@misc{10481/87030,
year = {2020},
url = {https://hdl.handle.net/10481/87030},
abstract = {In this paper, we extend the methodology developed for Support Vector Machines (SVM) using the l2-norm (l2-SVM) to the more general case of lp-norms with p > 1 (lp-SVM). We derive second order cone formulations for the resulting dual and primal problems. The concept of kernel function, widely applied in l2-SVM, is extended to the more general case of lp-norms with p > 1 by de ning 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 e ciently 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 lp-SVM with p > 1.},
organization = {MTM2016-74983-C2-1- R (MINECO, Spain).,  MTM2016-74983-C2-2-R (MINECO, Spain), PP2016-PIP06 (Universidad de Granada) and the research group SEJ-534 (Junta de Andalucía).},
publisher = {JMLR},
keywords = {Support Vector Machines},
keywords = {Kernel functions},
keywords = {l_p-norms},
keywords = {Mathematical Optimization.},
title = {On lp-support vector machines and multidimensional kernels},
author = {Blanco, Víctor and Puerto, Justo and Rodríguez-Chía, Antonio},
}