Abstract
It has been well known that ICA can extract edge filters from natural scenes. However, it has been also known that the existing cumulant-based ICA can not extract edge filters. It suggests that the simple ICA model is insufficient for explaining the properties of natural scenes. In this paper, we propose a highly overcomplete model for natural scenes. Besides, we show that the 4-th order covariance has a positive constant lower bound under this model. Then, a new cumulant-based ICA algorithm is proposed by utilizing this lower bound. Numerical experiments show that this cumulant-based algorithm can extract edge filters.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Hyvärinen, A., Karhunen, J., Oja, E.: Independent Component Analysis. Wiley, Chichester (2001)
Cichocki, A., Amari, S.: Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications. Wiley, Chichester (2002)
Bell, A.J., Sejnowski, T.J.: The ”independent components” of natural scenes are edge filters. Vision Research 37(23), 3327–3338 (1997)
Hyvaerinen, A., Hurri, J., Hoyer, P.O.: Natural Image Statistics: A Probabilistic Approach to Early Computational Vision (Computational Imaging and Vision), 1st edn. Springer, Heidelberg (2009)
Comon, P.: Independent component analysis - a new concept? Signal Processing 36, 287–314 (1994)
Hyvärinen, A.: Fast and robust fixed-point algorithms for independent component analysis. IEEE Transactions on Neural Networks 10(3), 626–634 (1999)
Cardoso, J.F.: High-order contrasts for independent component analysis. Neural Computation 11(1), 157–192 (1999)
Olshausen, B.A., Field, D.J.: Sparse coding with an overcomplete basis set: a strategy employed by v1? Vision research 37(23), 3311–3325 (1997)
Hyvärinen, A., Hoyer, P.O., Inki, M.: Estimating overcomplete independent component bases for image windows. Journal of Mathematical Imaging and Vision 17, 139–152 (2002)
Teh, Y.W., Welling, M., Osindero, S., Hinton, G.E.: Energy-based models for sparse overcomplete representations. J. Mach. Learn. Res. 4, 1235–1260 (2003)
Matsuda, Y., Yamaguchi, K.: Semi-invariant function of jacobi algorithm in independent component analysis. In: Proceedings of IJCNN 2004, Budapest, Hungary, pp. 2147–2151. IEEE, Los Alamitos (2004)
Matsuda, Y., Yamaguchi, K.: A simple overcomplete ICA algorithm by non-orthogonal pair optimizations. In: Proceedings of IJCNN 2009, Atlanta, Georgia, USA, pp. 2027–2031. IEEE, Los Alamitos (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Matsuda, Y., Yamaguchi, K. (2010). Partial Extraction of Edge Filters by Cumulant-Based ICA under Highly Overcomplete Model. In: Wong, K.W., Mendis, B.S.U., Bouzerdoum, A. (eds) Neural Information Processing. Models and Applications. ICONIP 2010. Lecture Notes in Computer Science, vol 6444. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17534-3_78
Download citation
DOI: https://doi.org/10.1007/978-3-642-17534-3_78
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17533-6
Online ISBN: 978-3-642-17534-3
eBook Packages: Computer ScienceComputer Science (R0)