Abstract
The computation of non-negative tensor factorization may become very time-consuming when large datasets are used. This study shows how to accelerate NTF using multiresolution approach. The large dataset is preprocessed with an integer wavelet transform and NTF results from the low resolution dataset are utilized in the higher resolution dataset. The experiments show that the multiresolution based speed-up for NTF computation varies in general from 2 to 10 depending on the dataset size and on the number of required basis functions.
Chapter PDF
References
Lee, D.D., Seung, N.S.: Learning the Parts of Objects by Non-negative Matrix Factorization. Nature 401, 788–791 (1999)
Hazan, T., Polak, S., Shashua, A.: Sparse Image Coding using a 3D Non-negative Tensor Factorization. In: IEEE International Conference on Computer Vision (ICCV’05) (2005)
Hoyer, P.O.: Non-negative Matrix Factorization with Sparseness Constraints. Journal of Machine Learning Research 5, 1457–1469 (2004)
Li, S., Hou, X.W., Zhang, H.J., Cheng, Q.S.: Learning Spatially Localized, Part-Based Representation. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR’01), Hawaii, USA, pp. 207–212 (2001)
Wild, S., Curry, J., Dougherty, A.: Improving Non-negative Matrix Factorizations through Structured Initialization. Pattern Recognition 37, 2217–2232 (2004)
Shashua, A., Hazan, T.: Non-negative Tensor Factorization with Applications to Statistics and Computer Vision. In: Proceedigs of the 22nd International Conference on Machine Learning, Bonn, Germany, pp. 792–799 (2005)
Heiler, M., Schnörr, C.: Controlling Sparseness in Non-negative Tensor Factorization. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3951, pp. 56–67. Springer, Heidelberg (2006)
Yuan, Z., Oja, E.: Projective Nonnegative Matrix Factorization for Image Compression and Feature Extraction. In: Kalviainen, H., Parkkinen, J., Kaarna, A. (eds.) SCIA 2005. LNCS, vol. 3540, pp. 333–342. Springer, Heidelberg (2005)
Daubechies, I.: Ten Lectures on Wavelets, CBMS-NSF. Regional Conference Series in Applied Mathematics, vol. 61. SIAM, Philadelphia (1992)
Adams, M.D., Kossentini, F.: Reversible integer-to-integer wavelet transforms for image compression: performance evaluation and analysis. IEEE Transactions on Image Processing 9(6), 1010–1024 (2000)
Calderbank, A.R., Daubechies, I., Sweldens, W., Yeo, B.-L.: Wavelet transforms that map integers to integers. Applied and Computational Harmonic Analysis 5(3), 332–369 (1998)
Calderbank, A.R., Daubechies, I., Sweldens, W., Yeo, B.-L.: Lossless Image Compression using Integer to Integer Wavelet Transforms. In: IEEE International Conference on Image Processing (ICIP’97), vol. 1, pp. 596–599 (1997)
Daubechies, I.: Recent results in wavelet applications. Journal of Electronic Imaging 7(4), 719–724 (1998)
Spectral Database. University of Joensuu Color Group, Accessed: October 26, 2006, Available: http://spectral.joensuu.fi/
Face Recognition Database. MIT-CBCL, accessed: November 10, 2006, availabe: http://cbcl.mit.edu/software-datasets/heisele/facerecognition-database.html
Homepage, AVIRIS: accessed: November 10, 2006, available: http://aviris.jpl.nasa.gov/
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Kaarna, A., Andriyashin, A., Nakauchi, S., Parkkinen, J. (2007). Multiresolution Approach in Computing NTF. In: Ersbøll, B.K., Pedersen, K.S. (eds) Image Analysis. SCIA 2007. Lecture Notes in Computer Science, vol 4522. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73040-8_34
Download citation
DOI: https://doi.org/10.1007/978-3-540-73040-8_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73039-2
Online ISBN: 978-3-540-73040-8
eBook Packages: Computer ScienceComputer Science (R0)