A survey of kernels for structured data

By Thomas Gärtner. 2003

509 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, background): “40) coincides with that of classical set kernel of Haussler (1999) and Gärtner et al. (2002) (see also Kondor and Jebara (2003)).”
Kernel methods in machine learning (2007, neutral): “allenge: one may both design a kernel on vertices of them and also a kernel between them. In the former case, the graph itself becomes the object deﬁning the metric between the vertices. See Ga¨rtner [56] and Kashima et al. [82] for details on the latter. In the following we discuss kernels on graph”
Dimensionality Reduction of Multimodal Labeled Data by Local Fisher Discriminant Analysis (2007, background): “Recently, kernel functions for non-vectorial structured data such as strings, trees, and graphs have been proposed (see, e.g., Lodhi et al., 2002; Duffy and Collins, 2002; Kashima and Koyanagi, 2002; Kondor and Lafferty, 2002; Kashima et al., 2003; Gärtner et al., 2003; Gärtner, 2003).”
A review of unsupervised feature learning and deep learning for time-series modeling (2014, methodology): “(2012) compares the gas discrimination and 676 localization between three approaches: SVM on raw data, SVM on features 677 extracted from auto-regressive and linear dynamical systems, and nally a 678 SVMs with kernels specialized for structured data (Gärtner, 2003).”
Neural networks for relational learning: an experimental comparison (2011, background): “They extend support vector machines [Kondor and Lafferty, 2002, Gärtner, 2003], neural networks [Sperduti and Starita, 1997,Frasconi et al., 1998,Gori et al., 2005] and SOMs [Hagenbuchner et al., 2003] to structured data.”
Sufficient Dimension Reduction via Squared-Loss Mutual Information Estimation (2010, methodology): “…trees, and graphs), we may employ kernels for structured data as φ y ( y ) (Lodhi, Saunders, Shawe-Taylor, Cristianini, & Watkins, 2002; Collins & Duffy, 2002; Kashima & Koyanagi, 2002; Kondor & Lafferty, 2002; Kashima, Tsuda, & Inokuchi, 2003; G¨artner, 2003; G¨artner, Flach, & Wrobel, 2003).”
Classification of small molecules by two- and three-dimensional decomposition kernels (2007, background): “Although some of the above kernels can be computed efficiently, matching arbitrary substructures may be intractable because it involves subgraph isomorphism (Gärtner, 2003).”
False rumors detection on Sina Weibo by propagation structures (2015, background): “However, it is not always reasonable as many objects in the real world are structured by nature[34].”
The Pyramid Match Kernel: Efficient Learning with Sets of Features (2007, background): “In order to more fully leverage existing kernel-based learning tools for situations where the data cannot be naturally represented by a Euclidean vector space—such as graphs, strings, or trees—researchers have developed specialized similarity measures (Gartner, 2003).”
Graph kernels and Gaussian processes for relational reinforcement learning (2006, methodology): “The rbf-parameter gives an indication of the amount of generalisation that should be done.”
Neural Network for Graphs: A Contextual Constructive Approach (2009, background): “We are recently witnessing an increasing attention in this area to the development of various kernel-based approaches for structured data (e.g., see [ 4 ]‐[8] for overviews).”
Least-squares two-sample test (2011, methodology): “…of non-vectorial structured objects such as strings, trees, and graphs by employing kernel functions defined for such structured data (Lodhi et al., 2002; Duffy & Collins, 2002; Kashima & Koyanagi, 2002; Kondor & Lafferty, 2002; Kashima et al., 2003; Gärtner et al., 2003; Gärtner, 2003).”
Neural methods for non-standard data (2004, methodology): “Analogously, other kernel based methods such as kernel principal component analysis rely solely on an appropriate choice of (cid:2) and the task thus reduces to the design of kernels for structured data.”