This article presents a short discussion on optimum neighborhood size selection in a spherical selforganizing feature map (SOFM). A majority of the literature on the SOFMs have addressed the issue of selecting optimal learning parameters in the case of Cartesian topology SOFMs. However, the use of a Spherical SOFM suggested that the learning aspects of Cartesian topology SOFM are not directly translated. This article presents an approach on how to estimate the neighborhood size of a spherical SOFM based on the data. It adopts the L-curve criterion, previously suggested for choosing the regularization parameter on problems of linear equations where their right-hand-side is contaminated with noise. Simulation results are presented on two artificial 4D data sets of the coupled Hénon-Ikeda map., {"references":["T. Kohonen, \"Self-organized formation of topologically correct feature\nmaps\", Biological Cybernetics, vol. 43, pp. 59-69, 1982","G. Deboeck, T. Kohonen, Visual Explorations in Finance with Selforganizing\nMaps. London: Springer-Verlag, 1998","M. Gross, F. Seibert, \"Visualization of multi-dimensional image data\nsets using a neural network\", The Visual Computer, International\nJournal of Computer Graphics, vol. 10, pp. 145-159, 1993","M. Gross, Visual Computing: The Integration of Computer Graphics,\nVisual Perception and Imaging. Berlin: Springer-Verlag, 1994","J. Vesanto, \"SOM-based data visualization methods\", Journal of\nIntelligent Data Analysis, vol. 3, pp. 111-126, 1999","J. Vesanto, E. Alhoniemi, \"Clustering of the self-organizing map\", IEEE\nTransactions on Neural Networks, vol. 11, pp. 586-600, 2000","H. Ritter, \"Self-organizing maps on non-Euclidean spaces\", in Kohonen\nMaps, E. Oja and S. Kaski, Amsterdam: Elsevier Science B. V., 1999,\npp. 97-109","A. Sangole, G. K. Knopf, \"Representing high-dimensional data sets as\nclose surfaces\", Journal of Information Visualization, vol. 1, pp. 111-\n119, 2002","A. P. Sangole, \"Data-driven Modeling using Spherical Self-organizing\nFeature Maps\", Ph.D. dissertation, Dept. of Mech. and Mat. Eng., The\nUniversity of Western Ontario, London, ON, Canada, 2003\n[10] A. Sangole, G. K. Knopf, \"Geometric representations for highdimensional\ndata using a spherical SOFM\", International Journal of\nSmart Engineering System Design, vol. 5, pp. 11-20, 2003\n[11] A. Sangole, G. K. Knopf, \"Visualization of random ordered numeric\ndata sets using self-organized feature maps\", Computers and Graphics,\nvol. 27, pp. 963-976, 2003\n[12] K. Haese, \"Self-organizing feature maps with self-adjusting learning\nparameters\", IEEE Transactions on Neural Networks, vol. 9, pp. 1270-\n1278, 1998\n[13] P. C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems. SIAM,\n1997, pp. 186-193\n[14] M. Hénon, \"A two-dimensional map with strange attractor\",\nCommunications in Mathematical Physics, vol. 50, pp. 69-77, 1976\n[15] K. Ikeda, \"Multiple-valued stationary state and its instability of the\ntransmitted light by a ring cavity system\", Optics Communications, vol.\n30, p. 257, 1979"]}