Function learning enhancement with Delaunay linear interpolation and K-D tree nearest neighbor retrieval

Tools from computer science, namely data structures and computational geometry, may be useful to control engineers. In this paper we investigate KD tree data structures with Delaunay triangulation as an alternative approach to supervised learning neural networks. For comparison purposes a function is also learned by a neural net with error backpropagation. The KD tree is used to extract a specified number of nearest neighbors to a query point. The essential idea is to then construct a continuous linear approximation by building Delaunay triangulations from neighborhood points of the query. We conclude that KD tree nearest neighbor retrieval combined with interpolation can be very fast and effective in function learning