Visualization of transformed multivariate data sets with autoassociative neural networks

The experimental study of the effectiveness of Kohonen maps and autoassociative neural networks in the qualitative analysis of multidimensional data by the example of real data describing coal susceptibility to fluidal gasification

The qualitative analysis of multidimensional data using their visualization allows to observe some characteristics of data in a way which is the most natural for a human, through the sense of sight. Thanks to such an approach, some characteristics of the analyzed data are simply visible. This allows to avoid using often complex algorithms allowing to examine specific data properties. Visualization of multidimensional data consists in using the representation transforming a multidimensional space into a two-dimensional space representing a computer screen. The important information which can be obtained in this way is the possibility to separate points belonging to different classes in the multidimensional space. Such information can be directly obtained if images of points belonging to different classes occupy other areas of the picture presenting these data. The paper presents the effectiveness of the qualitative analysis of multidimensional data conducted in this way through their visualization with the application of Kohonen maps and autoassociative neural networks. The obtained results were compared with results obtained using the perspective-based observational tunnels method, PCA, multidimensional scaling and relevance maps. Effectiveness tests of the above methods were performed using real seven-dimensional data describing coal samples in terms of their susceptibility to fluidal gasification. The methods’ effectiveness was compared using the criterion for the readability of the multidimensional visualization results, introduced in earlier papers.

The examination of the effect of the criterion for neural network’s learning on the effectiveness of the qualitative analysis of multidimensional data

A variety of multidimensional visualization methods are applied for the qualitative analysis of multidimensional data. One of the multidimensional data visualization methods is a method using autoassociative neural networks. In order to perform visualizations of n-dimensional data, such a network has n inputs, n outputs and one of the interlayers consisting of two outputs whose values represent coordinates of the analyzed sample’s image on the screen. Such a criterion for the network’s learning consists in that the same value as the one at the ith input appears at each ith output. If the network is trained in this way, the whole information from n inputs was compressed to two outputs of the interlayer and then decompressed to n network outputs. The paper shows the application of different learning criteria can be more beneficial from the point of view of the results’ readability. Overall analysis was conducted on seven-dimensional real data representing three coal classes, five-dimensional data representing printed characters, 216-dimensional data representing hand-written digits and, additionally, in order to illustrate additional explanations using artificially generated seven-dimensional data. Readability of results of the qualitative analysis of these data was compared using the multidimensional visualization utilizing neural networks for different learning criteria. Also, the obtained results of applying all analyzed criteria on 20 randomly selected sets of multidimensional data obtained from one of the publicly available repositories are presented.