Journal:Informatica
Volume 27, Issue 2 (2016), pp. 323–334
Abstract
This paper reviews the interplay between global optimization and probability models, concentrating on a class of deterministic optimization algorithms that are motivated by probability models for the objective function. Some complexity results are described for the univariate and multivariate cases.
Journal:Informatica
Volume 25, Issue 4 (2014), pp. 563–580
Abstract
Abstract
Clustering is one of the better known unsupervised learning methods with the aim of discovering structures in the data. This paper presents a distance-based Sweep-Hyperplane Clustering Algorithm (SHCA), which uses sweep-hyperplanes to quickly locate each point’s approximate nearest neighbourhood. Furthermore, a new distance-based dynamic model that is based on -tree hierarchical space partitioning, extends SHCA’s capability for finding clusters that are not well-separated, with arbitrary shape and density. Experimental results on different synthetic and real multidimensional datasets that are large and noisy demonstrate the effectiveness of the proposed algorithm.
Journal:Informatica
Volume 22, Issue 4 (2011), pp. 489–505
Abstract
In this paper, we consider the so-called structured low rank approximation (SLRA) problem as a problem of optimization on the set of either matrices or vectors. Briefly, SLRA is defined as follows. Given an initial matrix with a certain structure (for example, Hankel), the aim is to find a matrix of specified lower rank that approximates this initial matrix, whilst maintaining the initial structure. We demonstrate that the optimization problem arising is typically very difficult; in particular, the objective function is multiextremal even in simple cases. We also look at different methods of solving the SLRA problem. We show that some traditional methods do not even converge to a locally optimal matrix.
Journal:Informatica
Volume 22, Issue 4 (2011), pp. 471–488
Abstract
We describe an adaptive algorithm for approximating the global minimum of a continuous univariate function. The convergence rate of the error is studied for the case of a random objective function distributed according to the Wiener measure.
Journal:Informatica
Volume 19, Issue 3 (2008), pp. 377–390
Abstract
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.