[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

Recognition and Location of Objects in the Visual Field of a UAV Vision System 35
3.2 The MSE Algorithm
The idea, that is used in this algorithm, relies on estimating the parameters of the
w weight vector, which could minimize the mean square error, MSE between the
known perceptron output value, for the training set , and the value obtained from
the hyperplane described in weight W vector equation. Therefore, this problem
can be written as follows:
min
(21)
For the following quality indicator:
| | (22)
It can be also show that, the following weight vector is the solution of the above
problem:
(23)
where the matrix:
Rx
T
= =
[ 1 1] E[ x1xl
]
[ ] E[ x x ]
E x x
E x2x1 2 l
E
xx
E[ xlx1
] E[ xlxl]
(24)
Is also called a correlation matrix and in many cases it is also equal to the covariance
matrix. The vector
Yx
[ xy]
[ 1 ]
[ ]
E x y
E x y
E[ xl
y]
2
= E =
Is a cross-correlation vector between the expected output and the ((entrance)of the
learning feature vectors.
(25)
4 Classification of Objects in the Multiclass Case
The above methods describe the case of appointing the hyperplane in the problem
of the dimension separation of features of two class objects. In the described approach,
the number of objects in the works pace May, in general, be greater. This
raises the question how to take advantage of those algorithms in the multiclass