154
T.-S. Chon . Y.S. Park· I.-S. Kwak . E.Y. Cha
The forecast of 'changes-in-density' could effectively pinpoint the shifting of
ecological status in communities (Chon et al. 2000b).
8.3.3
Fully Connected Recurrent Network
From the previous training, recurrent property in artificial neural networks was
shown to be effective in extracting information on the time development of
community. A fully connected recurrent network was further implemented for
patterning community dynamics under the scheme of real-time recurrent learning
(Willians and Zipser 1989). This real-time recurrent network (RTRN) has been
characterized as containing hidden neurons and allowing arbitrary dynamics, in
comparison with other recurrent networks such as the Hopfield network (Hopfield
1982). The RTRN is especially capable of dealing with time-varying input or
output through its own temporal operations (Haykin 1994).
The RTRN consists of N neurons with M external input connections (Fig.
8.15a). The external input vector of community data x(t) of size M is applied to
the network at a discrete time t. Lety(t) denote the corresponding vector of size N
of individual neuron outputs produced one step later at time t. The N neuron
outputs at the upper processing layer consist of M neuron outputs and (N-M)
hidden neuron outputs. The input vector x(t) and the one-step delayed output
vector y(t-l) are concatenated to form the vector u(t) of size (M+N) whose ith
element is denoted by ult) (Haykin 1994). In total, an N by (M+N) recurrent
weight matrix is formed.
The net internal activity of neuronj at time t is as follows:
(8.15)
where vP) is x/t) if j denotes the external input, and YP-l) if j denotes the
neuron for outputs. wit) is the weight between the input and the hidden layers.
At the next time step 1+1, the output of neuron j is computed by passing vP)
through the nonlinearity 11'0 (logistic function in this case), resulting in the
following (Haykin 1994):
(8.16)
The backpropagation algorithm (Rumelhart et al. 1986) was further
implemented in this study. The real time recurrent learning handles weight
feedback in the real time process and allows faster convergence in recurrent
learning. The detailed algorithm could be referred to Williams and Zipser (1989).
T.-S. Chon . Y.S. Park· I.-S. Kwak . E.Y. Cha
The forecast of 'changes-in-density' could effectively pinpoint the shifting of
ecological status in communities (Chon et al. 2000b).
8.3.3
Fully Connected Recurrent Network
From the previous training, recurrent property in artificial neural networks was
shown to be effective in extracting information on the time development of
community. A fully connected recurrent network was further implemented for
patterning community dynamics under the scheme of real-time recurrent learning
(Willians and Zipser 1989). This real-time recurrent network (RTRN) has been
characterized as containing hidden neurons and allowing arbitrary dynamics, in
comparison with other recurrent networks such as the Hopfield network (Hopfield
1982). The RTRN is especially capable of dealing with time-varying input or
output through its own temporal operations (Haykin 1994).
The RTRN consists of N neurons with M external input connections (Fig.
8.15a). The external input vector of community data x(t) of size M is applied to
the network at a discrete time t. Lety(t) denote the corresponding vector of size N
of individual neuron outputs produced one step later at time t. The N neuron
outputs at the upper processing layer consist of M neuron outputs and (N-M)
hidden neuron outputs. The input vector x(t) and the one-step delayed output
vector y(t-l) are concatenated to form the vector u(t) of size (M+N) whose ith
element is denoted by ult) (Haykin 1994). In total, an N by (M+N) recurrent
weight matrix is formed.
The net internal activity of neuronj at time t is as follows:
(8.15)
where vP) is x/t) if j denotes the external input, and YP-l) if j denotes the
neuron for outputs. wit) is the weight between the input and the hidden layers.
At the next time step 1+1, the output of neuron j is computed by passing vP)
through the nonlinearity 11'0 (logistic function in this case), resulting in the
following (Haykin 1994):
(8.16)
The backpropagation algorithm (Rumelhart et al. 1986) was further
implemented in this study. The real time recurrent learning handles weight
feedback in the real time process and allows faster convergence in recurrent
learning. The detailed algorithm could be referred to Williams and Zipser (1989).