Shklovets A. Piecewise-smooth self organization Kohonen maps for multidimensional data visualization

The research object - process of multidimensional data visualization. The research target - development of methods for piecewise smooth Kohonen self-organizing maps, which by piece-wise linear approximation of the Kohonen maps cubic splines allow more accurate visualization of multidimensional data. Methods of the research: to construct a piecewise linear mapping of multidimensional data in a low-dimensional space with low labor intensity used the theory of artificial neural networks; to construct a piecewise smooth Kohonen self-organizing maps - spline, differential geometry and graph theory and optimization theory; to display multidimensional data on discrete smooth self-organizing map - numerical methods. The scientific novelty: 1. The first method of constructing one-dimensional piecewise smooth Kohonen self-organizing maps, based on an approximation of one-dimensional piecewise linear Kohonen self-organizing maps cubic parametric splines, which allows you to create self-organizing maps of Kohonen without breaks in neurons to increase the accuracy of multi-dimensional data visualization in one-dimensional space is offered. 2. The first method of constructing two-dimensional piecewise smooth Kohonen self-organizing maps, which are characterized by two-dimensional approximation of the piecewise-linear self-organizing Kohonen maps cubic parametric spline surfaces, which makes it possible to build a two-dimensional self-organizing maps of Kohonen without breaks in contact sides of the triangles of the Delaunay triangulation to increase the accuracy of multidimensional visualization data in two-dimensional space is offered. 3. The first methods of multi-dimensional data mappingon piecewise smooth Kohonen self-organizing maps, which are based on the use of Newton's method with multiple initial approximation, which allows to distinguish between the data on the self-organizing Kohonen map and reduce error visualization of multidimensional data while maintaining the computational complexity is offered. 4. Further developed method for calculating distances between the elements of multidimensional data on Kohonen self-organizing maps by introducing them to the metric tensor, computed bending Kohonen self-organizing maps, which allows to reduce the error display data visualized. The degree of implementation - research results have been introduced to: market analysis of polymers CIS companies in the department of monitoring and annual reports and strategic consulting LLC "Market Report" (the act from 02.07.2012) The task of effective planning and development rates in the department of work with consumers' Ukrtelecom "(the act from 15.12.2011), in the learning process of Kharkov National University of Radio Electronics (the act from 03.13.2012). The scope of use - to increase the efficiency and productivity of labor-intensive solutions of neural problems that have difficulty handling large amounts of input data to increase the accuracy of visualization of multidimensional data in intelligent systems which handle a significant amount of input data in various fields for the preliminary analysis of the structure of multi-dimensional data in the training during the preparation of specialists in the fields of intellectual computer systems and neural network processing.