, but this process has to be carried out only
once. The U-matrix computation and the different displays last a very short time (a
few seconds).
2.5
Conclusion
We presented in this paper some ways to use SOMs for visualizing an abundance
dataset. Due to its extreme adaptability, the SOM can have a number of variants
that make it a very convenient tool for studying the ecological communities.
The SOM enhanced by the U-matrix method is an effective clustering method
including techniques to display the species abundance or abiotie variables.
The SOM is a promising approach and completes the results obtained by
classical methods of classification.