Data mining with sparse grids using simplicial basis functions

Recently we presented a new approach [18] to the classification problem arising in data mining. It is based on the regularization network approach but, in contrast to other methods which employ ansatz functions associated to data points, we use a grid in the usually high-dimensional feature space for the minimization process. To cope with the curse of dimensionality, we employ sparse grids [49]. Thus, only O(h-1 n nd-1 ) instead of O(h-d n ) grid points and unknowns are involved. Here d denotes the dimension of the feature space and hn = 2-n gives the mesh size. We use the sparse grid combination technique [28] where the classification problem is discretized and solved on a sequence of conventional grids with uniform mesh sizes in each dimension. The sparse grid solution is then obtained by linear combination. In contrast to our former work, where d-linear functions were used, we now apply linear basis functions based on a simplicial discretization. This allows to handle more dimensio...

• Type: Conference
• Year: 2001
• Where: KDD
• Authors: Jochen Garcke, Michael Griebel
• Keywords: Data Mining, Grid Combination Technique, KDD 2001, Sparse Grid Combination, Sparse Grid Solution