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Content available On the clustering of correlated random variables
EN
In this work, the possibility of clustering correlated random variables was examined, both because of their mutual similarity and because of their similarity to the principal components. The k-means algorithm and spectral algorithms were used for clustering. For spectral methods, the similarity matrix was both the matrix of relation established on the level of correlation and the matrix of coefficients of determination. For four different sets of data, different ways of measuring the disimilarity of variables were analyzed, and the impact of the diversity of initial points on the efficiency of the k-means algorithm was analyzed.
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Content available New Interpretation of Principal Components Analysis
EN
A new look on the principal component analysis has been presented. Firstly,ageometric interpretation of determination coefficient was shown. In turn, the ability to represent the analyzed data and their interdependencies in the form of easy-tounderstand basic geometric structures was shown. As a result of the analysis of these structures it was proposed to enrich the classical PCA. In particular, it was proposed a new criterion for the selection of important principal components and a new algorithm for clustering primary variables by their level of similarity to the principal components. Virtual and real data spaces, as well as tensor operations on data, have also been identified.The anisotropy of the data was identified too.
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