and N,,,,,, representing the number of PEs in the
input, hidden, and output layers, respectively, the
geometric pyramid rule defines that:
NHidden = N Input X N output
A more general approach applied here to
determine the optimal number of hidden PEs was
to start with a small number of hidden PEs,
increasing the number of hidden PEs, and
training and testing the network performance
again. This was repeated until the error was
acceptably small, or no significant improvement
was noted. As result, a hidden layer with
twenty-two hidden PEs was adopted as the
architecture of the local BPANN.
The gating network has four hidden PEs
and two output PEs. The two gating output PEs
represent the gating output for the two local
BPANNs. The gating network controls the
competition and learns to assign different regions
of the data space to different local expert
networks. The selected training samples was
used to train the MANN. The trained MANN
was then used to classify multisource spatial
data. Three data combination cases were
considered and tested.
1. Classification of eighteen band Landsat TM
data
The above architecture was applied in the
eighteen band multispectral, multitemporal
Landsat TM data classification. During the
networking training, several ^ monitoring
procedures were applied. One was to monitor
the RMS error between the desired output and
the response of the network. The monitoring
window plots the RMS error of the output layer.
As learning progresses, the error graph should
converge to zero or asymptote near zero. The
monitoring procedure also include the network
weights distribution, in which a normalized
histogram showing the weights going into the
output layer is displayed. A normal distribution
to these weights indicates that the network is
performing well. In addition to the RMS error
and network weight, two more monitoring
procedures were added. One procedure named
Gating-Lrn was used to monitor the gating
activity during network learning. In Gating-Lrn,
the outputs of the gating network are shown on
strip chart. The outputs initially show fairly
constant graphs, but as the gating networks start
to learn to allocate responsibility to different
local networks, the graph begin to oscillate as
input data are randomly presented. The other
procedure named Gating-Rcl was used to
monitor the gating activity during network
classification. In Gating-Rcl, output of the gating
network is shown as a bar graph, each bar
corresponding to an individual local network.
For each input vector through the network, the
size of each bar shows the contribution of the
corresponding local network to the composite
output. Hyperbolic tangent transfer function was
adopted. As an experimental protocol, 100,000
iterations were adopted. The trained MANN was
then applied in the eighteen bands Landsat TM
data classification. Based on the reserved test
data, an overall classification accuracy of
93.11% was achieved. The Kappa index of
agreement indicated that a good classification
(over 80% classification accuracy) was achieved
for most of the categories.
2. Classification of nineteen-dimension TM and
transportation data
The MANN in nineteen-dimension data
classification was designed to have almost the
same architecture as the one in eighteen band
Landsat TM data classification, except that each
local BPANN network had nineteen PEs in the
input layer. The nineteen input PEs represent the
eighteen input Landsat TM band data, and one
input from the transportation data. The MANN
was trained by the same group of training data as
used in eighteen-dimension cases but also had
the transportation data involved. The same
monitoring procedures were used. The trained
MANN was applied in the nineteen-dimension
multisource spatial data classification. Based on
the reserved test data, an overall classification
accuracy of 91.27% was achieved. Visually, all
of the transportation lines appeared successfully
classified.
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