Universal Approximation Using Shuffled Linear Models
This provides a theoretical foundation for a new type of local linear model in machine learning, but it appears incremental as it builds on existing Extreme Learning Machine and fuzzy model frameworks.
The paper tackles the problem of universal function approximation by proposing Shuffled Linear Models (SLMs), which use randomly chosen local linear models, and proves mathematically that SLMs can universally approximate functions with an upper bound on the number of models required.
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.