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Big Bang-Like Phenomenon in Multidimensional Data

Authors: Jiřina, M. (Marcel);

Big Bang-Like Phenomenon in Multidimensional Data

Abstract

Notion of the Big Bang in Data was introduced, when it was observed that the quantity of data grows very fast and the speed of this growth rises with time. This is parallel to the Big Bang of the Universe which expands and the speed of the expansion is the larger the farther the object is, and the expansion is isotropic. We observed another expansion in data embedded in metric space. We found that when distances in data space are polynomially expanded with a proper exponent, the space around any data point displays similar growth that is the larger the larger is the distance. We describe this phenomenon here on the basis of decomposition of the correlation integral. We show that the linear rule holds for logarithm of distance from any data point to another and proportionality constant is the scaling exponent, especially the correlation dimension. After this transformation of distances the data space appears as locally uniform and isotropic.

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Keywords

expansion of distances, Big Bang, scaling, correlation dimension, polynomial transformation

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green