Hierarchic Kernel Recursive Least-Squares

We present a new hierarchic kernel based modeling technique for modeling evenly distributed multidimensional datasets that does not rely on input space sparsification. The presented method reorganizes the typical single-layer kernel based model in a hierarchical structure, such that the weights of a kernel model over each dimension are modeled over the adjacent dimension. We show that the imposition of the hierarchical structure in the kernel based model leads to significant computational speedup and improved modeling accuracy (over an order of magnitude in many cases). For instance the presented method is about five times faster and more accurate than Sparsified Kernel Recursive LeastSquares in modeling of a two-dimensional real-world data set.