AUTOMATED PARAMETER SEARCH FOR FRACTAL FUNCTIONS IN DATA FITTING PROBLEMS

Abstract

Parameter optimization is an important problem in the theory of fractal interpolation functions and data fitting. In the literature, the methods for determining values of parameters in data fitting problems are developed only for affine and recurrent affine fractal interpolation functions. There is still no direct method to determine the optimum values of parameters for various types of fractal functions. The aim of this paper is to apply an automated parameter search algorithm from machine learning to the problem of parameters optimization when we use a class of fractal functions to fit a given data set. We first establish a finite set of fractal interpolation functions, and then consider three linear combinations of these functions to fit a given data set. We apply Optuna to find the optimum values of hyperparameters in our approach that minimize the given empirical error. Two examples are given to show the results. Our approach can be applied to many types of fractal functions, and even their linear combinations. The advantage of tuning hyperparameters of fractal functions by AI-based algorithms is that it is not limited to the construction methods and forms of fractal functions.