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Big Bang-Like Phenomenon in Multidimensional Data
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SYSNO ASEP 0427692 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title Big Bang-Like Phenomenon in Multidimensional Data Author(s) Jiřina, Marcel (UIVT-O) SAI, RID Source Title Proceedings of the International Conference on Computing Technology and Information Management ICCTIM 2014. - Wilmington : SDIWC, 2014 / Malakooti M.V. - ISBN 978-0-9891305-5-4 Pages s. 262-269 Number of pages 8 s. Publication form Medium - C Action ICCTIM 2014. International Conference on Computing Technology and Information Management Event date 09.04.2014-11.04.2014 VEvent location Dubai Country AE - United Arab Emirates Event type WRD Language eng - English Country US - United States Keywords Big Bang ; scaling ; correlation dimension ; expansion of distances ; polynomial transformation Subject RIV BB - Applied Statistics, Operational Research R&D Projects LG12020 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) Institutional support UIVT-O - RVO:67985807 Annotation 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. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2015
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