A Continuous Self-Organizing Map using Spline Technique for Function Approximation

We propose a new method called C-SOM for function approximation. C-SOM extends the standard Self-Organizing Map (SOM) with a combination of Local Linear Mapping (LLM) and cubic spline based interpolation techniques to improve standard SOMs' generalization capabilities. CSOM uses the gradient information provided by the LLM technique to compute a cubic spline interpolation in the input space between neighbouring neurons of the map, bringing a first-order continuity at the border hyperplanes of their respective Voronoï's regions. We present the case of a onedimensional map and show C-SOM performs better than SOM and LLM in an approximation test.