Spatially adaptive sparse grids for high-dimensional data-driven problems

Journal of Complexity

Volumn 26, Issue 5, 2010, Pages 508-522

  Pflger, Dirk ^a   Peherstorfer, Benjamin ^a   Bungartz, Hans Joachim ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Classification; High dimensional approximation; Non smooth functions; Regularization; Spatially adaptive sparse grids

Indexed keywords

CLUSTERING ALGORITHMS; DATA MINING; DISCRETE EVENT SIMULATION; EDGE DETECTION;

ADAPTIVE GRID REFINEMENT; HIGH DIMENSIONAL DATA; HIGH-DIMENSIONAL; HIGH-DIMENSIONAL PROBLEMS; NON-SMOOTH FUNCTIONS; REGULARIZATION; REGULARIZATION TECHNIQUE; SPARSE GRID;

CLASSIFICATION (OF INFORMATION);

EID: 83755201307     PISSN: 0885064X     EISSN: 10902708     Source Type: Journal    
DOI: 10.1016/j.jco.2010.04.001     Document Type: Conference Paper

References (33)

1. D.M. Allen The relationship between variable selection and data augmentation and a method for prediction Technometrics 16 1 1974 125 127
2. K. Babenko Approximation by trigonometric polynomials in a certain class of periodic functions of several variables Soviet Math. Dokl. 1 1960 672 675 Russian original in Dokl. Akad. Nauk SSSR 132 1960 982 985
3. J. Blank, R. Rttger, Data Mining mit Dnnen Gittern, Student project (SEP), Fakultt fr Informatik, Technische Universitt Mnchen, Jan. 2008.
4. H.-J. Bungartz, and M. Griebel A note on the complexity of solving Poisson's equation for spaces of bounded mixed derivatives J. Complexity 15 2 1999 167 199
5. H.-J. Bungartz, and M. Griebel Sparse grids Acta Numer. 13 2004 147 269
6. H.-J. Bungartz, D. Pflger, and S. Zimmer Adaptive sparse grid techniques for data mining H. Bock, E. Kostina, X. Hoang, R. Rannacher, Modelling, Simulation and Optimization of Complex Processes, Proceedings of the High Performance Scientific Computing 2006 2008 Springer Hanoi, Vietnam 121 130
7. V.S. Devi, and M.N. Murty An incremental prototype set building technique Pattern Recognit. 35 2 2002 505 513
8. T. Evgeniou, M. Pontil, and T. Poggio Regularization networks and support vector machines Advances in Computational Mathematics 2000 MIT Press 1 50
9. J. Garcke Regression with the optimised combination technique ICML'06: Proceedings of the 23rd International Conference on Machine Learning 2006 ACM Press New York, NY, USA 321 328
10. J. Garcke A dimension adaptive sparse grid combination technique for machine learning W. Read, J.W. Larson, A.J. Roberts, Proceedings of the 13th Biennial Computational Techniques and Applications Conference, CTAC-2006 ANZIAM J. 48 2007 C725 C740
11. J. Garcke, M. Griebel, Semi-supervised learning with sparse grids, in: M.-R. Amini, O. Chapelle, R. Ghani (Eds.), Proceedings of ICML, Workshop on Learning with Partially Classified Training Data, 2005, pp. 1928.
12. J. Garcke, M. Griebel, and M. Thess Data mining with sparse grids Computing 67 3 2001 225 253
13. J. Garcke, and M. Hegland Fitting multidimensional data using gradient penalties and the sparse grid combination technique Computing 84 12 2009 1 25
14. G.H. Golub, M. Heath, and G. Wahba Generalized cross-validation as a method for choosing a good ridge parameter Technometrics 21 2 1979 215 223
15. M. Griebel, and P. Oswald On additive Schwarz preconditioners for sparse grid discretizations Numer. Math. 66 1994 449 464 also as Bericht Math/92/7, Institut fr Angewandte Mathematik, Friedrich-Schiller-Universitt Jena, 1992
16. M. Griebel, M. Schneider, and C. Zenger A combination technique for the solution of sparse grid problems Proceedings of the IMACS International Symposium on Iterative Methods in Linear Algebra 1992 Elsevier Amsterdam 263 281
17. M. Hegland, Adaptive sparse grids, in: K. Burrage, R.B. Sidje (Eds.), Proc. of 10th Computational Techniques and Applications Conference, CTAC-2001, vol. 44, 2003, pp. C335C353.
18. M. Hegland, J. Garcke, and V. Challis The combination technique and some generalisations Linear Algebr. Appl. 420 23 2007 249 275
19. M. Hegland, O.M. Nielsen, and Z. Shen Multidimensional smoothing using hyperbolic interpolatory wavelets Electron. Trans. Numer. Anal. 17 2004 168 180
20. L. Johansson, Einsatz der Dnngitterklassifikation fr Benchmark-probleme, Diplomarbeit, Fakultt fr Informatik, Technische Universitt Mnchen, Apr. 2008.
21. D. Newman, S. Hettich, C. Blake, C. Merz, UCI repository of machine learning databases, University of California, Irvine, Dept. of Information and Computer Sciences, 1998.
22. A.L.I. Oliveira, F.B.L. Neto, and S.R.L. Meira Improving rbf-dda performance on optical character recognition through parameter selection Pattern Recognition, International Conference on vol. 4 2004 625 628
23. B. Peherstorfer, Adaptive sparse grid representation for indicator functions, Bachelor's thesis, Fakultt fr Informatik, Technische Universitt Mnchen, Nov. 2008.
24. B. Peherstorfer, More on Adaptive Sparse Grid Representation for Indicator Functions, Student project (IDP), Fakultt fr Informatik, Technische Universitt Mnchen, Mar. 2009.
25. D. Pflger, I.L. Muntean, and H.-J. Bungartz Adaptive sparse grid classification using grid environments Y. Shi, D. van Albada, J. Dongarra, P. Sloot, ICCS 2007, International Conference on Computational Science LNCS vol. 4487 2007 Springer Berlin, Heidelberg 708 715
26. D. Pflger, Data Mining mit Dnnen Gittern, Diplomarbeit, IPVS, Universitt Stuttgart, Mar. 2005.
27. B.D. Ripley, and N.L. Hjort Pattern Recognition and Neural Networks 1995 Cambridge University Press New York, NY, USA
28. S. Smolyak Quadrature and interpolation formulas for tensor products of certain classes of functions Soviet Math. Dokl. 4 1963 240 243 Russian original in Dokl. Akad. Nauk SSR, 148 (1963), 10421045
29. A. Tikhonov, and V. Arsenin Solutions of Ill-Posed Problems 1977 W.H. Winston Washington, DC
30. J. Traub, G. Wasilkowski, and H. Wozniakowski Information-Based Complexity 1988 Academic Press London
31. G. Wahba Spline Models for Observational Data CBMS-NSF Regional Conference Series in Applied Mathematics vol. 59 1990 SIAM Philadelphia
32. I.H. Witten, and E. Frank Data mining: practical machine learning tools and techniques with Java implementations ACM SIGMOD Rec. 31 1 2002 76 77
33. C. Zenger Sparse grids W. Hackbusch, Parallel Algorithms for Partial Differential Equations Notes on Numerical Fluid Mechanics vol. 31 1991 Vieweg 241 251