DANCo: An intrinsic dimensionality estimator exploiting angle and norm concentration

Pattern Recognition - Tập 47 - Trang 2569-2581 - 2014
Claudio Ceruti1, Simone Bassis2, Alessandro Rozza3, Gabriele Lombardi2, Elena Casiraghi2, Paola Campadelli2
1Dipartimento di Matematica, Università degli Studi di Milano, Via Saldini 50, Milan, Italy
2Dipartimento di Informatica, Università degli Studi di Milano, Via Comelico 39/41, Milan, Italy
3Dipartimento di Scienze e Tecnologie, Università degli Studi di Napoli – Parthenope, Centro Direzionale, Isola C4, Naples, Italy

Tài liệu tham khảo

K. Fukunaga, Intrinsic dimensionality extraction, in: P.R. Krishnaiah, L.N. Kanal (Eds.), Classification, Pattern Recognition and Reduction of Dimensionality, 1982. Bellman, 1961 Kirby, 1998 Vapnik, 1998 Friedman, 2009 Camastra, 2009, A comparative evaluation of nonlinear dynamics methods for time series prediction, Neural Comput. Appl., 18, 1021, 10.1007/s00521-009-0266-y Valle, 2010, Crystal fingerprint space – a novel paradigm for studying crystal-structure sets, Acta Crystallogr. Sect. A, 66, 507, 10.1107/S0108767310026395 Camastra, 2002, Estimating the intrinsic dimension of data with a fractal-based method, IEEE Trans. Pattern Anal. Mach. Intell., 24, 1404, 10.1109/TPAMI.2002.1039212 G. Lombardi, A. Rozza, C. Ceruti, E. Casiraghi, P. Campadelli, Minimum neighbor distance estimators of intrinsic dimension, in: Proceedings of ECML-PKDD, vol. 6912, 2011, pp. 374–389. A. Rozza, G. Lombardi, M. Rosa, E. Casiraghi, P. Campadelli, IDEA: intrinsic dimension estimation algorithm, in: Proceedings of ICIAP, vol. 6978, 2011, pp. 433–442. Rozza, 2012, Novel high intrinsic dimensionality estimators, Mach. Learn., 89, 37, 10.1007/s10994-012-5294-7 Camastra, 2003, Data dimensionality estimation methods, Pattern Recognit., 36, 2945, 10.1016/S0031-3203(03)00176-6 Jollife, 1986, 10.1007/978-1-4757-1904-8 Lin, 2008, Riemannian manifold learning, IEEE Trans. Pattern Anal. Mach. Intell., 30, 796, 10.1109/TPAMI.2007.70735 Fukunaga, 1971, An algorithm for finding intrinsic dimensionality of data, IEEE Trans. Comput., 20, 176, 10.1109/T-C.1971.223208 Verveer, 1995, An evaluation of intrinsic dimensionality estimators, IEEE Trans. Pattern Anal. Mach. Intell., 17, 81, 10.1109/34.368147 Tipping, 1997, Probabilistic principal component analysis, J. R. Stat. Soc. Ser. B, 61, 611 C.M. Bishop, Bayesian PCA, in: Proceedings of NIPS, vol. 11, 1998, pp. 382–388. J. Li, D. Tao, Simple exponential family PCA, in: Proceedings of AISTATS, 2010, pp. 453–460. Zou, 2004, Sparse principal component analysis, J. Comput. Gr. Stat., 15, 265, 10.1198/106186006X113430 Guan, 2009, Sparse probabilistic principal component analysis, J. Mach. Learn. Res.—Proc. Track, 5, 185 Levina, 2005, Maximum likelihood estimation of intrinsic dimension, Proc. NIPS, 171, 777 Pettis, 1979, An intrinsic dimensionality estimator from near-neighbor information, IEEE Trans. Pattern Anal. Mach. Intell., 1, 25, 10.1109/TPAMI.1979.4766873 Mordohai, 2010, Dimensionality estimation, manifold learning and function approximation using tensor voting, J. Mach. Learn. Res., 11, 411 Grassberger, 1983, Measuring the strangeness of strange attractors, Phys. D: Nonlinear Phenom., 9, 189, 10.1016/0167-2789(83)90298-1 Brand, 2003, Charting a manifold, Adv. Neural Inf. Process. Syst., 15, 961 M. Hein, Intrinsic dimensionality estimation of submanifolds in euclidean space, in: Proceedings of ICML, 2005, pp. 