# On Cluster Analysis Via Neuron Proximity in Monitored Self-Organizing Maps

### Susana Vegas-Azcárate, Jorge Muruzábal

#### 2005

#### Abstract

A potential application of self-organizing or topographic maps is clustering and visualization of high-dimensional data. It is well-known that an appropriate choice of the degree of smoothness in topographic maps is crucial for obtaining sensible results. Indeed, experimental evidence suggests that suitably monitored topographic maps should be preferred as they lead to more accurate performance. This paper reconsiders the basic toolkit for cluster analysis —based on the relative distance from each pointer to its immediate neighbours on the network— from this monitoring perspective. It is shown that the idea works nicely, that is, much useful information can be encoded and recovered via the trained map alone (ignoring any possible density estimate available). Moreover, the fact that a topographic map is not restricted to metric vector spaces makes this learning structure a perfect tool to deal with biological data, such as DNA or protein sequences of living organisms, for which only a similarity measure is readily available.

#### References

- Kohonen, T.: Self-Organizing Maps. Springer-Verlag, 3rd extended ed., Berlin (2001)
- Ferrán, E.A., Ferrara, P.: Topological maps of protein sequences. Biological Cybernetics 65 (1991) 451-458
- Kohonen, T., Somervuo, P.: How to make large self-organizing maps for nonvectorial data. Neural Networks 15 (2002) 945-952
- Gray, A.G., Moore, A.W.: Nonparametric density estimation: Toward computational tractability. In Barbará, D., Kamath, C., eds.: SDM: Proceedings of the Third SIAM International Conference on Data Mining, San Francisco, CA, USA, May 1-3, 2003, SIAM (2003)
- Davies, P.L., Kovac, A.: Densities, spectral densities and modality. Annals of Statistics 32 (2004) 1093-1136
- Scott, D.W., Szewczyk, W.F.: The stochastic mode tree and clustering. Journal of Computational and Graphical Statistics (2000)
- Muruzábal, J., Vegas-Azcárate, S.: On equiprobabilistic maps and plausible density estimation. In: 5th Workshop On Self-Organizing Maps, Paris. (2005)
- Zheng, Y., Greenleaf, J.F.: The effect of concave and convex weight adjustements on selforganizing maps. In: IEEE Transactions on Neural Networks. Volume 7-1. (1996) 87-96
- Bishop, C.M., Svensén, M., Williams, C.K.I.: Gtm: The generative topographic mapping. Neural Computation 10 (1997) 215-235
- Van Hulle, M.M.: Kernel-based equiprobabilistic topographic map formation. Neural Computation 10(7) (1998) 1847-1871
- Bauer, H.U., Pawelzik, K.: Quantifying the neighborhood preservation of self-organizing feature maps. IEEE Trans. Neural Networks 3 (1992) 570-579
- Kaski, S., Lagus, K.: Comparing self-organizing maps. In von der Malsburg, C., v.S.W.V.J.C., Sendhoff, B., eds.: Proceedings of ICANN'96, International Conference on Artificial Neural Networks, Lecture Notes in Computer Science. Volume 1112., Springer, Berlin (1996) 809-814
- Villmann, T., Der, R., Herrmann, M., Martinetz, T.: Topology preservation in self-organizing feature maps: Exact definition and measurement. IEEE Trans. Neural Networks 8(2) (1997) 256-266
- Lampinen, J., Kostiainen, T.: Overtraining and model selection with the self-organizing map. In: Proc. IJCNN'99, Washington, DC, USA. (1999)
- Haese, K., Goodhill, G.J.: Auto-som: Recursive parameter estimation for guidance of selforganizing feature maps. Neural Computation 13 (2001) 595-619
- Van Hulle, M.M.: Faithful representations and topographic maps: From distortion- to information-based self-organization. Wiley, New York (2000)

#### Paper Citation

#### in Harvard Style

Vegas-Azcárate S. and Muruzábal J. (2005). **On Cluster Analysis Via Neuron Proximity in Monitored Self-Organizing Maps** . In *Proceedings of the 1st International Workshop on Biosignal Processing and Classification - Volume 1: BPC, (ICINCO 2005)* ISBN 972-8865-35-X, pages 50-59. DOI: 10.5220/0001192800500059

#### in Bibtex Style

@conference{bpc05,

author={Susana Vegas-Azcárate and Jorge Muruzábal},

title={On Cluster Analysis Via Neuron Proximity in Monitored Self-Organizing Maps},

booktitle={Proceedings of the 1st International Workshop on Biosignal Processing and Classification - Volume 1: BPC, (ICINCO 2005)},

year={2005},

pages={50-59},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001192800500059},

isbn={972-8865-35-X},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 1st International Workshop on Biosignal Processing and Classification - Volume 1: BPC, (ICINCO 2005)

TI - On Cluster Analysis Via Neuron Proximity in Monitored Self-Organizing Maps

SN - 972-8865-35-X

AU - Vegas-Azcárate S.

AU - Muruzábal J.

PY - 2005

SP - 50

EP - 59

DO - 10.5220/0001192800500059