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Volumn 36, Issue 12, 2003, Pages 2945-2954

Data dimensionality estimation methods: A survey

Author keywords

Fractal dimension; Fukunaga Olsen's algorithm; Intrinsic dimensionality; Multidimensional scaling; Topological dimension

Indexed keywords

ALGORITHMS; DATA PROCESSING; PARAMETER ESTIMATION;

EID: 0142025120     PISSN: 00313203     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0031-3203(03)00176-6     Document Type: Article
Times cited : (251)

References (84)
  • 7
    • 0015011520 scopus 로고
    • An algorithm for finding intrinsic dimensionality of data
    • Fukunaga K. Olsen D.R. An algorithm for finding intrinsic dimensionality of data IEEE Trans. Comput. 20 2 1976 165-171
    • (1976) IEEE Trans. Comput. , vol.20 , Issue.2 , pp. 165-171
    • Fukunaga, K.1    Olsen, D.R.2
  • 10
    • 0018918171 scopus 로고
    • An algorithm for vector quantizer design
    • Linde Y. Buzo A. Gray R. An algorithm for vector quantizer design IEEE Trans. Commun. 28 1 1980 84-95
    • (1980) IEEE Trans. Commun. , vol.28 , Issue.1 , pp. 84-95
    • Linde, Y.1    Buzo, A.2    Gray, R.3
  • 11
    • 0016917031 scopus 로고
    • Statistical estimation of the intrinsic dimensionality of a noisy signal collection
    • Trunk G.V. Statistical estimation of the intrinsic dimensionality of a noisy signal collection IEEE Trans. Comput. 25 1976 165-171
    • (1976) IEEE Trans. Comput. , vol.25 , pp. 165-171
    • Trunk, G.V.1
  • 13
    • 0032070312 scopus 로고    scopus 로고
    • Intrinsic dimensionality estimation with optimally topology preserving maps
    • Bruske J. Sommer G. Intrinsic dimensionality estimation with optimally topology preserving maps IEEE Trans. Pattern Anal. Mach. Intell. 20 5 1998 572-575
    • (1998) IEEE Trans. Pattern Anal. Mach. Intell. , vol.20 , Issue.5 , pp. 572-575
    • Bruske, J.1    Sommer, G.2
  • 14
    • 0037818076 scopus 로고
    • Application of topological-representing networks to the estimation of the intrinsic dimensionality of data
    • F. Fogelman-Soulie, P. Gallinari (Eds.), Paris, France
    • F. Frisone, F. Firenze, P. Morasso, L. Ricciardiello, Application of topological-representing networks to the estimation of the intrinsic dimensionality of data, in: F. Fogelman-Soulie, P. Gallinari (Eds.), Proceedings of International Conference on Artificial Neural Networks, 1995, Paris, France, pp. 323-329.
    • (1995) Proceedings of International Conference on Artificial Neural Networks , pp. 323-329
    • Frisone, F.1    Firenze, F.2    Morasso, P.3    Ricciardiello, L.4
  • 18
    • 0028272776 scopus 로고
    • Representations and separation of signals using nonlinear pca type learning
    • Karhunen J. Joutsensalo J. Representations and separation of signals using nonlinear pca type learning Neural Networks 7 1 1994 113-127
    • (1994) Neural Networks , vol.7 , Issue.1 , pp. 113-127
    • Karhunen, J.1    Joutsensalo, J.2
  • 19
    • 0347243182 scopus 로고    scopus 로고
    • Nonlinear component analysis as a kernel eigenvalue problem
    • Schölkopf B. Smola A. Muller K.R. Nonlinear component analysis as a kernel eigenvalue problem Neural Computat. 10 1998 1299-1319
    • (1998) Neural Computat. , vol.10 , pp. 1299-1319
    • Schölkopf, B.1    Smola, A.2    Muller, K.R.3
  • 21
    • 0031254418 scopus 로고    scopus 로고
