Handwritten digit classification using higher order singular value decomposition

Pattern Recognition

Volumn 40, Issue 3, 2007, Pages 993-1003

  Savas, Berkant ^a   Eldén, Lars ^a  

^a LINKÖPING UNIVERSITY   (Sweden)

Author keywords

Handwritten digit classification; Higher order singular value decomposition; Least squares; Tensor approximation; Tensors

Indexed keywords

ALGORITHMS; BIT ERROR RATE; COMPUTATIONAL METHODS; DATA PROCESSING; DECOMPOSITION; LEAST SQUARES APPROXIMATIONS; TENSORS;

HANDWRITTEN DIGIT CLASSIFICATION; HIGHER ORDER SINGULAR VALUE DECOMPOSITION (HOSVD); TENSOR APPROXIMATION;

CLASSIFICATION (OF INFORMATION);

EID: 33750527967     PISSN: 00313203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.patcog.2006.08.004     Document Type: Article

References (21)

1. Duda R.O., Hart P.E., and Stork D.G. Pattern Classification. second ed. (2001), Wiley-Interscience, New York
2. Hastie T., Tibshirani R., and Friedman J. The elements of statistical learning (2001), Springer Series in Statistics, Springer, New York
3. Y. LeCun, L. Jackel, L. Bottou, C. Cortes, J. S. Denker, H. Drucker, I. Guyon, U. A. Müller, E. Säckinger, P. Simard, V. Vapnik, Learning algorithms for classification: a comparison on handwritten digit recognition, Neural Network: The Statistical Mechanics Perspective (1995) 261-276.
4. LeCun Y., Bottou L., Bengio Y., and Haffner P. Gradient-based learning applied to document recognition. Proc. IEEE 86 11 (1998) 2278-2324
5. Simard P.Y., LeCun Y.A., Denker J.S., and Victorri B. Transformation invariance in pattern recognition-tangent distance and tangent propagation. Internat. J. Imag. Systems Technol. 11 3 (2000) 181-197
6. D. Keysers, J. Dahmen, T. Theiner, H. Ney, Experiments with an extended tangent distance, Technical Report, Lehrstuhl für Informatik VI, RWTH Aachen - University of Technology, 52056 Aachen Germany, 2000.
7. P. Scattolin, Recognition of handwritten numerals using elastic matching, Master's Thesis, Department of Computer Science, Concordia University, Montréal, Québeck, Canada, 1995.
8. Hinton G.E., Dayan P., and Revow M. Modelling the manifolds of images of handwritten digits. IEEE Trans. Neural Networks 8 1 (1997) 65-74
9. De Lathauwer L., De Moor B., and Vandewalle J. A multilinear singular value decomposition. SIAM J. Matrix Anal. Appl. 21 4 (2000) 1253-1278
10. Wold S. Pattern recognition by means of disjoint principal components models. Pattern Recognition 8 (1975) 127-139
11. Smilde A., Bro R., and Geladi P. Multi-way Analysis: Applications in the Chemical Sciences (2004), Wiley, New York
12. M. Vasilescu, D. Terzopoulos, Multilinear subspace analysis of image ensembles, in: IEEE Conference on Computer Vision and Pattern Recognition (CVPR'03), Madison WI, 2003.
13. M. Vasilescu, D. Terzopoulos, Multilinear analysis of image ensembles: tensorfaces, in: Proceedings of Seventh European Conference on Computer Vision (ECCV'02), Lecture Notes in Computer Science, vol. 2350, Springer, Copenhagen, Denmark, 2002, pp. 447-460.
14. B. Bader, T. Kolda, Matlab tensor classes for fast algorithm prototyping, Tech. Rep. SAND2004-5187, Sandia National Laboratories (October 2004).
15. S. Kobayashi, K. Nomizu, Foundations of Differential Geometry, vol. 1, Wiley, New York, 1963.
16. Golub G.H., and Van Loan C.F. Matrix Computations. third ed. (1996), Johns Hopkins Studies in the Mathematical Sciences, Johns Hopkins University Press, Baltimore, MD
17. Tucker L. The extension of factor analysis to three-dimensional matrices. In: Gulliksen H., and Frederiksen N. (Eds). Contributions to Mathematical Psychology (1964), Holt, Rinehart and Winston, New York 109-127
18. Eckart C., and Young G. The approximation of one matrix by another of lower rank. Psychometrika 1 (1936) 211-218
19. n) approximation of higher-order tensors. SIAM Matrix Anal. Appl. 21 4 (2000) 1324-1342
20. B. Savas, Analyses and tests of handwritten digit recognition algorithms, Master's Thesis, Linköping University, 〈http://www.mai.liu.se/∼besav/〉 (2003).
21. Mori S., Nishida H., and Yamada H. Optical Character Recognition (1999), Wiley, New York