kernel

Sparse Multiple Kernel Learning: Alternating Best Response and Semidefinite Relaxations

  • Dimitris Bertsimas
  • Caio de Próspero Iglesias
  • Nicholas A. G. Johnson
    • Categories Convex Optimization, Semi-definite Programming, Statistics Tags , , , ,

    We study Sparse Multiple Kernel Learning (SMKL), which is the problem of selecting a sparse convex combination of prespecified kernels for support vector binary classification. Unlike prevailing \(\ell_1\)‐regularized approaches that approximate a sparsifying penalty, we formulate the problem by imposing an explicit cardinality constraint on the kernel weights and add an \(\ell_2\) penalty for robustness. … Read more

    A mathematical introduction to SVMs with self-concordant kernel

  • Florian Jarre
    • Categories Data Science Algorithms, Data-Mining, Quadratic Programming Tags , ,

    A derivation of so-called “soft-margin support vector machines with kernel” is presented along with elementary proofs that do not rely on concepts from functional analysis such as Mercer’s theorem or reproducing kernel Hilbert spaces which are frequently cited in this context. The analysis leads to new continuity properties of the kernel functions, in particular a … Read more