An introduction to kernel-based learning algorithms

By K. Müller, Sebastian Mika, Gunnar Rätsch, Koji Tsuda, Bernhard Schölkopf. 2001

3,777 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Probabilistic & Bayesian Methods, Statistical Learning Theory

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Citations in the corpus

Security analysis of online centroid anomaly detection (2010, methodology): “Despite its straightforwardness, a centroid model can represent arbitrary complex density level sets using a kernel mapping (Schölkopf and Smola, 2002; Müller et al., 2001) (see Fig.”
Explaining nonlinear classification decisions with deep Taylor decomposition (2015, neutral): “They include, for example, graphical models [1], kernels [2, 3], Gaussian processes [4], neu-”
How to Explain Individual Classification Decisions (2009, methodology): “Instead we can apply sophisticated learning machinery like Support Vector Machines (Vapnik, 1995; Sch¨olkopf and Smola, 2002; M¨uller, Mika, R¨atsch, Tsuda, and Sch¨olkopf, 2001) that estimates some classiﬁer g that tries to mimic g ∗ .”
Toward Supervised Anomaly Detection (2014, methodology): “As a consequence, the input data can be expressed equivalently by a kernel function k ( x i , x j ) = φ ( x i ) T φ ( x j ) on X that corresponds to a feature map φ : X → F into a reproducing kernel Hilbert space F (see, e.g., Müller, Mika, Rätsch, Tsuda, & Schölkopf, 2001).”
Support vector machines for temporal classification of block design fMRI data (2005, background): “For a more general treatment, please refer to Burges (1998), Cherkassky and Mulier (1998), and Muller et al. (2001).”
Multiple support vector machines for land cover change detection: An application for mapping urban extensions (2006, background): “Statistical learning theory shows that it is imperative to restrict the class of functions so that its capacity is suitable to the amount of available training data (Müller et al., 2001).”
One-Class Novelty Detection for Seizure Analysis from Intracranial EEG (2006, methodology): “Several excellent tutorials provide historical context and details on the SVM (Burges, 1998; Bennett & Campbell, 2000; Müller et al., 2001).”
On layer-wise representations in deep neural networks (2013, neutral): “See, for example, Müller et al. (2001) for an introduction to kernel-based learning algorithms.”
Automatic analysis of malware behavior using machine learning (2011, neutral): “As many real-world application fall into this concept of learning, a large body of research exists on designing and applying classiﬁcation methods (e.g., [15,39,42, 58]).”
Machine learning bandgaps of double perovskites (2016, methodology): “…of the best primary and compound Ω − D descriptors (with Ω ∈ [1, 16]) identified above was then reassessed in a Kernel ridge regression (KRR) 53,54 model—a state-of-the-art ML method capable of handling complex non-linear relationships—which has recently been shown to be promising for…”
Short-Term Wind Speed or Power Forecasting With Heteroscedastic Support Vector Regression (2016, methodology): “To move from linear to nonlinear functions, we can perform the following generalization [23]: we map the input vectors xi into a high-dimensional feature space H through some nonlinear function, Φ : R → H (H is Hilbert space), chosen a priori.”
Spatio-spectral filters for improving the classification of single trial EEG (2005, background): “…into a control signal, either by simple threshold criteria (cf. [3]), or by means of machine learning, where given some training examples for each brain state, the task is to infer a possibly nonlinear discriminating function to distinguish between different states (e.g. [3], [6]–[9], [15], [16]).”
Robust image segmentation using FCM with spatial constraints based on new kernel-induced distance measure (2004, methodology): “gorithm that only uses inner products can be easily extended to a nonlinear version only through the kernels satisfying the Mercer’s conditions [11].”
Recipes for the linear analysis of EEG (2005, background): “The optimization problem for SVMs is a quadratic programming (QP) problem, so there is one optimum, and the algorithms to solve it are relatively fast (Burges, 1998; Müller et al., 2001).”