RT journal article
T1 On ℓp-Support Vector Machines and Multidimensional Kernels
A1 Blanco, Víctor
A1 Puerto, Justo
A1 Rodríguez Chía, Antonio Manuel
A2 Estadística e Investigación Operativa
K1 Support Vector Machines
K1 Kernel functions
K1 p-norms
K1 Mathematical Optimization
AB In this paper, we extend the methodology developed for Support Vector Machines (SVM) using the `2-norm (`2-SVM) to the more general case of `p-norms with p > 1 (`p-SVM). We derive second order cone formulations for the resulting dual and primal problems. The concept of kernel function, widely applied in `2-SVM, is extended to the more general case of `p-norms with p > 1 by defining a new operator called multidimensional kernel. This object gives rise to reformulations of dual problems, in a transformed space of the original data, where the dependence on the original data always appear as homogeneous polynomials. We adapt known solution algorithms to efficiently solve the primal and dual resulting problems and some computational experiments on real-world datasets are presented showing rather good behavior in terms of the accuracy of `p-SVM with p > 1.
SN 1533-7928
YR 2020
FD 2020
LK http://hdl.handle.net/10498/38445
UL http://hdl.handle.net/10498/38445
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 08-nov-2026