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An Evaluation of Intrinsic Dimensionality Estimators
January 1995 (vol. 17 no. 1)
pp. 81-86
Abstract—The intrinsic dimensionality of a data set may be useful for understanding the properties of classifiers applied to it and thereby for the selection of an optimal classifier.
In this paper we compare the algorithms for two estimators of the intrinsic dimensionality of a given data set and extend their capabilities. One algorithm is based on the local eigenvalues of the covariance matrix in several small regions in the feature space. The other estimates the intrinsic dimensionality from the distribution of the distances from an arbitrary data vector to a selection of its neighbors.
The characteristics of the two estimators are investigated and the results are compared. It is found that both can be applied successfully, but that they might fail in certain cases. The estimators are compared and illustrated using data generated from chromosome banding profiles.
[1] 81 T.J. Sejnowski and C.R. Rosenberg,“NETtalk: a parallel network that learns to read aloud,” The John Hopkins University Electrical Engineering and Comp. Science, Technical Report JHU/EECS-86/01, 1986, Reprinted in J.A. Anderson and E. Rosenfeld, Neurocomputing: Foundations of Research, MIT Press, Cambridge, 1988[2] D.A. Pomerleau,“ALVINN: an autonomous land vehicle in a neural network,” Advances in neural information processing systems, ed Touretzky, Morgan, Kaufman Publishers, San Mateo, pp. 305-331, 1989[3] B.A. Golomb, D.T. Lawrence, and T.J. Sejnowski, “Sexnet: A Neural Network Identifies Sex from Human Faces,” Advances in Neural Information Processing Systems, R.P. Lippman, J. Moody, and D.S. Touretzky, eds., vol. 3, pp. 572-577, San Mateo, Calif.: Morgan Kaufmann, 1991.[4] S.I. Kamata,R.O. Eason,A. Perez, and E. Kawaguchi,“A neural network classifier for LANDSAT image data,” Proceedings 11th IAPR International Conference onPattern Recognition, VolumeII, Conference B: Pattern Recognition Methodology and Systems (ICPR11, The Hague,The Netherlands, August 30 - September 3, 1992), IEEE Computer Society Press, Los Alamitos, California, pp. 573-576, 1992[5] R.P.W. Duin,“Superlearning capabilities of neural networks?,” Proc. of the 8th Scandinavian Conference on Image Analysis, NOBIM,Norwegian Society for Image Processing and Pattern Recognition, Tromsø, Norway, pp. 547-554, 1993[6] R.S. Bennet, The Intrinsic Dimensionality of Signal Collections IEEE Trans. Information Theory, vol. 15, no. 5, pp. 517-525, Sept. 1969.[7] G.V. Trunk,“Statistical estimation of the intrinsic dimensionality of a noisy signal collection,” IEEE Trans. Comp., vol. C-25, pp. 165-171, 1976[8] A.K. Jain and R.C. Dubes, Algorithms for Clustering Data. Englewood Cliffs, N.J.: Prentice Hall, 1988.[9] N. Wyse,R. Dubes, and A.K. Jain,“A critical evaluation of intrinsic dimensionality algorithms,” Pattern Recognition in Practice, ed Gelsema, E.S. and Kanal, L.N., North-Holland Publishing Company, pp. 415-425, 1980[10] K. Fukunaga and D.R. Olsen,“An algorithm for finding intrinsic dimensionality of data,” IEEE Trans. Comp., vol. C-20, pp. 176-183, 1971[11] K.W. Pettis,T.A. Bailey,A.K. Jain, and R.C. Dubes,“An intrinsic dimensionality estimator from near-neighbor information,” IEEE Trans. Patt. Anal. Machine Intell., vol. 1, pp. 25-37, 1979[12] K. Fukunaga, Introduction to Statistical Pattern Recognition, second edition. Academic Press, 1990.[13] P.J. Verveer and R.P.W Duin,“Estimators for the intrinsic dimensionality evaluated and applied,” Delft University of Technology, Faculty of Applied Physics,Pattern Recognition Group, Technical Report, 1993[14] Ph.A. Errington and J. Graham,“Application of artificial neural networks to chromosome classification,” Cytometry, vol. 14, pp. 627-639, 1993
Citation:
Peter J. Verveer, Robert P.W. Duin, "An Evaluation of Intrinsic Dimensionality Estimators," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 17, no. 1, pp. 81-86, Jan. 1995, doi:10.1109/34.368147
