nips nips2002 nips2002-34 nips2002-34-reference knowledge-graph by maker-knowledge-mining
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Author: Nicholas P. Hughes, David Lowe
Abstract: We consider the problem of illusory or artefactual structure from the visualisation of high-dimensional structureless data. In particular we examine the role of the distance metric in the use of topographic mappings based on the statistical field of multidimensional scaling. We show that the use of a squared Euclidean metric (i.e. the SS TRESS measure) gives rise to an annular structure when the input data is drawn from a highdimensional isotropic distribution, and we provide a theoretical justification for this observation.
[1] T. F. Cox and M. A. A. Cox. Multidimensional scaling. Chapman and Hall, London, 1994.
[2] J. deLeeuw and B. Bettonvil. An upper bound for sstress. Psychometrika, 51:149 – 153, 1986.
[3] G. J. Goodhill, M. W. Simmen, and D. J. Willshaw. An evaluation of the use of multidimensional scaling for understanding brain connectivity. Philosophical Transactions of the Royal Society, Series B, 348:256 – 280, 1995.
[4] H. Klock and J. M. Buhmann. Multidimensional scaling by deterministic annealing. In M. Pelillo and E. R. Hancock, editors, Energy Minimization Methods in Computer Vision and Pattern Recognition, Proc. Int. Workshop EMMCVPR ’97, Venice, Italy, pages 246–260. Springer Lecture Notes in Computer Science, 1997.
[5] D. Lowe and M. E. Tipping. Neuroscale: Novel topographic feature extraction with radial basis function networks. In M. C. Mozer, M. I. Jordan, and T. Petsche, editors, Advances in Neural Information Processing Systems 9. Cambridge, MA: MIT Press, 1997.
[6] K. V. Mardia, J. T. Kent, and J. M. Bibby. Multivariate analysis. Academic Press, 1997.
[7] S. T. Roweis, L. K. Saul, and G. E. Hinton. Global coordination of local linear models. In T. G. Dietterich, S. Becker, and Z. Ghahramani, editors, Advances in Neural Information Processing Systems 14. Cambridge, MA: MIT Press, 2002.
[8] J. W. Sammon. A nonlinear mapping for data structure analysis. IEEE Transactions On Computers, C-18(5):401 – 409, 1969.
[9] M. W. Simmen, G. J. Goodhill, and D. J. Willshaw. Scaling and brain connectivity. Nature, 369:448–450, 1994.
[10] J. B. Tenenbaum. Mapping a manifold of perceptual observations. In M. I. Jordan, M. J. Kearns, and S. A. Solla, editors, Advances in Neural Information Processing Systems 10. Cambridge, MA: MIT Press, 1998.
[11] C. K. Williams. On a connection between kernel PCA and metric multidimensional scaling. In T. K. Leen, T. G. Diettrich, and V. Tresp, editors, Advances in Neural Information Processing Systems 13. Cambridge, MA: MIT Press, 2001.
[12] M. P. Young. Objective analysis of the topological organization of the primate cortical visual system. Nature, 358:152–155, 1992.
[13] M. P. Young, J. W. Scannell, M. A. O’Neill, C. C. Hilgetag, G. Burns, and C. Blakemore. Non-metric multidimensional scaling in the analysis of neuroanatomical connection data and the organization of the primate cortical visual system. Philosophical Transactions of the Royal Society, Series B, 348:281 – 308, 1995.