Big Bang-Like Phenomenon in Multidimensional Data

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.