C - Som : a Continuous Self - Organizing Map for Function Approximation

We propose a new method called C-SOM using a Self-Organizing Map (SOM) for function approximation. C-SOM takes care about the output values of the «win-ning» neuron's neighbors of the map to compute the output value associated with the input data. Our work extends the standard SOM with a combination of Local Linear Mapping (LLM) and cubic spline based interpolation techniques to improve its generalization capabilities. We use the gradient information provided by the LLM technique to interpolate in the input space between neighboring neurons of the map in order to get a first-order continuity at the border hyperplanes of Voronoï regions between these neurons. We present the case of a one-dimensional map and show this method performs better than standard SOM and standard LLM in different function approximation tests.