[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

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case, where it is possible to distinguish M- different objects classes. The easiest
solution is the M- hyperplane construction in the values dimension, where each of
them separates one 1 class from the others. The multiclass problem is actually
the problem of resolving the one dimensional problems of . In that case
the weight vector for 1…, allows to determine the attachment of the
value vector to the class . The classification problem of the - class process can
be defined as follows:
0 0, , , 1,…, (26)
The idea of the construction of such a M -class perceptron is shown on the
picture 3.
Fig. 3. Perceptron construction for a multiclass problem
4.1 The Kesler Algorithm
In this algorithm, a methodology that is used is the developed idea of the perceptron
as a linear classifier from the dual-class to multiclass problem. As before, the
linear discrimination function with weights, 1,…, is defined for every
class of the objects. The vector of features described in the object is being
assigned to the class if:
, (27)
For all the training vectors of all classes, 1,…, are constructed 1
vectors 0 ,0 ,…, ,…, ,…,0 of a dimension 1 1. This
gives us a vector block with zero everywhere except for positions and in the
block, for which we have, respectively, vector and (for ). There is also
constructed a block weight vector ,…, . If then a natural
consequence is that 0,1,…, . This is how the linear