A Kernel Between Sets of Vectors

By Risi Kondor, Tony Jebara. 2003

321 citations recorded by the source corpus.

Subfields: Representation & Self-Supervised Learning, Statistical Learning Theory

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, background): “Moreover, the empirical version of (3.49) and (3.40) coincides with that of classical set kernel of Haussler (1999) and Gärtner et al. (2002) (see also Kondor and Jebara (2003)).”
Learning Theory for Distribution Regression (2014, background): “Typical examples with explicit formulas include Gaussians, finite mixtures of Gaussians, and distributions from the exponential family (with known log-normalizer function and zero carrier measure, see Kondor and Jebara, 2003; Jebara et al., 2004; Wang et al., 2009; Nielsen and Nock, 2012).”
Generative and Latent Mean Map Kernels (2010, methodology): “The computation follows almost directly from the formulation of Jebara and Kondor [11] for the probability product kernel (described in Section 5).”
Propagation kernels: efficient graph kernels from propagated information (2014, methodology): “Edge weights are represented by weighted adjacency matrices A ( i ) ∈ R n i × n i and the label function (cid:96) endows nodes with label and attribute information as defined in the previous section.”
The Multiscale Laplacian Graph Kernel (2016, methodology): “Similarly to kernel PCA [17] or the Bhattacharyya kernel [14], the easiest way to construct the basis {ξ1, .”
Probability Product Kernels (2004, background): “For the setting of ρ = 1/2 the kernel is none other than the classical Bhattacharyya similarity measure (Kondor and Jebara, 2003), the affinity corresponding to Hellinger divergence (Jebara and Kondor, 2003).”
Beyond Covariance: Feature Representation with Nonlinear Kernel Matrices (2015, methodology): “i) For example, we can evaluate the similarity of feature distributions, by applying the Bhattacharyya kernel [11]”
The pyramid match kernel: discriminative classification with sets of image features (2005, methodology): “A performance evaluation given in [7] compares the methods of [12, 27, 25] in the context of an object categorization task using images from the publicly available ETH80 database.”
Kernel Descriptors for Visual Recognition (2010, background): “Therefore, Kh(P, Q) is a match kernel over sets (here the sets are image patches) as in [8, 1, 11, 17, 7].”
Neural methods for non-standard data (2004, methodology): “A similar procedure is presented in [ 54 ] for sets of vectors.”
An SVM learning approach to robotic grasping (2004, background): “For instance, a kernel function was recently proposed between two vectors-sets (as opposed to two vectors in our formulation) [20].”
Support Measure Data Description for group anomaly detection (2015, background): “However, there is a growing interest in machine learning methods for datasets whose individual observations are clusters, groups or sets of points in R [32, 33, 20, 19, 25, 35, 10, 34, 26, 15, 18].”
Linear-Time Learning on Distributions with Approximate Kernel Embeddings (2015, methodology): “2012a; Oliva, Póczos, and Schneider 2013) or Mercer kernels (Moreno, Ho, and Vasconcelos 2003; Kondor and Jebara 2003; Jebara, Kondor, and Howard 2004; Póczos et al. 2012b).”
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).”
On classification with bags, groups and sets (2014, background): “When both the training objects and test objects are bags, but no additional assumptions about the labels are present, the goal is classification of sets of feature vectors [26] (not to be confused with set classification which is an unfortunate name for a different scenario, discussed in Section 3.”