Optimizavimo algoritmai daugiamatėms skalėms su miesto kvartalo atstumais ir jų lygiagretinimas /

In this dissertation, a problem related to a visualization of elements of a multidimensional data set is considered. Here, for the sake of simplicity, an element of a multidimensional data set is called a multidimensional element. There are many techniques for visualizing multidimensional elements. Multidimensional scaling (MDS) is one of them. In applying MDS, a certain real function has to be constructed and minimized. In order to construct the function, a desired distance function has to be selected. If city-block distances are selected, the problem of minimizing such a function becomes a complicated optimization problem. In this work, this complicated optimization problem is the main research problem. Here, we formulate a new optimization problem and we show that it is equivalent to the original optimization problem arising in MDS with city-block distances. Also, we propose two sequential algorithms and one parallel algorithm for the newly formulated problem. Finally, we present the results of numerical investigations of the proposed algorithms.

Grantor dc:publisher

Institutional Repository of Vilnius University

Year dc:date

2015

Author dc:creator

• Galiauskas, Nerijus,

• multidimensional scaling ; city-block distances ; optimization ; parallel computing

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

lit

Repository record dc:identifier

https://repository.vu.lt/VU:ELABAETD11816503&prefLang=en_US

OAI identifier oai:identifier

oai:vu.lt:elaba:11816503