Vörös A. szerk.: Fragmenta Mineralogica Et Palaentologica 14. 1989. (Budapest, 1989)

with extrem value appears commonly as a wild-shot point and may cause some distortion in the plot. These points can be easily recognized (HOWARTH 1973

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, e.g. by comparing it with the result of the cluster analysis, and can be corrected by increasing the number of iterations, or by changing the random numbers responsible for the initial configuration. Non-linear mapping of 67 samples of Mecsek volcanics was carried out using both measures (Euclidean distance and theta coefficient) one by one (Fig. 3). The results were found to be similar. Mapping for the samples without P2O5 did not cause essential differences in the data structure, indicating that P2O5 is a non-informative constituent. In addition, non- linear mapping can be employed to reveal differentiation trends of a vocanic suite. The plots for the Mecsek volcanics indicate two different trends within the suite, ending with phonolites and trachytes respectively. PRINCIPAL COMPONENT ANALYSIS The study of processes affected the major element composition is essential in the petrochemistry. The characteristic variation of the oxides and their correlation with one another may indicate these processes. They can be revealed by the use of the Principal Component Analysis (PCA, Cooley and Lohnes 1971), which is a popular method of the multivariate statistical techniques in the geological studies. Efficient examples for the application of PCA can be found in LE MAITRE (1968), BERTRAND and COFFRANT (1977) and UPADHYAYA et al. (1988). Descriptions of the method with numerical examples are given by DAVIS (1973) and LE MAITRE (1982). x

3 *1 Fig. 4 Geometric explanation of PCA (after LE MAITRE, 1968) In order to understand the substance of PCA, a brief geometric explanation are given here (Fig. 4). Imagine that every sample is represented by a series of unique points in an m-dimensional space where the axes are the variables respectively. After computing the variance-covariance matrix or the correlation matrix from the data set, the method defines the eigenvectors and eigenvalues. The eigenvectors (MV1, MV2, MV3) indicate the directions of the maximum dispersion of the data in the m-dimensional space at right angles to one another, in decreasing order. The corresponding eigenvalues represent the length of these vectors, i.e. they are the measures of the dispersion in the direction of the eigenvectors. In this manner a new group of orthogonal axes appear in the data space. The re-