Classification with sparse grids using simplicial basis functions

Recently we presented a new approach [20] 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 [52]. 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 [30] 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. The method computes a nonlinear classifier but scales only linearly with the number of data points and is well suited for data mining applications where the amount of data is ve...

• Type: Journal
• Year: 2002
• Where: IDA
• Authors: Jochen Garcke, Michael Griebel
• Keywords: Data Points, Grid, IDA 2002, Information Technology, Sparse Grid