    • Nonlinear principal component analysis of neuronal spike train data
    • Fotheringhame D. Baddeley R.J. Nonlinear principal component analysis of neuronal spike train data Biol. Cybernet. 77 1997 282-288
    • (1997) Biol. Cybernet. , vol.77 , pp. 282-288
    • Fotheringhame, D.1    Baddeley, R.J.2
  • 22
    • 0031646493 scopus 로고    scopus 로고
    • Limitations of nonlinear pca as performed with generic neural networks
    • Malthouse E.C. Limitations of nonlinear pca as performed with generic neural networks IEEE Trans. Neural Networks 9 1 1998 165-173
    • (1998) IEEE Trans. Neural Networks , vol.9 , Issue.1 , pp. 165-173
    • Malthouse, E.C.1
  • 25
    • 0034476075 scopus 로고    scopus 로고
    • A new approach to dimensionality reduction: Theory and algorithms
    • Broomhead D.S. Kirby M. A new approach to dimensionality reduction: Theory and algorithms SIAM J. Appl. Math. 60 6 2000 2114-2142
    • (2000) SIAM J. Appl. Math. , vol.60 , Issue.6 , pp. 2114-2142
    • Broomhead, D.S.1    Kirby, M.2
  • 26
    • 0001295575 scopus 로고
    • Differentiable manifolds
    • Whitney H. Differentiable manifolds Ann. Math. 37 1936 645-680
    • (1936) Ann. Math. , vol.37 , pp. 645-680
    • Whitney, H.1
  • 29
    • 0041654220 scopus 로고
    • Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis
    • Kruskal J.B. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis Psychometrika 29 1964 1-27
    • (1964) Psychometrika , vol.29 , pp. 1-27
    • Kruskal, J.B.1
  • 30
    • 34250926052 scopus 로고
    • The analysis of proximities: Multidimensional scaling with an unknown distance function
    • Shepard R.N. The analysis of proximities: Multidimensional scaling with an unknown distance function Psychometrika 27 1962 125-140
    • (1962) Psychometrika , vol.27 , pp. 125-140
    • Shepard, R.N.1
  • 31
    • 0014563685 scopus 로고
    • The intrinsic dimensionality of signal collections
    • Bennett R.S. The intrinsic dimensionality of signal collections IEEE Trans. Inf. Theory 15 1969 517-525
    • (1969) IEEE Trans. Inf. Theory , vol.15 , pp. 517-525
    • Bennett, R.S.1
  • 32
    • 84887006810 scopus 로고
    • A nonlinear mapping for data structure analysis
    • Sammon J.W.J. A nonlinear mapping for data structure analysis IEEE Trans. Comput. C-18 1969 401-409
    • (1969) IEEE Trans. Comput. , vol.18 C , pp. 401-409
    • Sammon, J.W.J.1
  • 34
    • 84910237391 scopus 로고
    • A nonlinear mapping for data structure analysis
    • Kruskal J.B. A nonlinear mapping for data structure analysis IEEE Trans. Comput. C-20 1971 1614
    • (1971) IEEE Trans. Comput. , vol.20 C , pp. 1614
    • Kruskal, J.B.1
  • 35
    • 0142112329 scopus 로고
    • A heuristic relaxation method for nonlinear mapping in cluster analysis
    • Chang C.L. Lee R.C.T. A heuristic relaxation method for nonlinear mapping in cluster analysis IEEE Trans. Comput. C-23 1974 178-184
    • (1974) IEEE Trans. Comput. , vol.23 C , pp. 178-184
    • Chang, C.L.1    Lee, R.C.T.2
  • 36
    • 0003326616 scopus 로고
    • Parametric representation of nonlinear data structures
    • K.V. Mardia, J.T. Kent, J.M. Bibby (Eds.), Academic Press, New York
    • R.N. Shepard, J.D. Carroll, Parametric representation of nonlinear data structures, in: K.V. Mardia, J.T. Kent, J.M. Bibby (Eds.), Multivariate Analysis, Academic Press, New York, 1969, pp. 561-592.
