Environmental Engineering Reference
In-Depth Information
TABLE 7.6 Summary of the training algorithm performance.
Training algorithms a
Convergence rate (%) b
Classification Accuracy c
Mean (%)
Mean iterations
Standard deviation
SGD
65460
100
77.8
2.3
GDM
65432
100
76.1
3.3
RP
805
100
76.4
2.3
CGF
1452
30
61.7
16.6
CGP
865
100
75.1
4.4
CGB
627
50
64.5
17.8
SCG
1486
100
76.1
4.5
BFG
389
0
36.8
17.8
LM
15
100
77.7
2.7
a Full names of the training algorithms are given in Table 7.2.
b The convergence rate is defined as the ratio between the number of the converged experiments and the total number of the experiments for each training
algorithm.
c The results are based on 10 experiments.
250 pixels were collected as the training data, and the training
performance was measured by the MSE.
Several network training parameters were initiated before
actually training. Specifically, the training goal was set at 0.03
in terms of MSE, the training time and iterations were infinite,
and both minimum gradient and minimum step were defined
as 1
efficiency of training algorithms (Kanellopoulos and Wilkinson,
1997; Kisi, 2007). Here, we used the average number of iterations
during the ten experiments to quantify the training efficiency
(Table 7.6).
From Table 7.6, it is clear that the training efficiency of
different algorithms varied greatly. The LM algorithm was the
most efficient. Several algorithms, such as RP, CGF, CGP, CGB,
SCG, and BFG, showed a moderate training efficiency. Both the
SGD and GDM algorithms were extremely poor in terms of the
training efficiency.
10 6 . Note that the learning rate was set as 0.01 for the
SGD algorithm or 0.02 for the GDM algorithm. The momentum
factor for the GDM algorithm was defined as 0.6. The training
process was stopped when the MSE error reached the training
goal, indicating that the training successfully converged, or when
the minimum gradient or the minimum step was met, showing
that the training failed to converge. To minimize the impacts of
the initial weights, we used each of the nine training algorithms
to train the network ten times with the above training parameters
settings. As a result, 90 network models were created, which
were further used to classify the ETM
×
7.4.3.2 Capability of convergence
The capability of convergence provides the information on how
often a training algorithm can reach the training goal. Failure
to converge usually leads to a poor classification performance.
Therefore, the capability of convergence has been considered as an
important criterion for measuring the performance of training
algorithms (Skinner and Broughton, 1995; Kanellopoulos and
Wilkinson, 1997). Here, the capability of convergencewas defined
as the rate of convergence, which is actually the ratio between the
number of the converged experiments and the total number of
the experiments by a specific algorithm (Table 7.6).
All the three back-propagation algorithms (SGD, GDM, and
RP) successfully converged in every experiment. Two of the
conjugate gradient algorithms, namely, CGP and SCG, and the
LM algorithm were also quite good in this regard. However,
the other two conjugate gradient algorithms, namely, CGF and
CGB, were quite poor in terms of their capability of conver-
gence. The BFG algorithm failed to converge in all experiments,
which may be due to the emergence of non-quadratic error
surfaces.
scene into 10 land cover
classes or subclasses which were finally merged into the six major
land use/cover classes. In total, 90 land use/cover maps were
produced.
+
7.4.3 Performance evaluation
The performance of each training algorithm was evaluated by
using the four criteria, namely, training efficiency, capability of
convergence, classification accuracy, and stability of the classifi-
cation accuracy.
7.4.3.1 Training efficiency
Different training algorithms vary in their computational inten-
sity and the time to reach the training goal. An efficient training
algorithm can considerably reduce the time cost for image classi-
fication by neural networks. Therefore, the training efficiency has
been considered as a critical criterion for examining the useful-
ness of training algorithms (Skinner and Broughton, 1995). The
number of iterations used for training is a good indicator of the
7.4.3.3 Classification accuracy
The performance of a pattern classifier is usually assessed by esti-
mating its classification accuracy. Training algorithms resulting in
a poor classification accuracy are less useful in practice. Here, we
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