Informatica

Multidimensional scaling is a technique for exploratory analysis of multidimensional data widely usable in different applications. By means of this technique the image points in a low-dimensional embedding space can be found whose inter-point distances fit the given dissimilarities between the considered objects. In this paper dependence of relative visualization error on the dimensionality of embedding space is investigated. Both artificial and practical data sets have been used. The images in three-dimensional embedding space normally show the structural properties of sets of considered objects with acceptable accuracy, and widening of applications of stereo screens makes three-dimensional visualization very attractive.

We investigate applicability of quantitative methods to discover the most fundamental structural properties of the most reliable political data in Lithuania. Namely, we analyze voting data of the Lithuanian Parliament. Two most widely used techniques of structural data analysis (clustering and multidimensional scaling) are compared. We draw some technical conclusions which can serve as recommendations in more purposeful application of these methods.

A random walk dan be used to model various types of discrete random processes. It may be of interest at some point to find the peak of this function. A direct method of doing so involves evaluating the function at every point and recording the highest value. However, it may be desirable to find the peak without having, to evaluate the function at every point. A search technique was developed to find the peak of a random walk with a minimal number of function evaluations using probabilistic means to guess at where the peak will most likely occur given the parameters of a specific function. A computer program was written to implement the search strategy and a series-of random walk functions of varying lengths were generated to test its performance. Data was compiled and the results show that the search is capable of finding the peak with a significant reduction in the number of function evaluations needed for a point by point search, especially for functions of greater walk length.

In well-known statistical models of global optimization only values of objective functions are taken into consideration. However, efficient algorithms of local optimization are also based on the use of gradients of objective functions. Thus, we are interested in a possibility of the use of gradients in statistical models of multimodal functions, aiming to create productive algorithms of global optimization.

In the paper the global optimization is described from the point of an interactive software design. The interactive software that implements numeric methods and other techniques to solve global optimization problems is presented. Some problems of such a software design are formulated and discussed.