1. Planar projection of the principal components of fractal Brownian functions
- Author
-
Irina V. Gridneva, Lyudmila I. Fedulova, and Pavel V. Moskalev
- Subjects
History ,Fractal ,Materials science ,Planar projection ,Principal component analysis ,Mathematical analysis ,Brownian motion ,Computer Science Applications ,Education - Abstract
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.
- Published
- 2020
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