289–296. A.M. Farahmand, C. Szepesvari, J.Y. Audibert, Manifold-adaptive dimension estimation, in: Proceedings of ICML, 2007, pp. 265–272. Kégl, 2002, Intrinsic dimension estimation using packing numbers, 681 M. Raginsky, S. Lazebnik, Estimation of intrinsic dimensionality using high-rate vector quantization, in: NIPS, 2005, pp. 1105–1112. Graf, 2000 J.A. Costa, A.O. Hero, Learning intrinsic dimension and entropy of high-dimensional shape spaces, in: Proceedings of EUSIPCO, 2004, pp. 1–22. Costa, 2004, Geodesic entropic graphs for dimension and entropy estimation in manifold learning, IEEE Trans. Signal Process., 52, 2210, 10.1109/TSP.2004.831130 Tenenbaum, 2000, A global geometric framework for nonlinear dimensionality reduction, Science, 290, 2319, 10.1126/science.290.5500.2319 Eckmann, 1992, Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems, Phys. D: Nonlinear Phenom., 56, 185, 10.1016/0167-2789(92)90023-G Q. Wang, S.R. Kulkarni, S. Verdu, A nearest-neighbor approach to estimating divergence between continuous random vector, in: Proceedings of ISIT, 2006, pp. 242–246. Mardia, 1972 Sodergren, 2011, On the distribution of angles between the N shortest vectors in a random lattice, J. Lond. Math. Soc., 84, 749, 10.1112/jlms/jdr032 Mardia, 2009 Breitenberger, 1963, Analogues of the normal distribution on the circle and the sphere, Biometrika, 50, 81, 10.1093/biomet/50.1-2.81 Upton, 1974, New approximations to the distribution of certain angular statistics, Biometrika, 61, 369, 10.1093/biomet/61.2.369 Abramowitz, 1964 Hill, 1976, New approximations to the von Mises distribution, Biometrika, 63, 673, 10.2307/2335751 Upton, 1986, Approximate confidence intervals for the mean direction of a von Mises distribution, Biometrika, 73, 525, 10.1093/biomet/73.2.525 Fisher, 1996 A.P.N. Vo, S. Oraintara, T.T. Nguyen, Statistical image modeling using von Mises distribution in the complex directional wavelet domain, in: Proceedings of ISCAS 2008, 2008, pp. 2885–2888. O׳Neill, 2006 Lord, 1954, The use of the Hankel transform in statistics I. General theory and examples, Biometrika, 41, 44, 10.2307/2333004 Coleman, 1996, An interior, trust region approach for nonlinear minimization subject to bounds, SIAM J. Optim., 6, 418, 10.1137/0806023 Fishman, 1996 LeCun, 1998, Gradient-based learning applied to document recognition, Proc. IEEE, 86, 2278, 10.1109/5.726791 F.J. Pineda, J.C. Sommerer, Estimating generalized dimensions and choosing time delays: a fast algorithm, in: Time Series Prediction. Forecasting the Future and Understanding the Past, 1994, pp. 367–385. A. Frank, A. Asuncion, UCI Machine Learning Repository, 2010, 〈http://archive.ics.uci.edu/ml〉. J.A. Costa, A.O. Hero, Learning intrinsic dimension and entropy of shapes, in: Statistics and Analysis of Shapes, Birkhauser, 2005, pp. 650–663. Ott, 1993 I. Kivimäki, K. Lagus, I. Nieminen, J. Väyrynen, T. Honkela, Using correlation dimension for analysing text data, in: Proceedings of the ICANN, Springer-Verlag, Berlin, Heidelberg, 2010, pp. 368–373. Chua, 1985, The double scroll, IEEE Trans. Circuits Syst., 32, 797, 10.1109/TCS.1985.1085791 Demšar, 2006, Statistical comparisons of classifiers over multiple data sets, J. Mach. Learn. Res., 7, 1 J.A. Parejo, J. García, A. Ruiz-Cortés, J.C. Riquelme, Statservice: Herramienta de análisis estadístico como soporte para la investigación con metaheurísticas, in: Actas del VIII Congreso Expañol sobre Metaheurísticas, Algoritmos Evolutivos y Bio-inspirados, 2012.