Support vector machine classification with indefinite kernels

By Ronny Luss, Alexandre d'Aspremont. 2007

141 citations recorded by the source corpus.

We propose a method for support vector machine classification using indefinite kernels. Instead of directly minimizing or stabilizing a nonconvex loss function, our algorithm simultaneously computes support vectors and a proxy kernel matrix used in forming the loss. This can be interpreted as a penalized kernel learning problem where indefinite kernel matrices are treated as noisy observations of a true Mercer kernel. Our formulation keeps the problem convex and relatively large problems can be solved efficiently using the projected gradient or analytic center cutting plane methods. We compare the performance of our technique with other methods on several standard data sets.

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

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Citations in the corpus

Matching Node Embeddings for Graph Similarity (2017, methodology): “We can formulate the following extension of the SVM for indefinite kernels (Luss and d’Aspremont 2008):”
Optimal Transport for structured data with application on graphs (2018, methodology): “For the classiﬁcation task, we run a SVM using the in-deﬁnite kernel matrix e − γFGW which is seen as a noisy observation of the true positive semideﬁnite kernel (Luss & d’Aspremont, 2007).”
Similarity-based Classification: Concepts and Algorithms (2009, background): “Recently, a robust extension of SVM has been proposed for indefinite kernels [21].”