
Probabilistic
Neural Networks
209
distance between the vectors, and the weighting function is the
(unnormalized) Gaussian function:
W(z) = e~
z2 12
"
6
The number of components of the multivariate sample vector is p.
This makes σ less dependent on the dimensionality of the sample, as
discussed previously.
A special case in which computation can be reduced should be
mentioned. First, note that the squared Euclidean distance between
two vectors X and Y can be written in vector notation as
d
2
(X
9
Y) = (X-Y)-(X-Y) = X-X + Y Y - 2X-Y
η
'
Ί
In many problems, the sampled vector will always lie on the surface
of a sphere of fixed radius. In other words, th ...