Informatica

Derivative-free DIRECT-type global optimization algorithms are increasingly favoured for their simplicity and effectiveness in addressing real-world optimization challenges. This review examines their practical applications through a systematic analysis of scientific journals and computational studies. In particular, significant challenges in reproducibility have been identified with practical problems. To address this, we conducted an experimental study using practical problems from reputable CEC libraries, comparing DIRECT-type techniques against their state-of-the-art counterparts. Therefore, this study sheds light on current gaps, opportunities, and future prospects for advanced research in this domain, laying the foundation for replicating and expanding the research findings presented herein.

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.

In this paper, the relative multidimensional scaling method is investigated. This method is designated to visualize large multidimensional data. The method encompasses application of multidimensional 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 MDS, the visualization process is divided into three steps: the set of basis vectors is constructed using the k-means clustering method; this set is projected onto the plane using the MDS algorithm; the set of remaining data is visualized using the relative mapping algorithm. We propose a modification, which differs from the original algorithm in the strategy of selecting the basis vectors. The experimental investigation has shown that the modification exceeds the original algorithm in the visualization quality and computational expenses. The conditions, where the relative MDS efficiency exceeds that of standard MDS, are estimated.

Recent publications on multidimensional scaling express contradicting opinion on multimodality of STRESS criterion. An example has been published with rigorously provable multimodality of STRESS. We present an example of data and the rigorous proof of multimodality of SSTRESS for this data. Some comments are included on widely accepted opinion that minimization of SSTRESS is easier than minimization of STRESS.