document: 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 ( hn-1nd-1 ) instead of O ( hn-d ) 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 dimensions and the algorithm needs less operations per data point . We describe the sparse grid combination technique for the classification problem , give implementational details and discuss the complexity of the algorithm . It turns out that the method scales linearly with the number of given data points . Finally we report on the quality of the classifier built by our new method on data sets with up to 10 dimensions . It turns out that our new method achieves correctness rates which are competitive to that of the best existing methods .
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