Universal Approximation Using Shuffled Linear Models

This paper proposes a specific type of Local Linear Model, the Shuffled Linear Model (SLM), that can be used as a universal approximator. Local operating points are chosen randomly and linear models are used to approximate a function or system around these points. The model can also be interpreted as an extension to Extreme Learning Machines with Radial Basis Function nodes, or as a specific way of using Takagi-Sugeno fuzzy models. Using the available theory of Extreme Learning Machines, universal approximation of the SLM and an upper bound on the number of models are proved mathematically, and an efficient algorithm is proposed.