    • (1969) Multivariate Analysis , pp. 561-592
    • Shepard, R.N.1    Carroll, J.D.2
  • 37
    • 40649095632 scopus 로고
    • Linear transformation of multivariate data to reveal clustering
    • A.K. Romney, R.N. Shepard, S.B. Nerlove (Eds.), Seminar Press, New York
    • J.B. Kruskal, Linear transformation of multivariate data to reveal clustering, in: A.K. Romney, R.N. Shepard, S.B. Nerlove (Eds.), Multidimensional Scaling, Vol. I, Seminar Press, New York, 1972, pp. 101-115.
    • (1972) Multidimensional Scaling , vol.1 , pp. 101-115
    • Kruskal, J.B.1
  • 38
    • 0000742860 scopus 로고
    • Geometrical models and badness-of-fit functions
    • K.V. Mardia, J.T. Kent, J.M. Bibby (Eds.), Academic Press, New York
    • J.B. Kruskal, J.D. Carroll, Geometrical models and badness-of-fit functions, in: K.V. Mardia, J.T. Kent, J.M. Bibby (Eds.), Multivariate Analysis, Vol. 2, Academic Press, New York, 1969, pp. 639-671.
    • (1969) Multivariate Analysis , vol.2 , pp. 639-671
    • Kruskal, J.B.1    Carroll, J.D.2
  • 39
    • 33645225931 scopus 로고
    • Representation of structure in similarity data problems and prospect
    • Shepard R.N. Representation of structure in similarity data problems and prospect Psychometrika 39 1974 373-421
    • (1974) Psychometrika , vol.39 , pp. 373-421
    • Shepard, R.N.1
  • 40
    • 0034704229 scopus 로고    scopus 로고
    • A global geometric framework for nonlinear dimensionality reduction
    • Tenenbaum J.B. de Silva V. Langford J.C. A global geometric framework for nonlinear dimensionality reduction Science 290 12 2000 2319-2323
    • (2000) Science , vol.290 , Issue.12 , pp. 2319-2323
    • Tenenbaum, J.B.1    de Silva, V.2    Langford, J.C.3
  • 41
    • 0034704222 scopus 로고    scopus 로고
    • Nonlinear dimensionality reduction by locally linear embedding
    • Roweis S. Saul L.K. Nonlinear dimensionality reduction by locally linear embedding Science 290 12 2000 2323-2326
    • (2000) Science , vol.290 , Issue.12 , pp. 2323-2326
    • Roweis, S.1    Saul, L.K.2
  • 42
    • 0030736375 scopus 로고    scopus 로고
    • Curvilinear component analysis: A self-organizing neural network for nonlinear mapping in cluster analysis
    • Demartines P. Herault J. Curvilinear component analysis: A self-organizing neural network for nonlinear mapping in cluster analysis IEEE Trans. Neural Networks 8 1 1997 148-154
    • (1997) IEEE Trans. Neural Networks , vol.8 , Issue.1 , pp. 148-154
    • Demartines, P.1    Herault, J.2
  • 46
    • 35949018382 scopus 로고
    • Ergodic theory of chaos and strange attractors
    • Eckmann J.P. Ruelle D. Ergodic theory of chaos and strange attractors Rev. Mod. Phys. 57 1985 617-659
    • (1985) Rev. Mod. Phys. , vol.57 , pp. 617-659
    • Eckmann, J.P.1    Ruelle, D.2
  • 48
    • 34250950477 scopus 로고
    • Dimension und äusseres mass
    • Hausdorff F. Dimension und äusseres mass Math. Ann. 79 1919 157-179
    • (1919) Math. Ann. , vol.79 , pp. 157-179
    • Hausdorff, F.1
  • 49
    • 5544314929 scopus 로고
    • An optimized box-assisted algorithm for fractal dimension
    • Grassberger P. An optimized box-assisted algorithm for fractal dimension Phys. Lett. A 148 1990 63-68
    • (1990) Phys. Lett. A , vol.148 , pp. 63-68
    • Grassberger, P.1
  • 50
    • 0037247254 scopus 로고    scopus 로고
    • Suboptimal minimum cluster volume cover-based method for measuring fractal dimension
    • Tolle C.R. Mc Junkin T.R. Gorisch D.J. Suboptimal minimum cluster volume cover-based method for measuring fractal dimension IEEE Trans. Pattern Anal. Mach. Intell. 25 1 2003 32-41
    • (2003) IEEE Trans. Pattern Anal. Mach. Intell. , vol.25 , Issue.1 , pp. 32-41
    • Tolle, C.R.1    Mc Junkin, T.R.2    Gorisch, D.J.3
  • 51
    • 84898957854 scopus 로고    scopus 로고
    • Intrinsic dimension estimation using packing numbers
    • S. Becker, S. Thrun, K. Obermayer (Eds.), MIT Press, Cambridge, MA
    • B. Kégl, Intrinsic dimension estimation using packing numbers, in: S. Becker, S. Thrun, K. Obermayer (Eds.), Advances in Neural Information Processing, Vol. 15, MIT Press, Cambridge, MA, 2003.
