NDLI: Data mining with sparse grids using simplicial basis functions

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Data mining with sparse grids using simplicial basis functions

Content Provider	ACM Digital Library
Author	Garcke, Jochen Griebel, Michael
Abstract	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 $O(hn^{-1}n^{d-1})$ 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.
Starting Page	87
Ending Page	96
Page Count	10
File Format	PDF
ISBN	158113391X
DOI	10.1145/502512.502528
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2001-08-26
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Sparse grids Approximation Classification Simplicial discretization Combination technique Data mining
Content Type	Text
Resource Type	Article

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