Geoscience Reference
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lead to different clustering results.
2
The discrimination analysis is to build
a model to assign an ungauged site to a known cluster, so that a proper
extrapolation model can be selected to estimate the specific hydrological
information. Some studies use only cluster analysis for regionalization.
4
,
5
It
is insucient to allocate an ungauged site to a known cluster. Therefore,
the discrimination analysis is necessary for regionalization.
Artificial neural network is now a popular tool to deal with massive and
complex data to derive useful information. The artificial neural network
used herein is self-organizing map (SOM) proposed by Kohonen.
6
SOM is a
competitive and unsupervised network. Mangiameli
et al
.
7
compared SOM
with other seven hierarchical clustering methods. The result of the study
shows that the performance of SOM in clustering messy data is better than
it of the other seven hierarchical clustering methods. Michaelides
et al
.
8
adopted the SOM to classify the rainfall variability to provide prototype
classes of weather variability. The result shows that SOM can detect much
more detail of rainfall variability than hierarchical clustering methods.
The purpose of this paper is to propose a simple procedure that can
classify the hydrological factors and simultaneously allocate an ungaued
site to a known cluster properly.
2. Method
SOM is known as one kind of artificial neural networks. The essential mecha-
nism of SOM is the competitive and unsupervised learning process in which
the neurons of the network compete each other to be activated. The attrac-
tive capabilities of SOM are to map the high-dimensional input patterns
into a lower-dimensional output space and to preserve the topological rela-
tions of input patterns. Readers can refer to Kohonen's
6
and Haykin's
9
topics for more details.
A fascinating feature of SOM is that the relationships of input patterns
can be stored within the network, after the training process is completed.
Since the relationships of input patterns can be stored, an SOM-based clus-
ter and discrimination analysis (SOMCD) method is proposed.
After the SOM training is done, feeding the SOM with all input patterns
that have learned by the SOM can lead to the feature map. The way to
obtain the feature map is to label all winning neurons in the output space
with the identities of corresponding input patterns.
If a neuron responds to a specific input pattern, the neuron is called
the image of the specific input pattern or the neuron is “imaged” by the
