On lp-support vector machines and multidimensional kernels Blanco, Víctor Puerto, Justo Rodríguez-Chía, Antonio Support Vector Machines Kernel functions l_p-norms Mathematical Optimization. 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. 2024-01-22T08:31:59Z 2024-01-22T08:31:59Z 2020 journal article Journal of Machine Learning Research 21, p 1-29 https://hdl.handle.net/10481/87030 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional JMLR