A Kullback-Leibler Divergence Based Kernel for SVM Classification in Multimedia Applications

By Pedro J. Moreno Mengibar, Purdy Ho, Nuno Vasconcelos. 2003

469 citations recorded by the source corpus.

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In Statistical Learning Theory

Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “However, since this minimizer will depend on the unknown μP, Muandet et al. (2016) consider an estimate of α which when plugged in (3.”
Distribution-Free Distribution Regression (2013, background): “For comprehensive reviews and references, see Ramsay and Silverman [2005], Ferraty and Vieu [2006].”
Learning from Distributions via Support Measure Machines (2012, methodology): “This kernel can be shown to be closely related to well-known kernels such as the Bhattacharyya kernel (Bhattacharyya 1943) and the exponential symmetrized Kullback-Leibler (KL) divergence (Moreno et al. 2004).”
Propagation kernels: efficient graph kernels from propagated information (2014, background): “Finally, propagation kernels mark another connection, namely between graph kernels and kernels between probability distributions (Jaakkola andHaussler 1998; Lafferty and Lebanon 2002; Moreno et al. 2003; Jebara et al. 2004) and between sets (Kondor and Jebara 2003; Shi et al.”
Bregman Divergences for Infinite Dimensional Covariance Matrices (2014, background): “Note that while the kernel kJ(·, ·) was claimed to be positive definite [17], we are not aware of any formal proof of this claim.”
Learning with Distance Substitution Kernels (2004, methodology): “Statements on theoretical properties of the kernels follow in Section 3 and comments on consequences for use in SVMs are given in Section 4.”
Iterative Weighted Maximum Likelihood Denoising With Probabilistic Patch-Based Weights (2009, methodology): “This corresponds to the Kullback-Leibler divergence based kernel used in [41].”
Proposal : Scalable , Active and Flexible Learning on Distributions (2015, unknown): “It is thus possible to fit a parametric model to each distribution and compute distances between the fits; this is done for machine learning applications by e.g. Jebara et al. (2004) and Moreno et al. (2004).”
Kernel Archetypal Analysis for Clustering Web Search Frequency Time Series (2014, background): “Based on a symmetric measure DKL(f1, f2) +DKL(f2, f1), we can thus define a kernel function [26] to compare Weibull distributions based on their parameters.”
Estimation of Information Theoretic Measures for Continuous Random Variables (2008, background): “There are other relevant applications in different research areas in which divergence estimation is used to measure the difference between two density functions, such as multimedia [19] and text [13] classification, among others.”
Semigroup Kernels on Measures (2005, background): “The expression of Equation (2) fits our framework of devising semigroup kernels, unlike the direct use of the KL divergence (Moreno et al., 2004) which is neither symmetric nor negative definite.”
The Pyramid Match Kernel: Efficient Learning with Sets of Features (2007, background): “Other approaches to this problem have recently been proposed (Wallraven et al. 2003; Lyu 2005; Boughhorbel et al. 2004; Kondor and Jebara 2003; Wolf and Shashua 2003; Moreno et al. 2003; Shashua and Hazan 2005; Cuturi and Vert 2005; Boughorbel et al. 2005; Lafferty and Lebanon 2002), but unfortunate”
Distribution to Distribution Regression (2013, methodology): “The most straight forward of these methods is to fit a parametric model to distributions for estimating inner products (Jebara et al., 2004; Jaakkola et al., 1999; Moreno et al., 2003).”
Hilbertian Metrics and Positive Definite Kernels on Probability Measures (2005, background): “Instead of the work in [9] where they have a heuristic approach to get from the Kullback-Leibler divergence to a pd matrix, the Jensen-Shannon divergence is a theoretically sound alternative.”