Abstract
Multidimensional scaling (MDS) is a prevalent method for presenting multidimensional data visually. MDS minimizes some stress function. We have proposed in [1] and [2] to consider the stress function and multidimensional scaling, in general, from the geometric point of view, and the so-called Geometric MDS has been developed. Geometric MDS allows finding the proper direction and step size forwards the minimum of the stress function analytically when coordinates of a separate point of the projected space are varied. In this paper, we examine the stress function theoretically and experimentally when simultaneously changing the position of all the points of the projected space in the directions, defined by the Geometric MDS strategy for a separate point. Several new properties and capabilities of the Geometric MDS have been discovered. The obtained results allow us to extend the understanding of properties and ideas of Geometric MDS for the future development of a class of new effective algorithms for multidimensional data visualization and its dimensionality reduction.
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This research has received funding from the Research Council of Lithuania (LMTLT), agreement No S-MIP-20-19.
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Dzemyda, G., Sabaliauskas, M. (2021). New Capabilities of the Geometric Multidimensional Scaling. In: Rocha, Á., Adeli, H., Dzemyda, G., Moreira, F., Ramalho Correia, A.M. (eds) Trends and Applications in Information Systems and Technologies . WorldCIST 2021. Advances in Intelligent Systems and Computing, vol 1366. Springer, Cham. https://doi.org/10.1007/978-3-030-72651-5_26
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DOI: https://doi.org/10.1007/978-3-030-72651-5_26
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