nips nips2004 nips2004-114 nips2004-114-reference knowledge-graph by maker-knowledge-mining
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Author: Elizaveta Levina, Peter J. Bickel
Abstract: We propose a new method for estimating intrinsic dimension of a dataset derived by applying the principle of maximum likelihood to the distances between close neighbors. We derive the estimator by a Poisson process approximation, assess its bias and variance theoretically and by simulations, and apply it to a number of simulated and real datasets. We also show it has the best overall performance compared with two other intrinsic dimension estimators. 1
[1] S. T. Roweis and L. K. Saul. Nonlinear dimensionality reduction by locally linear embedding. Science, 290:2323–2326, 2000.
[2] J. B. Tenenbaum, V. de Silva, and J. C. Landford. A global geometric framework for nonlinear dimensionality reduction. Science, 290:2319–2323, 2000.
[3] M. Belkin and P. Niyogi. Laplacian eigenmaps and spectral techniques for embedding and clustering. In Advances in NIPS, volume 14. MIT Press, 2002.
[4] D. L. Donoho and C. Grimes. Hessian eigenmaps: New locally linear embedding techniques for high-dimensional data. Technical Report TR 2003-08, Department of Statistics, Stanford University, 2003.
[5] M. Belkin and P. Niyogi. Using manifold structure for partially labelled classification. In Advances in NIPS, volume 15. MIT Press, 2003.
[6] M. Vlachos, C. Domeniconi, D. Gunopulos, G. Kollios, and N. Koudas. Non-linear dimensionality reduction techniques for classification and visualization. In Proceedings of 8th SIGKDD, pages 645–651. Edmonton, Canada, 2002.
[7] M. Brand. Charting a manifold. In Advances in NIPS, volume 14. MIT Press, 2002.
[8] K.W. Pettis, T.A. Bailey, A.K. Jain, and R.C. Dubes. An intrinsic dimensionality estimator from near-neighbor information. IEEE Trans. on PAMI, 1:25–37, 1979.
[9] K. Fukunaga and D.R. Olsen. An algorithm for finding intrinsic dimensionality of data. IEEE Trans. on Computers, C-20:176–183, 1971.
[10] J. Bruske and G. Sommer. Intrinsic dimensionality estimation with optimally topology preserving maps. IEEE Trans. on PAMI, 20(5):572–575, 1998.
[11] P. Verveer and R. Duin. An evaluation of intrinsic dimensionality estimators. IEEE Trans. on PAMI, 17(1):81–86, 1995.
[12] P. Grassberger and I. Procaccia. Measuring the strangeness of strange attractors. Physica, D9:189–208, 1983.
[13] F. Camastra and A. Vinciarelli. Estimating the intrinsic dimension of data with a fractal-based approach. IEEE Trans. on PAMI, 24(10):1404–1407, 2002.
[14] B. Kegl. Intrinsic dimension estimation using packing numbers. In Advances in NIPS, volume 14. MIT Press, 2002.
[15] J. Costa and A. O. Hero. Geodesic entropic graphs for dimension and entropy estimation in manifold learning. IEEE Trans. on Signal Processing, 2004. To appear.
[16] D. L. Snyder. Random Point Processes. Wiley, New York, 1975.