Geodesic entropic graphs for dimension and entropy estimation in manifold learning

By Jose A. Costa, A. Hero. IEEE Transactions on Signal Processing, 2004

306 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Ecology, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/3d09149170341e3726c37163b4b3c2b2c8e91258

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Citations in the corpus

Parametric Bayesian Estimation of Differential Entropy and Relative Entropy (2010, unknown): “[12–14].”
Towards a comprehensive assessment of model structural adequacy (2012, methodology): “…this regard, methods from the fields of nonlinear time series analysis [Kantz and Schreiber, 2004], Bayesian belief networks [Pearl, 1986], graph theory [Gerasoulis and Yang, 1993], information theory [Cover and Thomas, 2006], and manifold learning [Costa and Hero, 2004] are likely to prove useful.”
Riemannian Manifold Learning (2008, background): “distances [41], [42], [43], [44] or fractal dimensions [45].”
Random Projections of Smooth Manifolds (2009, methodology): “Additional algorithms have also been proposed for characterizing manifolds from sampled data without constructing an explicit embedding in RM [12, 14, 31] and for constructing functions on the point samples in RN that reflect the intrinsic structure of the manifold [4, 13].”
Topological Data Analysis (2016, background): “Some examples include Little et al. (2011); Lombardi et al. (2011); Hein & Audibert (2005); Levina & Bickel (2004); K´egl (2002); Costa & Hero (2004).”
Intrinsic dimension estimation: Advances and open problems (2016, methodology): “Costa-Hero’s algorithm [19], Lin-Zha’s simplex-based method [61], IDEA [81,82] and DANCo [14] algorithms belong to this category.”
Nearest-Neighbor Searching and Metric Space Dimensions (2005, methodology): “In the setting of Euclidean manifolds, Costa and Hero [CH04] propose the use as dimension estimators of the minimum spanning tree, matching, k-NN graph, or other extremal graphs.”
Maximum Likelihood Estimation of Intrinsic Dimension (2004, methodology): “…of sample size and dimension is not well understood or studied beyond the obvious “curse of dimensionality”; the statistical properties of the estimators, such as bias and variance, have not been looked at (with the exception of [15]); and comparisons between methods are not always presented.”
Regression on manifolds: Estimation of the exterior derivative (2011, methodology): “This can either be done with dimensionality estimators [12, 23, 35] or with resampling-based approaches.”