Computational Methods for Data Analysis

In this section, applications are within this range 0 <H< 1 and we use 2D fBm Hölder different functions (polynomial [49–51] and exponential [49–51]) that take as input the points (x, y) of the dataset and provide as output the desired regularity; these functions are used to show the dataset singularities:

(a)	A polynomial of degree n is a function of the form

$H_1\left(x,y\right)=a_n{x}^n{y}^n+a_{n-1}{x}^{n-1}{y}^{n-1}+\cdots +a_2{x}^2{y}^2+a_{1}xy+a_0\left(11.12\right)$

where a0, ..., n are constant values.

(b)	The general definition of the exponential function is[52]

$H_2\left(x,y\right)=\frac{L}{1+e^{-k\left(x-x_{0}y\right)}}\left(11.13\right)$

where e is the natural logarithm base, x0