    • (2003) Advances in Neural Information Processing , vol.15
    • Kégl, B.1
  • 52
    • 40749093037 scopus 로고
    • Measuring the strangeness of strange attractors
    • Grassberger P. Procaccia I. Measuring the strangeness of strange attractors Physica D 9 1983 189-208
    • (1983) Physica D , vol.9 , pp. 189-208
    • Grassberger, P.1    Procaccia, I.2
  • 53
    • 0008626528 scopus 로고
    • Time series analysis
    • London Ser. A
    • Broomhead D.S. Jones R. Time series analysis Proc. R. Soc. London Ser. A 423 1989 103-121
    • (1989) Proc. R. Soc. , vol.423 , pp. 103-121
    • Broomhead, D.S.1    Jones, R.2
  • 54
    • 0001226331 scopus 로고
    • Optimal estimation of fractal dimension
    • M. Casdagli, S. Eubank (Eds.), .Addison-Wesley, Reading, MA
    • R.L. Smith, Optimal estimation of fractal dimension, in: M. Casdagli, S. Eubank (Eds.), Nonlinear Modeling and Forecasting, SFI Studies in the Sciences of Complexity, Vol. XII, Addison-Wesley, Reading, MA, 1992, pp. 115-135.
    • (1992) Nonlinear Modeling and Forecasting, SFI Studies in the Sciences of Complexity , vol.12 , pp. 115-135
    • Smith, R.L.1
  • 55
    • 0002405786 scopus 로고
    • On the numerical determination of the dimension of an attractor
    • B. Braaksma, H. Broer, F. Takens (Eds.), Springer, Berlin
    • F. Takens, On the numerical determination of the dimension of an attractor, in: B. Braaksma, H. Broer, F. Takens (Eds.), Dynamical Systems and Bifurcations, Proceedings Groningen 1984, Springer, Berlin, 1984, pp. 99-106.
