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8: Stefan A. Robila, Pramod K. Varshney
Let us define Vas:
(8.1I)
We proceed with the computation of the gradient:
aE {log (p(u))} _ aE {log (Jde~~!vT)) }
aw
aw
aE {log (p(x)) } aE {log (J det (WWT)) }
aw
aw
=
aE {log (Jdet(V)) }
aw
a log ( Jdet(V))
aw
1 a log (det(V))
2
aw
1
1 a det(V)
- - -
2 det(V) aw
(8.12)
We compute the gradient for each of the elements Wij. Let Vit denote the
determinant of the (m - I) x (m - I) matrix obtained by eliminating the line
i and the column t from the matrix V = WW T • Then, we can express the
determinant of V using the co factors associated with the elements in the line i: