| Abstract [eng] |
Often there is a need to establish and understand the structure of multidimensional data: their clusters, outliers, similarity and dissimilarity. One of solution ways is a dimensionality reduction and visualization of the data. If a huge datasets is analyzed, it is purposeful to reduce the number of the data items before visualization. The area of research is reduction of the number of the data analyzed and mapping the data in a plane. In the dissertation, vector quantization methods, based on artificial neural networks, and visualization methods, based on a dimensionality reduction, have been investigated. The consecutive and integrated combinations of neural gas and multidimensional scaling have been proposed here as an alternative to combinations of self-organizing maps and multidimensional scaling. The visualization quality is estimated by König’s topology preservation measure, Spearman’s rho and MDS error. The measures allow us to evaluate the similarity preservation quantitatively after a transformation of multidimensional data into a lower dimension space. The ways of selecting the initial values of two-dimensional vectors in the consecutive combination and the first training block of the integrated combination have been proposed and the ways of assigning the initial values of two-dimensional vectors in all the training blocks, except the first one, of the integrated combination have been developed. The dependence of the quantization error on the values of training parameters, the number of epochs, neurons and neuron-winners has been defined experimentally. The fact that the consecutive and integrated combinations of the neural gas and multidimensional scaling is more suitable than the combination of the self-organizing map and multidimensional scaling for visualization of the multidimensional data has been experimentally tested and proved. |
