# A Simple Algorithm for Topographic ICA

### Ewaldo Santana, Allan Kardec Barros, Christian Jutten, Eder Santana, Luis Claudio Oliveira

#### Abstract

A number of algorithms have been proposed which find structures that resembles that of the visual cortex. However, most of the works require sophisticated computations and lack a rule for how the structure arises. This work presents an unsupervised model for finding topographic organization with a very easy and local learning algorithm. Using a simple rule in the algorithm, we can anticipate which kind of structure will result. When applied to natural images, this model yields an efficient code for natural images and the emergence of simple-cell-like receptive fields. Moreover, we conclude that the local interactions in spatially distributed systems and local optimization with norm L2 are sufficient to create sparse basis, which normally requires higher order statistics.

#### References

- Barlow, H. B., Unsupervised learning, Neural Computation,v.01, pp. 295-311, 1989.
- Barros, A. K. and Ohnishi, N., Wavelet like Receptive fields emerge by non-linear minimization of neuron error, International Journal of Neural Systems,v.13, n. 2, pp. 87-91, 2002.
- Bell, Anthony J. and Sejnowski, Terrence J., An Information-Maximixation Approach to Blind Separation and Blind Deconvolution, Neural Computation, n. 7, pp. 61-72, 1995.
- Butko, N. J. and Triesch, J., Learning sensory representations with intrinsic plasticity, Neurocomputing, v. 70, pp. 1130-1138, 2007.
- Comon, Pierre. Independent component analysis, A new concept?. Signal Processing, v.36,p 287-314, 1994.
- Durbin, R and Mitchison, G., A dimension reduction framework for understanding cortical maps, Nature, n.343, pp. 644-647, 2007.
- Field, David J., Relation between the statistics of natural images and the response properties of cortical cells. J. Optical Society of America, v. 04, n.12, pp. 2379 - 2394, 1987.
- FoldiĆ”k, P., Some Aspects of Linear Estimation wiht NonMean Squares error Criteria. Biological Cybernetics, v. 64, pp. 165 - 170, 1990.
- Gersho, A., Forming sparse representations by local antiHebbian learning., Proc. Asilomar Ckts. and Systemas Conf. (1969).
- Hyvarinen, Aapo; Hoyer, Patrik O. and Inki, Mika., Topographic ICA as a Model of V1 Receptive Fields. Proc. of International Joint Conference on Neural Networks, v.03, pp 83-88, 2000.
- Hyvarinen, Aapo and Hoyer, Patrik O., Topographic Independent Component Analysis. Neural Computation, v.13, pp 1527-1558. (2000).
- Kohonen, T., Self-Organizing Maps. Springer, 2000.
- Linsker, R., Local Synaptic Rules Suffice to maximize Mutual Information in a Linear Network. Neural Computation, v.04, pp 691-702, 1992.
- Laughlin, Simon., A Simple Coding Procedure Enhances a Neuron's Information Capacity. Z. Naturforsch, v.36, pp 910-912, 1981.
- Oja, E., Neural Networks,Principal Components and Linear Neural Networks. Neural Networks, v.05, pp 27-935, 1989.
- Olshausen, B. A. and Field, D. J., Emergence of SimpleCell Receptive Field Properties by Learning a Sparse Coding for natural Images. Nature, v.381, pp 607-609, 1996.
- Osindero, Simon; Welling, Max and Hinton, Geoffrey E., Topographic Products Models Applied to Natural Scene Statistics. Neural Computation, v.18, pp 381- 414, 2006.
- Ray, K. L., McKay, D. R., Fox, P. M., Riedel, M. C., Uecker, A. M., Beckmann, C. F., Smith, S. M., Fox, P. T., Laird, A. ICA model order selection of task coactivation networks. Front. Neurosci. 7:237; 2013
- Simoncelli, E. P and Olshausen, B. A., Natural Image Statistics and Neural representations. Annu. Rev. Neuroscience, n. 24, pp 1193-1216, 2001.
- Shannon C. E., A Mathematical Theory of Communication. Bell Systems Technical Journal, v. 27, pp 379- 423, 1948.
- Stork, D.G. and Wilson, H.R. Do Gabor functions provide appropriate descriptions of visual cortical receptive fields? J Opt Soc Am A7, 1362-1373, 1990.
- Vinje, W. E. and Gallant, J. L., Sparse Coding and Decorrelation in Primary Visual Cortex During natural Vision. Vision Science, v. 287, pp 1273-1276, 2000.

#### Paper Citation

#### in Harvard Style

Santana E., Barros A., Jutten C., Santana E. and Oliveira L. (2016). **A Simple Algorithm for Topographic ICA** . In *Proceedings of the 9th International Joint Conference on Biomedical Engineering Systems and Technologies - Volume 4: BIOSIGNALS, (BIOSTEC 2016)* ISBN 978-989-758-170-0, pages 150-155. DOI: 10.5220/0005683501500155

#### in Bibtex Style

@conference{biosignals16,

author={Ewaldo Santana and Allan Kardec Barros and Christian Jutten and Eder Santana and Luis Claudio Oliveira},

title={A Simple Algorithm for Topographic ICA},

booktitle={Proceedings of the 9th International Joint Conference on Biomedical Engineering Systems and Technologies - Volume 4: BIOSIGNALS, (BIOSTEC 2016)},

year={2016},

pages={150-155},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005683501500155},

isbn={978-989-758-170-0},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 9th International Joint Conference on Biomedical Engineering Systems and Technologies - Volume 4: BIOSIGNALS, (BIOSTEC 2016)

TI - A Simple Algorithm for Topographic ICA

SN - 978-989-758-170-0

AU - Santana E.

AU - Barros A.

AU - Jutten C.

AU - Santana E.

AU - Oliveira L.

PY - 2016

SP - 150

EP - 155

DO - 10.5220/0005683501500155