[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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38 R. Bieda et al. In the case of the MSE algorithm, the solution to the problem of finding then vectors od the weight vectors described in perceptrons is always possible if only the correlation matrix is reversible. In the case of the MSE algorithm, the linear separation assumption is not essentials in individual classes , 1,… the features’ dimension. However, if the given assumption is not fulfilled there is no guarantee that the obtained vector will make it possible to correctly classify all the training vectors. What follows is that the value of the vector (4) will always be more than zero. Sample results of the classification of the objects based on the multiclass perceptron are shown on picture 5. a. b. c. d. ( ω1 -red, ω2 -green, ω3 -blue, ω4 -baby blue) Fig. 5. The result of the object classification with the usage of the perceptron : a. analyzed picture, b. the result for the perceptron trained on the Rosenblatt algorithm, c. the result for the perceptron trained on the Kesler algorithm, d. the result for the perceptron trained on the MSE algorithm. 6 Reduction of the Features Dimension One of the stages of designing a classifier is often the extraction or feature selection. This process is designed to minimize the number of features in the vector that is described in the object. Very often, the information contained in the selected is in excess, and the values ,that describe different object values, are strongly
Recognition and Location of Objects in the Visual Field of a UAV Vision System 39 correlated. In consequence, the description is redundant, and repeatedly the large dimension of features makes the analysis more difficult. One of the stages of designing the classified is the extraction stage or features selection. This process is used to minimize the number of features in the vector that is described in the given object. Many times the information contained in the selected is in excess, and the values describing different objects are greatly corralled with each other. In consequence, the description is redundant and a big features’ dimension makes the analysis more difficult. In the experiment that was carried out, some algorithms enabling to determine the transition to the other -dimensional space were analyzed, in the space, which features describing will not be redundant and at the same time, where there space of this dimension can be reduced. In general, the transformation of the state vector from the space -dimensional to space -dimensional can be described as , (28) where is the matrix of a dimension. 6.1 The FLD Algorithm One of the methods allowing to distinguish the matrix of transformation is the method that is based on the analysis of so-called scatter matrices. The genesis of this method taken from the description of the construction of the Fisher’s linear discriminant also known as the FLD. The size of the constructed index of discrimination enables to describe both the degree of the separation of given classes and the degree of scattering vectors from each class. In order to determine the transformation matrix it is necessary to define and determine the few values describing the classes in our features’ dimension. The scattering matrix of the intra-class ∑ , (29) where is the covariance matrix of class elements: (30) is the given a’priori probability of the appearance of the -th class. Such greatness is of the appointed as a ratio of the abundance of the -th class to the abundance of all the elements in analyzed classes (31)
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Studies in Computational Intelligen
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Omnidirectional Video Acquisition D
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Probabilistic Approach to Planning
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206 Practical Applications of Class
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344 Conclusions Control algorithms
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[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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