Abstract
Data fitting is the process of constructing a curve, or a set of mathematical functions, that has the best fit to a series of data points. Different with constructing a fitting model from same type of function, such as the polynomial model, we notice that a hybrid fitting model with multiple types of function may have a better fitting result. Moreover, this also shows better interpretability. However, a perfect smooth hybrid fitting model depends on a reasonable combination of multiple functions and a set of effective parameters. That is a high-dimensional multi-objective optimization problem. This paper proposes a novel data fitting model construction approach. In this approach, the model is expressed by an improved tree coding expression and constructed through an evolution search process driven by the genetic programming. In order to verify the validity of generated hybrid fitting model, 6 prediction problems are chosen for experiment studies. The experimental results show that the proposed method is superior to 7 typical methods in terms of the prediction accuracy and interpretability.
Highlights
The goal of constructing a data fitting model is to seek a set of functions, which can describe the approximate correlation among a group of variables, and subject to constraints
This paper presents the method of constructing a hybrid data fitting model based on improved expression tree (I-ET) coding and evolutionary search
The results suggest that the proposed method for model construction can bring forth hybrid model with higher prediction accuracy and lower complexity
Summary
The goal of constructing a data fitting model is to seek a set of functions, which can describe the approximate correlation among a group of variables, and subject to constraints. It is found that the hybrid fitting model with lower complexity and higher fitting accuracy can be constructed by mixing different types of functions Constructing such a model firstly calls for mechanisms with more effective coding expression and optimization ability. Concerning this issue, this paper proposes a method for constructing the hybrid fitting model based on representation by tree coding and co-optimization of model structure and parameters by evolutionary search.
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