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have the capability to learn the underlying
relationships between the inputs and outputs of a
process, without needing the explicit knowledge of
how these variables are related.
Recently, numerous applications of AANs to
estimate air temperature data have been presented,
e.g. in areas with sparse network of meteorological
stations (Snell et al., 2000); (Chronopoulos et al.,
2008) for the prediction of hourly (Tasadduq,
Rehman and Bubshait, 2002), daily (Dombayc and
Golcu, 2009) and year-round air temperature (Smith
et al., 2009) or room temperature (Mustafaraj et al.,
2011) as well as for simulating the Heat Island
(Mihalakakou et al., 2002).
In this work first we briefly present the
theoretical background of ANN methodologies
applicable to the field of air temperature time series
and spatial modeling. Next, we focus on
implementation issues and on evaluating the
accuracy of the aforementioned methodologies using
a set of metrics in the case of a specific region with
complex terrain at Chania, Crete Island, Greece. A
number of alternative Feed-forward ANN topologies
are applied in order to assess the spatial and time
series air temperature prediction capabilities in
different time horizons.
2 ANN PREDICTION MODELING
Artificial Neurons are Process Element (PE) that
attempt to simulate in a simplistic way the structure
and function of the real physical biological neurons.
A PE in its basic form can be modelled as non-liner
element that first sums its weighted inputs x
1
, x
2
, x
3
,
...x
n
(coming either from original data, or from the
output of other neurons in a neural network) and
then passes the result through an activation function
Ψ (or transfer function) according to the formula:
n
i
jjiii
wxy
1
(1)
where y
j
is the output of the artificial neuron, θ
j
is an
external threshold (or bias value) and w
ji
are the
weight of the respective input x
i
which determines
the strength of the connection from the previous
PE’s to the corresponding input of the current PE.
Depending on the application, various non-linear or
linear activation functions Ψ have been introduced
(Fausett, 1994); (Bishop, 1995) like the: signum
function (or hard limiter), sigmoid limiter, quadratic
function, saturation limiter, absolute value function,
Gaussian and hyperbolic tangent functions. Artificial
Neural Networks (ANN) are signal or information
processing systems constituted by an assembly of a
large number of simple Processing Elements, as they
have been described above. The PE of a ANN are
interconnected by direct links called connections and
cooperate to perform a Parallel Distributed
Processing in order to solve a specific computational
task, such as pattern classification, function
approximation, clustering (or categorization),
prediction (or forecasting or estimation),
optimization and control. One the main strength of
ANNs is their capability to adapt themselves by
modifying the interaction between their PE. An-
other important feature of ANNs is their ability to
automatically learn from a given set of
representative examples.
The architectures of ANNs can be classified into
two main topologies: a) Feed-forward multilayer
networks (FFANN) in which feedback connections
are not allowed and b) Feedback recurrent networks
(FBANN) in which loops exist. FFANNs are
characterized mainly as static and memory-less
systems that usually produce a response to an input
quickly (Jain et al., 1996). Most FFANNs can be
trained using a wide variety of efficient conventional
numerical methods. FBANNs are dynamic systems.
In some of them, each time an input is presented, the
ANN must iterate for a potentially long time before
it produces a response. Usually, they are more
difficult to train FBANNs compared to FFANNs.
FFANNs have been found to be very effective
and powerful in prediction, forecasting or estimation
problems (Zhang et al., 1998). Multilayer
perceptrons (MLPs) and radial basis function (RBF)
topologies are the two most commonly-used types of
FFANNs. Essentially, their main difference is the
way in which the hidden PEs combine values
coming from preceding layers: MLPs use inner
products, while RBF constitutes a multidimentional
function which depends on the distance
cxr
between the input vector x and the center c (where
denotes a vector norm) (Powell, 1987). As a
consequence, the training approaches between MLPs
and RBF based FFANN is not the same, although
most training methods for MLPs can also be applied
to RBF ANNs. In RBF FFANNs the connections of
the hidden layer are not weighted and the hidden
nodes are PEs with a RBF, however the output layer
performs simple weighted summation of its inputs,
like in the case of MLPs. One simple approach to
approximate a nonlinear function is to represent it as
a linear combination of a number of fixed nonlinear
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