Search

Cluster analysis of existing database of spinal shape of patients attending a scoliosis clinic.To determine whether patients with scoliosis can be classified into distinct groups by 3-dimensional curve shape.Subjective or semiquantitative methods can be used to classify curve types in scoliosis, with the goal of rationalizing surgical planning. There are very few reports of using objective methods such as cluster analysis to improve this process. METHODS.: One hundred ten patients who underwent radiography of the spine by a stereo technique, at a scoliosis clinic in the period between 1982 and 1990, were studied. Fifty-six were studied longitudinally (average 3.4 clinic visits each), providing 245 total observations. Selected patients had 2 scoliosis curves with apex between T4 and L3, and both Cobb angles9 degrees by an automated measurement. The 3-dimensional spinal shape was reconstructed from stereoradiographs. Each curve was quantified by its Cobb angle, apex level, apex vertebra rotation, and rotation of the plane of maximum curvature (PMC) (8 variables). Cluster analysis classified each patient at each visit by these variables.When the analysis searched for 4 clusters, the largest cluster (148 of 245 observations) was the pattern having counterclockwise rotation of the PMC of both curves (typically, a right upper scoliosis curve with kyphosis and left lower scoliosis curve with lordosis). The other 3 clusters (48, 34, and 15 observations) were the other permutations of these variables. Substantial overlap of all the other variables between groups was observed. Of the 56 patients seen longitudinally, 25 were consistently grouped at all clinic visits.Spinal shape of patients in a clinic population with 2 scoliosis curves form distinct groups according to the 4 permutations of the signs of the rotations of the PMC in 2 curve regions. The pattern can change with repeated observation, often because a slight curvature in the sagittal plane can change because of postural variation and measurement errors. Overlap of the other curve-shape variables between groups suggests that these spinal deformity classifications alone should not determine treatment strategy.

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"]}