Abstract
A novel algorithm called independent subspace analysis (ISA) is introduced to estimate independent subspaces. The algorithm solves the ISA problem by estimating multi-dimensional differential entropies. Two variants are examined, both of them utilize distances between the k-nearest neighbors of the sample points. Numerical simulations demonstrate the usefulness of the algorithms.
An erratum to this chapter can be found at http://dx.doi.org/10.1007/11550907_163 .
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
Jutten, C., Herault, J.: Blind separation of sources, part 1: an adaptive algorithm based on neuromimetic architecture. Signal Processing 24, 1–10 (1991)
Comon, P.: Independent Component Analysis, a new concept? Signal Processing 36, 287–314 (1994); Special issue on Higher-Order Statistics
Cardoso, J.: Multidimensional independent component analysis. In: Proc. of Int. Conf. on Acoust. Speech and Signal Processing, Seattle, WA (1998)
Akaho, S., Kiuchi, Y., Umeyama, S.: Mica: Multimodal independent component analysis. In: Proc. of IJCNN 1999 (1999)
Hyvärinen, A., Hoyer, P.O.: Emergence of topography and complex cell properties from natural images using extensions of ica. In: Proc. of NIPS 1999, pp. 827–833 (2000)
Hyvärinen, A., Hoyer, P.: Emergence of phase and shift invariant features by decomposition of natural images into independent feature subspaces. Neural Computation 7, 1705–1720 (2000)
Vollgraf, R., Obermayer, K.: Multi dimensional ica to separate correlated sources. In: Proc. of NIPS 2000, pp. 993–1000 (2001)
Bach, F.R., Jordan, M.I.: Finding clusters in independent component analysis. In: Proc. of Fourth International Symposium on Independent Component Analysis and Blind Signal Separation (2003)
Yukich, J.E.: Probability Theory of Classical Euclidean Optimization Problems. Lecture Notes in Mathematics, vol. 1675. Springer, Berlin (1998)
Costa, J.A., Hero, A.O.: Manifold learning using k-nearest neighbor graphs. In: Proc. of Int. Conf. on Acoust. Speech and Signal Processing, Montreal, Canada (2004)
Kozachenko, L.F., Leonenko, N.N.: Sample estimate of entropy of a random vector. Problems of Information Transmission 23, 95–101 (1987)
Beirlant, J., Dudewicz, E.J., Györfi, L., van der Meulen, E.C.: Nonparametric entropy estimation: An overview. International Journal of Mathematical and Statistical Sciences 6, 17–39 (1997)
Amari, S., Cichocki, A., Yang, H.: A new learning algorithm for blind source separation. In: Proc of. NIPS 1995, pp. 757–763 (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Póczos, B., Lőrincz, A. (2005). Independent Subspace Analysis Using k-Nearest Neighborhood Distances. In: Duch, W., Kacprzyk, J., Oja, E., Zadrożny, S. (eds) Artificial Neural Networks: Formal Models and Their Applications – ICANN 2005. ICANN 2005. Lecture Notes in Computer Science, vol 3697. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11550907_27
Download citation
DOI: https://doi.org/10.1007/11550907_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28755-1
Online ISBN: 978-3-540-28756-8
eBook Packages: Computer ScienceComputer Science (R0)