Most of real-life data are not often truly high-dimensional. The data points just lie on a low-dimensional manifold embedded in a high-dimensional space. Nonlinear manifold learning methods automatically discover the low-dimensional nonlinear manifold in a high-dimensional data space and then embed the data points into a low-dimensional embedding space,… (More)
Estimation and modelling problems as they arise in many data analysis areas often turn out to be unstable and/or intractable by standard numerical methods. Such problems frequently occur in fitting of large data sets to a certain model and in predictive learning. Heuristics are general recommendations based on practical statistical evidence, in contrast to… (More)
Visual data mining is an efficient way to involve human in search for a optimal decision. This paper focuses on the optimization of the visual presentation of multidimensional data. A variety of methods for projection of multidimensional data on the plane have been developed. At present, a tendency of their joint use is observed. In this paper, two… (More)
In this paper, the relative multidimensional scaling method is investigated. This method is designated to visualize large multidimensional data. The method encompasses application of mul-tidimensional scaling (MDS) to the so-called basic vector set and further mapping of the remaining vectors from the analyzed data set. In the original algorithm of relative… (More)
The problem of visual presentation of multidimensional data is discussed. The projection methods for dimension reduction are reviewed. The chapter deals with the artificial neural networks that may be used for reducing dimension and data visualization, too. The stress is put on combining the self-organizing map (SOM) and Sammon mapping and on the neural… (More)
In the paper, we analyze the software that realizes the self-organizing maps: SOM-PAK, SOM-TOOLBOX, Viscovery SOMine, Nenet, and two academic systems. Most of the software may be found in the Internet. These are freeware, shareware or demo. The self-organizing maps assist in data clustering and analyzing data similarities. The software differs one from… (More)
The paper deals with the analysis of Research and Technology Development (RTD) in the Central European countries and the relation of RTD with economic and social parameters of countries in this region. A methodology has been developed for quantitative and qualitative ranking and estimates of relationship among multidimensional objects on the base of such… (More)
Recent changes in the intersection of the fields of intelligent systems optimization and statistical learning are surveyed. These changes bring new theoretical and computational challenges to the existing research areas racing from web page mining to computer vision, pattern recognition, financial mathematics, bioinformatics and many other ones.