Universal Functions Originator

Abstract

Nowadays, couples of computing systems have been introduced to perform many applications, such as function approximation, pattern classification, categorization/clustering, forecasting/prediction, control, and optimization. Linear regression (LR) is commonly used for simple data where the relation between its coefficients is linear, while nonlinear regression (NLR) is used when that relation is nonlinear. Artificial neural networks (ANNs) and support vector machines (SVMs) are more efficient and they can be used for complex applications. However, each one of these approaches has its own strengths and weaknesses. This study introduces a new computing system called “universal functions originator (UFO)”. This system is a new symbolic regression (SR) technique that can generate mathematical models universally through two independent optimization algorithms. Different arithmetic operators can be entered into the search pool. Also, any analytic function can be dragged into that pool. UFO has been mathematically designed and practically tested with function approximation problems. However, UFO can also be used for the applications listed above, including anomaly detection, function complication, function simplification, dimension expansion, dimension reduction, and high-dimensional function visualization. This novel computing system shows an impressive performance with many promising uses and distinct capabilities. This study reveals the mechanism of UFO and solves some numerical problems via an advanced graphical user interface (GUI) designed just to validate the process of this computing system.