Learning with Distance Substitution Kernels

By Bernard Haasdonk, Claus Bahlmann. 2004

163 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Barnab'as P'oczos
2. Jeff Schneider
3. Junier B. Oliva
4. Qingquan Song
5. Xia Hu
6. Danica J. Sutherland
7. Haifeng Jin
8. Julia Neumann

In Computer Vision and Pattern Recognition

1. Barnab'as P'oczos
2. Xia Hu
3. Jeff Schneider
4. Junier B. Oliva
5. Qingquan Song
6. Danica J. Sutherland
7. Haifeng Jin
8. Julia Neumann

Citations in the corpus

• Riemannian Approaches in Brain-Computer Interfaces: A Review (2017, unknown): “Finally, as explained in [62], it is possible to embed a distance in a radial kernel in order to benefit from the properties of both the kernel classifier and the embedded distance.”
• Auto-Keras: Efficient Neural Architecture Search with Network Morphism (2018, background): “Proof of Theorem 2: The kernel matrix of generalized RBF kernel in the form of e−γD 2(x,y) is positive definite if and only if there is an isometric embedding in Euclidean space for the metric space with metric D (Haasdonk & Bahlmann, 2004).”
• Linear-Time Learning on Distributions with Approximate Kernel Embeddings (2015, methodology): “We then use these distances in a generalized RBF kernel (1). d is a Hilbertian metric (Fuglede 2005), so K is positive definite (Haasdonk and Bahlmann 2004).”
• Efficient Neural Architecture Search with Network Morphism (2018, background): “The kernel matrix of generalized RBF kernel in the form of e−γd(x,y) is positive definite if and only if there is an isometric embedding in Euclidean space for the metric space with metric d [10].”
• Combined SVM-Based Feature Selection and Classification (2005, background): “According to Haasdonk and Bahlmann (2004), the kernel is positive definite.”
• Fast Global Alignment Kernels (2011, methodology): “Introduction Kernel methods (Hofmann et al., 2008) have been successfully applied in the last decade on a large variety of datatypes, such as images (Harchaoui & Bach, 2007), graphs (Vishwanathan et al., 2008) or strings on finite alphabets (Sonnenburg et al., 2007) to quote but a few recent referen”