    • (1984) Dynamical Systems and Bifurcations, Proceedings Groningen 1984 , pp. 99-106
    • Takens, F.1
  • 58
    • 0000478578 scopus 로고
    • Statistical precision of dimension estimators
    • Theiler J. Statistical precision of dimension estimators Phys. Rev. A 41 1990 3038-3051
    • (1990) Phys. Rev. A , vol.41 , pp. 3038-3051
    • Theiler, J.1
  • 59
    • 0000419983 scopus 로고
    • Lacunarity in a best estimator of fractal dimension
    • Theiler J. Lacunarity in a best estimator of fractal dimension Phys. Lett. A 133 1988 195-200
    • (1988) Phys. Lett. A , vol.133 , pp. 195-200
    • Theiler, J.1
  • 60
    • 44049117207 scopus 로고
    • Fundamental limitations for estimating dimensions and lyapounov exponents in dynamical systems
    • Eckmann J.P. Ruelle D. Fundamental limitations for estimating dimensions and lyapounov exponents in dynamical systems Phys. D 56 1992 185-187
    • (1992) Phys. D , vol.56 , pp. 185-187
    • Eckmann, J.P.1    Ruelle, D.2
  • 61
    • 0000201862 scopus 로고
    • Intrinsic limits on dimension calculations
    • Smith L.A. Intrinsic limits on dimension calculations Phys. Lett. A 133 1988 283-288
    • (1988) Phys. Lett. A , vol.133 , pp. 283-288
    • Smith, L.A.1
  • 62
  • 64
    • 0035425712 scopus 로고    scopus 로고
    • Intrinsic estimation of data: An approach based on grassberger-procaccia's algorithm
    • Camastra F. Vinciarelli A. Intrinsic estimation of data: An approach based on grassberger-procaccia's algorithm Neural Process. Lett. 14 1 2001 27-34
    • (2001) Neural Process. Lett. , vol.14 , Issue.1 , pp. 27-34
    • Camastra, F.1    Vinciarelli, A.2
  • 65
    • 0036807213 scopus 로고    scopus 로고
    • Estimating the intrinsic dimension of data with a fractal-based method
    • Camastra F. Vinciarelli A. Estimating the intrinsic dimension of data with a fractal-based method IEEE Trans. Pattern Anal. Mach. Intell. 24 10 2002 1404-1407
    • (2002) IEEE Trans. Pattern Anal. Mach. Intell. , vol.24 , Issue.10 , pp. 1404-1407
    • Camastra, F.1    Vinciarelli, A.2
  • 66
    • 0025236073 scopus 로고
    • Application of the karhunen-loève procedure for the characterization of human faces
    • Kirby M. Sirovich L. Application of the karhunen-loève procedure for the characterization of human faces IEEE Trans. Pattern Anal. Mach. Intell. 12 1 1990 103-108
    • (1990) IEEE Trans. Pattern Anal. Mach. Intell. , vol.12 , Issue.1 , pp. 103-108
    • Kirby, M.1    Sirovich, L.2
  • 67
    • 0028391786 scopus 로고
    • Can the fractal dimension of images be measured?
    • Huang Q. Lorch J.R. Dubes R.C. Can the fractal dimension of images be measured? Pattern Recognition 27 3 1994 339-349
    • (1994) Pattern Recognition , vol.27 , Issue.3 , pp. 339-349
    • Huang, Q.1    Lorch, J.R.2    Dubes, R.C.3
  • 68
    • 0031235435 scopus 로고    scopus 로고
    • Convergence of numerical box-counting and correlation integral multifractal analysis techniques
    • Meisel L.V. Johnson M.A. Convergence of numerical box-counting and correlation integral multifractal analysis techniques Pattern Recognition 30 9 1997 1565-1570
    • (1997) Pattern Recognition , vol.30 , Issue.9 , pp. 1565-1570
    • Meisel, L.V.1    Johnson, M.A.2
  • 69
    • 0001974770 scopus 로고
    • Statistical aspects of chaos: A review
    • O.E. Barndorff-Nielsen, J.L. Jensen, W.S. Kendall (Eds.), Chapman - Hall, London
    • V. Isham, Statistical aspects of chaos: A review, in: O.E. Barndorff-Nielsen, J.L. Jensen, W.S. Kendall (Eds.), Networks and Chaos-Statistical and Probabilistic Aspects, Chapman - Hall, London, 1993, pp. 124-200.
