process stabilises and the changes in validation error become smaller. According to our
termination criterion, training is stopped after 18,841 iterations. At this stopping point,
P, the model is used for testing (prediction).
(a) Training Set
0 5 10 15 20 25 30
Training Time in Terms of Iterations [in 1000]
(b) Validation Set
0 5 10 15 20 25 30
Training Time in Terms of Iterations [in 1000]
(c) Testing Set
0 5 10 15 20 25 30
Training Time in Terms of Iterations [in 1000]
Figure 3: Training, Validation and Testing Set Curves as a Function of Training Time
(the vertical line P indicates the stopping point): The Modular Product Unit
Neural Network for Origin Constrained Spatial Interactions
(d) Annealing Schedule
0 5 10 15 20 25 30
Training Time in Terms of Iterations [in 1000]
5.4 The Benchmark Models
The first benchmark model is the standard origin constrained gravity model, a special
case of the generic interaction model of the gravity type (see Equation (5))13:
(34)
τ grav = b r s “ d -p
ij ( i ) i j ij
with
26
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