From sample similarity to ensemble similarity: probabilistic distance measures in reproducing kernel Hilbert space

By Shaohua Kevin Zhou, Ramalingam Chellappa. 2006

195 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition

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Citations in the corpus

Log-Hilbert-Schmidt metric between positive definite operators on Hilbert spaces (2014, background): “Related work: The approach most closely related to our current work is [26], which computed probabilistic distances in RKHS.”
Approximate Log-Hilbert-Schmidt Distances between Covariance Operators for Image Classification (2016, methodology): “Infinite-dimensional covariance operators of low-level features have been applied to the task of image classification recently by [21], which formulated the Log-HS metric, and by [14], which used the formulation for Bregman divergences proposed in [35].”
On classification with bags, groups and sets (2014, background): “A similar assumption is made in works which regard bags as samples from probability distributions, and define the kernel through a divergence [58, 38].”
Mean Map Kernel Methods for Semisupervised Cloud Classification (2010, methodology): “the Gaussians obtained after mapping the set of vectors into H; in [34], kernel machines are combined with generative modeling using a kernel between distributions; and in [35], expressions for the most common probabilistic distance measures in the reproducing kernel Hilbert space”
Information-Geometric Dimensionality Reduction (2011, background): “For additional measures of probabilistic distance and details on their computation for empirical data, we refer the reader to [16] and [17].”
Kernel Embeddings of Conditional Distributions: A Unified Kernel Framework for Nonparametric Inference in Graphical Models (2013, background): “MMD and other distances between samples of points were also suggested in [22], although the injectivity of the map of probability measures to feature space, and the question of whether a metric was induced on probabilities, were not addressed.”
Grassmann discriminant analysis: a unifying view on subspace-based learning (2008, background): “Copyright 2008 by the author(s)/owner(s). the similarity between image vectors (Shakhnarovich et al., 2002; Kondor & Jebara, 2003; Zhou & Chellappa, 2006).”
Bregman Divergences for Infinite Dimensional Covariance Matrices (2014, methodology): “Here, we address this issue by exploiting ideas developed in the context of covariance matrix estimation from a limited number of observations [2, 27].”