Learning with non-positive kernels

By Cheng Soon Ong, Xavier Mary, Stéphane Canu, Alex Smola. International Conference on Machine Learning, 2004

296 citations recorded by the source corpus.

Subfields: Mathematical Physics, Mechanics of Materials, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9ecd3155ea1b5056c43c624a91e3d9523f303e74

How researchers see this paper

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

In Mathematical Physics

1. Lorenzo Rosasco
2. Alessandro Verri
3. Ernesto De Vito
4. Alexandre d'Aspremont
5. Daniel D. Lee
6. Francesca Odone
7. Tony Jebara
8. L. Lo Gerfo

In Mechanics of Materials

1. Alexandre d'Aspremont
2. Daniel D. Lee
3. Lorenzo Rosasco
4. Jihun Ham
5. Bernard Haasdonk

In Statistical and Nonlinear Physics

1. Richard I. Hartley
2. Daniel D. Lee
3. Mehrtash Harandi
4. Lorenzo Rosasco
5. Olivier Chapelle
6. Yihua Chen
7. Jihun Ham
8. Bernard Haasdonk

Citations in the corpus

• Probability Product Kernels (2004, background): “See Ong et al. (2004) for an interesting discussion and additional references.”
• 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].”
• Spectral Algorithms for Supervised Learning (2008, methodology): “For iterative methods, some partial results, which do not take into account the random sampling, are presented in Ong and Canu (2004) and Ong, Mary, Canu, and Smola (2004) .”
• Kernel Methods on the Riemannian Manifold of Symmetric Positive Definite Matrices (2013, background): “Although theories have been proposed to exploit non-positive definite kernels [12, 23], they have not experienced a widespread success.”
• 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.”
• Support vector machine classification with indefinite kernels (2007, background): “Mathematics Subject Classification (2000) Primary 62H30; Secondary 90C25 · 68T05”
• Learning with Distance Substitution Kernels (2004, background): “This would in particular support recent promising efforts to establish non-cpd kernels for machine learning [3].”
• Similarity-based Classification: Concepts and Algorithms (2009, background): “[18] interpret this as finding the stationary point in a reproducing kernel Kreı̆n space (RKKS), while Haasdonk [19] shows that this is equivalent to minimizing the distance between reduced convex hulls in a pseudo-Euclidean space.”