Applications of entropic spanning graphs

By A. Hero, Bing Ma, Olivier J. J. Michel, John D. Gorman. 2002

307 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Media Technology

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Citations in the corpus

On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles (2006, background): “statistical mechanics, physics of turbulence, cosmology, see [10,11,12] and references therein), but in various other areas such as in signal processing (time scale analysis, decision problems, machine learning, see [4,13,14,15] and references therein), or image processing (image matching, image reg”
On the Estimation of alpha-Divergences (2011, methodology): “Our work borrows ideas from Leonenko et al. (2008a) and Goria et al.”
Estimation of Renyi Entropy and Mutual Information Based on Generalized Nearest-Neighbor Graphs (2010, methodology): “Both entropy estimators and mutual information estimators have been used for independent component and subspace analysis (Learned-Miller and Fisher, 2003; P´oczos and L ˝ orincz, 2005; Hulle, 2008; Szab ´ o et al., 2007), and image registration (Kybic, 2006; Hero et al., 2002b,a).”
Estimating epistemic and aleatory uncertainties during hydrologic modeling: An information theoretic approach (2013, background): “A number of ‘‘nonplugin’’ estimators have been proposed to try to mitigate the curse of dimensionality; these include the R enyi entropy estimator [Hero et al., 2002] and the Shannon entropy estimator [Leonenko et al.”
Maximum Likelihood Estimation of Functionals of Discrete Distributions (2014, background): “ill largely open. In particular, the problem of estimating diﬀerential entropy R −f lnf, where f is a density, remains fertile ground for research, e.g. (Hall and Morton, 1993; Beirlant et al., 1997; Hero et al., 2002; Kraskov, Sto¨gbauer and Grassberger,2004; Paninski and Yajima, 2008; Wang, Kulkar”
Empirical estimation of entropy functionals with confidence (2010, background): “Entropy based applications for image matching, image registration and texture classification are developed in [20, 34].”
Geodesic entropic graphs for dimension and entropy estimation in manifold learning (2004, background): “This finite intrinsic entropy can be useful for exploring data compression over the manifold or, as suggested in [8], clustering of multiple subpopulations on the manifold.”
Families of Alpha- Beta- and Gamma- Divergences: Flexible and Robust Measures of Similarities (2010, background): “Actually, the Rényi divergence is increasing in α on the whole set (0,∞) [58–60].”
On the Estimation of α-Divergences (2011, methodology): “Our work borrows ideas from Leonenko et al. (2008a) and Goria et al.”
Minimax Estimation of Functionals of Discrete Distributions (2014, background): “For nonparametric estimation of differential entropy, the readers are referred to [80], [81], [82], [83], and [84].”
Practical and Consistent Estimation of f-Divergences (2019, background): “As an example of stronger assumptions, both distributions may be mixtures of Gaussians [17, 10], or we may have access to samples from Q and have full knowledge of P [15, 16] as in e.”
A closed-form expression for the Sharma–Mittal entropy of exponential families (2011, background): “e closed-form formula Eq. 17. We believe that Eq. 17, Eq. 22, Eq. 45 (numerically stable) and 54 will prove useful when experimenting for suitable parameters (α,β) in various statistical signal tasks [9]. Acknowledgments The authors would like to thank the anonymous reviewers for their helpful comme”
REGO: Rank-based Estimation of Renyi Information using Euclidean Graph Optimization (2010, methodology): “(2004); Kybic (2006); Hero and Michel (1998). The first four estimators all use nearest-neighbor graphs, while Hero and Michel (1998), building on previous results from the literature of probabilistic geometric optimization, propose to use the solution of certain Euclidean Geometric Optimization (EG”
Efficient mean-shift tracking via a new similarity measure (2005, background): “To overcome the flaws of Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05) 1063-6919/05 $20.00 © 2005 IEEE the information-theoretic similarity measures in higher dimensions, Hero et al [22] proposed estimating them using entropic graphs, s”
Deformable Medical Image Registration: A Survey (2013, methodology): “In [270, 271], a Minimum Spanning Tree (MST) was used to estimate the RE and the optimal transformation was estimated by minimizing it.”
Parametric Bayesian Estimation of Differential Entropy and Relative Entropy (2010, unknown): “[12–14].”