Regularization theory and neural networks architectures
Neural Computation
Approximation of scattered data using smooth grid functions
Journal of Computational and Applied Mathematics
The nature of statistical learning theory
The nature of statistical learning theory
Information complexity of multivariate Fredholm integral equations in Sobolev classes
Journal of Complexity
2D spiral pattern recognition with possibilistic measures
Pattern Recognition Letters
An equivalence between sparse approximation and support vector machines
Neural Computation
Data mining methods for knowledge discovery
Data mining methods for knowledge discovery
Proximal support vector machine classifiers
Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining
Learning from Data: Concepts, Theory, and Methods
Learning from Data: Concepts, Theory, and Methods
Computing
On Comparing Classifiers: Pitfalls toAvoid and a Recommended Approach
Data Mining and Knowledge Discovery
On the Parallelization of the Sparse Grid Approach for Data Mining
LSSC '01 Proceedings of the Third International Conference on Large-Scale Scientific Computing-Revised Papers
On the Parallel Solution of 3D PDEs on a Network of Workstations and on Vector Computers
Parallel Computer Architectures: Theory, Hardware, Software, Applications
Lagrangian support vector machines
The Journal of Machine Learning Research
Estimation of Dependences Based on Empirical Data: Springer Series in Statistics (Springer Series in Statistics)
Adaptive Sparse Grid Classification Using Grid Environments
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
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Recently we presented a new approach [20] to the classificationproblem arising in data mining. It is based on the regularizationnetwork approach but in contrast to other methods, which employansatz functions associated to data points, we use a grid in theusually high-dimensional feature space for the minimizationprocess. To cope with the curse of dimensionality, we employ sparsegrids [52]. Thus, only O(h_n^{-1} n^{d-1}) instead of O(h_n^{-d})grid points and unknowns are involved. Here d denotes the dimensionof the feature space and h_n = 2^{-n} gives the mesh size. We usethe sparse grid combination technique [30] where the classificationproblem is discretized and solved on a sequence of conventionalgrids with uniform mesh sizes in each dimension. The sparse gridsolution is then obtained by linear combination.The method computes a nonlinear classifier but scales onlylinearly with the number of data points and is well suited for datamining applications where the amount of data is very large, butwhere the dimension of the feature space is moderately high. Incontrast to our former work, where d-linear functions were used, wenow apply linear basis functions based on a simplicialdiscretization. This allows to handle more dimensions and thealgorithm needs less operations per data point. We further extendthe method to so-called anisotropic sparse grids, where nowdifferent a-priori chosen mesh sizes can be used for thediscretization of each attribute. This can improve the run time ofthe method and the approximation results in the case of data setswith different importance of the attributes.We describe the sparse grid combination technique for theclassification problem, give implementational details and discussthe complexity of the algorithm. It turns out that the methodscales linearly with the number of given data points. Finally wereport on the quality of the classifier built by our new method ondata sets with up to 14 dimensions. We show that our new methodachieves correctness rates which are competitive to those of thebest existing methods.