[Studies in Computational Intelligence 481] Artur Babiarz, Robert Bieda, Karol Jędrasiak, Aleksander Nawrat (auth.), Aleksander Nawrat, Zygmunt Kuś (eds.) - Vision Based Systemsfor UAV Applications (2013, Sprin

40 R. Bieda et al.
Vector is the mean vector of the elements composing a given class. The
value is the average to all classes of features variation.
The scattering matrix of inter-class
,
where is the global mean vector
(32)
(33)
The greatness of defines the average distance between given mean
vectors of given classes.
This is the form of the mixture of the matrix dispersal/scattered matrix:
(34)
Such matrix is known as the covariance matrix of the feature vectors in relation to
the global mean vector of all the analyzed classes. It can be easily shown that this
matrix can be determined using the (29) and (32) values in their form:
(35)
The Fisher ratio describing the separation degree of the classes In the feature dimension
is often defined in the following way:
(36)
The construction of the transformation matrix is based on the problem of maximizing
the ratio (36). The problem of maximizing is a classical problem of
appointing the individual value and the value of individual matrices corresponding
with them
(37)
where matrix is a diagonal matrix of which the elements on the diagonal are the
individual values of matrix:
D
λ1
0 0
0 λ 0
0 0 λl
2
=
(38)