M. Járó - L. Költő szerk.: Archaeometrical research in Hungary (Budapest, 1988)
Analysis - GEGUS Ernő, BORSZÉKI János: Investigation of archaeological metal findings by a laser-microspectral analysis method and characterization of results using pattern recognition methods
selected. The most simple feature selection is the so-called task-oriented selection of features in which the experience of the researcher forms the basis on which to eliminate unnecessary characteristics or even to add further important features to the data matrix. With mathematical methods of feature selection, the transformation of features serves to enhance the effectivity of classification or ranging into classes. Normalizing, standardization or weighting functions are mostly used for the individual tranformation of variables [16]. In several cases these simple data preprocessing methods give adequate results. The common transformation of variables may be divided into two groups: a) Characterization of the significance of features. One of the most widely used and effective means in this group is the Fisher weighting equation: F. - ^il~^i2^ where Fi is the Fisher weighting of the z'th feature , *il , Xi2 the average value of the z'th feature in the 1st and 2nd classes, SU > s i2 the standard deviation of the z'th variable in the 1st and 2nd classes. On the basis of the calculated Fisher weights, the features significantly influencing the selection of both classes give higher values while the less important ones show lower Fisher weights, and if the last values are eliminated the original data matrix can be rasonably reduced. b) An often used means of eliminating insignificant features is Karhunen-Loeve transformation: m 3 k=l where Cjj is the ith, /'th element (i, j = 1,n) of the covariance matrix of the data mass, Xi, Xj the average value of the zth and the /'th feature, n the number of measured features, k = 1, m the number of sample points; cv k =x k v k X k eigenvalues, V k eigenvectors, C covariance matrix. For two-dimensional display the eigenvectors V\ and V"2 belonging to the highest eigenvalues \\ and X2 are used. The information content of the transformation can be calculated according to the equation: ar 2 2 i+1 n i=l J 100 where n is the number of measured parameters (dimensions), Xi, Xj eigenvalues.
