Feature space interpretation of SVMs with indefinite kernels

By Bernard Haasdonk. 2005

272 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Mechanics, Computer Vision and Pattern Recognition

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Citations in the corpus

Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI (2019, neutral): “The work in [102] revolves around this issue with a geometrical interpretation of in-deﬁnite kernel SVMs, showing that these do not classify by hyper-plane margin optimization.”
Support vector machine classification with indefinite kernels (2007, background): “A first direction embeds data in a pseudo-Euclidean (pE) space: [10] for examp le, formulates the classification problem with an indefinite kernel as that of minimizing the distan ce between convex hulls formed from the two categories of data embedded in the pE space.”
Grassmann discriminant analysis: a unifying view on subspace-based learning (2008, methodology): “There have been efforts to use indefinite kernels for learning (Ong et al., 2004; Haasdonk, 2005), and several heuristics have been proposed to make an indefinite kernel matrix to a positive definite matrix (Pekalska et al.”
Semi-Supervised Classification by Low Density Separation (2005, background): “Moreover, recent papers have argued in favor of the use of nonpositive definite kernels for learning [11, 16].”
Supervised classification and mathematical optimization (2013, unknown): “[111, 157, 156].”
Hierarchical Aligned Cluster Analysis for Temporal Clustering of Human Motion (2013, background): “Unfortunately, DTAK is not a strictly positive definite kernel [47], [48].”
Linear-Time Computation of Similarity Measures for Sequential Data (2008, background): “…distances (e.g., Anderberg , 1973; Jacobs et al., 2000; von Luxburg and Bousquet, 2004), similarity or dissimilarity measures (e.g., Graepel et al., 1999; Roth et al., 2003; Laub and Müller, 2004; Laub et al., 2006) or non-positive kernel functions (e.g., Ong et al., 2004; Haasdonk, 2005).”
Similarity-based Classification: Concepts and Algorithms (2009, background): “Ong et al. [18] interpret this as finding the stationary point in a reproducing kernel Kre˘ ın space (RKKS), while Haasdonk [19] shows that this is equivalent to minimizing the distance between reduced convex hulls in a pseudo-Euclidean space.”
Explainable artificial intelligence: a comprehensive review (2021, background): “Haasdonk (2005) started the second simplification approach, which concentrated on simplifying the SVM kernel by providing arbitrary symmetric kernels.”