Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

In discrete timed system, we may write
Wij (t+1) = Wij (t) + ∆Wij (16.1)
where ∆Wij = f (ni) f (nj) (by Hebbian learning) (16.2)
and f is the nonlinear sigmoid function, given by
f (ni) = 1/ (1+ exp (- ni)). (16.3)
The model of forgetfulness of facts can be realized in a cognitive map by a
gradual decay in weights, which may be formally written as
∆Wij = - α Wij. (16.4)
Taking into account the superposition of (16.2) and (16.4), we find
∆Wij = - αWij + f (ni) f (nj). (16.5)
The weight adaptation equation in a cognitive map may thus follow from
expression (16.1) and (16.5) and is given by
Wij (t+1) = (1 - α ) Wij + f (ni) f(nj). (16.6)
16.3 The Recall in a Cognitive Map
After the encoding is over, the recall process in a cognitive map is started. The
recall model is designed based on the concept that the next value of belief ni
of node Ni can never decrease below its current value. Further, the belief of
node Ni is influenced by the nodes Nj, when there exists signal flow from
nodes Nj to Ni. Thus formally,
ni (t+1) = ni ( t ) ∨ [ ∨ (Wij ^ nj (t)) ]. (16.7)
∀j
It may be added here that the above model is due to Pal and Konar [8]. In
Kosko’s recall model, the term ni(t) is absent from the right hand side of
expression 16.7. This means that the recall model has no memory.
16.4 Stability Analysis
For the analysis of stability of the encoding and the recall model, we use the
following properties.