    • (1993) Networks and Chaos-Statistical and Probabilistic Aspects , pp. 124-200
    • Isham, V.1
  • 70
    • 0025178623 scopus 로고
    • Low-dimensional chaos in cardiac tissue
    • Chialvo D.R. Gilmour R.F. Jalife J. Low-dimensional chaos in cardiac tissue Nature 343 1990 653-658
    • (1990) Nature , vol.343 , pp. 653-658
    • Chialvo, D.R.1    Gilmour, R.F.2    Jalife, J.3
  • 71
    • 0033629141 scopus 로고    scopus 로고
    • Inverse covariation of spectral density and correlation dimension in cyclic eeg dimension of the human brain
    • Tirsch W.S. Keidel M. Perz S. Scherb H. Sommer G. Inverse covariation of spectral density and correlation dimension in cyclic eeg dimension of the human brain Biol. Cybernet. 82 2000 1-14
    • (2000) Biol. Cybernet. , vol.82 , pp. 1-14
    • Tirsch, W.S.1    Keidel, M.2    Perz, S.3    Scherb, H.4    Sommer, G.5
  • 72
    • 0029191714 scopus 로고
    • Detection of signals in chaos
    • Haykin S. Bo Li X. Detection of signals in chaos Proc. IEEE 83 1 1995 95-122
    • (1995) Proc. IEEE , vol.83 , Issue.1 , pp. 95-122
    • Haykin, S.1    Bo Li, X.2
  • 73
    • 0038173254 scopus 로고    scopus 로고
    • Speech dimensionality analysis on hypercubical self-organizing maps
    • Somervuo P. Speech dimensionality analysis on hypercubical self-organizing maps Neural Process. Lett. 17 2 2003 125-136
    • (2003) Neural Process. Lett. , vol.17 , Issue.2 , pp. 125-136
    • Somervuo, P.1
  • 74
    • 0001376652 scopus 로고
    • Nonlinear dynamics and stock returns
    • Scheinkman J.A. Le Baron B. Nonlinear dynamics and stock returns J. Bus. 62 1989 311-337
    • (1989) J. Bus. , vol.62 , pp. 311-337
    • Scheinkman, J.A.1    Le Baron, B.2
  • 78
    • 0000779360 scopus 로고
    • Detecting strange attractor in turbolence
    • D. Rand, L.S. Young (Eds.), Warwick, Springer, Berlin
    • F. Takens, Detecting strange attractor in turbolence, in: D. Rand, L.S. Young (Eds.), Dynamical Systems and Turbolence, Warwick 1980, Springer, Berlin, 1981, pp. 366-381.
    • (1980) Dynamical Systems and Turbolence , pp. 366-381
    • Takens, F.1
  • 79
    • 0003290175 scopus 로고
    • On the dimension of compact invariant sets of certain nonlinear maps
    • D. Rand, L.S. Young (Eds.), Warwick, Springer, Berlin
    • R. Mañé, On the dimension of compact invariant sets of certain nonlinear maps, in: D. Rand, L.S. Young (Eds.), Dynamical Systems and Turbolence, Warwick 1980, Springer, Berlin, 1981, pp. 230-242.
    • (1980) Dynamical Systems and Turbolence , pp. 230-242
    • Mañé, R.1
  • 80
    • 0033075129 scopus 로고    scopus 로고
    • Neural short-term prediction based on dynamics reconstruction
    • Camastra F. Colla A.M. Neural short-term prediction based on dynamics reconstruction Neural Process. Lett. 9 1 1999 45-52
    • (1999) Neural Process. Lett. , vol.9 , Issue.1 , pp. 45-52
    • Camastra, F.1    Colla, A.M.2
  • 82
    • 0000241853 scopus 로고
    • Deterministic non-periodic flow
    • Lorenz E.N. Deterministic non-periodic flow J. Atmos. Sci. 20 1963 130-141
    • (1963) J. Atmos. Sci. , vol.20 , pp. 130-141
    • Lorenz, E.N.1
  • 83
    • 0026281692 scopus 로고
    • The bakerian lecture 1991: The predictability of weather and climates
    • London Ser. A
    • Houghton J. The bakerian lecture 1991: The predictability of weather and climates Philos. Trans. R. Soc. London Ser. A 337 1991 521-572
    • (1991) Philos. Trans. R. Soc. , vol.337 , pp. 521-572
    • Houghton, J.1
  • 84
    • 4243746560 scopus 로고
    • Studies in astronomical time series analysis. iv. modeling chaotic and random processes with linear filters
    • Scargle J. Studies in astronomical time series analysis. iv. modeling chaotic and random processes with linear filters Astrophys. J. 359 1990 469-482
    • (1990) Astrophys. J. , vol.359 , pp. 469-482
    • Scargle, J.1


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