Open AccessPlanar projection of the principal components of fractal Brownian functions
Author(s) -
Pavel V. Moskalev,
Lyudmila I. Fedulova,
Irina V. Gridneva
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1479/1/012040
Subject(s) - projection (relational algebra) , mathematics , principal component analysis , dimension (graph theory) , fractal dimension , fractal , planar , brownian motion , mathematical analysis , fractional brownian motion , statistical physics , combinatorics , algorithm , statistics , physics , computer science , computer graphics (images)
The error in the planar projection of the principal components of a multidimensional data array strongly depends on the number and dimension of the column vectors of this array and the correlation between the vectors. In this work, we investigate the dependence of the error on the planar projection of the principal components of fractal Brownian functions on the number of statistically independent realizations in the multidimensional data array. As a result, we show that, under certain assumptions, the number of statistically independent realizations of fractal Brownian functions coincides with the effective dimension of the projection of the principal components.