where bii i ^ is the bias signal that can be thought as being generated by a ’dummy unit’
whose output is clamped at the scalar 1/ ti, The relation of (22) to the generic spatial
interaction model (5) becomes evident when setting x2j_1 = sj and x2j = fjj :
H
∑ ■■ hS f h
: " (v,wY = ⅛ Jh---------- j = 1,...,J (23)
∑∑ 7 ,'?h fh
1'=1 h'=1
Analogously one arrives at the modular product unit neural network for the destination
constrained case:
where b>^ j ^ is the bias signal that can be thought as being generated by a ’dummy unit’
whose output is clamped at the scalar 1/1,j. Set x2i_ 1 = r and x2j = fj then (24)
becomes
2Ol ( V, w )■ = Ьj )
H 2j
∑ yh ∏ χfhn
h=1 n =2 i-1________
I H 2 i1
∑∑Yh` ∏ xh'
i '=1 h '=1 n=2 i '-1
(24)
∑7h Гh1 jh2
:,:= J ( V, w )i= ⅛∣√⅛----------- i = 1,..., I (25)
∑∑ 7 «Гh ∙j
i,=1 h ,=1
3.4 Two Issues of Crucial Importance for Real-World Applications
Two major issues have to be addressed when applying the spatial interaction model
Ωsl in a real world context: first, the issue of finding a suitable number H of hidden
product units [the so-called representation problem], and second, the issue of network
training or learning [the so-called learning problem]. The first issue is a challenging
task because the number of hidden product units affects the generalisation performance
14
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