Local-to-Global Support Vector Machines (LGSVMs)

For supervised classification tasks that involve a large number of instances, we propose and study a new efficient tool, namely the Local-to-Global Support Vector Machine (LGSVM) method. Its background some-how lies in the framework of approximation theory and of local kernel-based models, such as the Par-tition of Unity (PU) method. Indeed, even if the latter needs to be accurately tailored for classification tasks, such as allowing the use of the cosine semi-metric for defining the patches, the LGSVM is a global method constructed by gluing together the local SVM contributions via compactly supported weights. When the number of instances grows, such a construction of a global classifier enables us to significantly reduce the usually high complexity cost of SVMs. This claim is supported by a theoretical analysis of the LGSVM and of its complexity as well as by extensive numerical experiments carried out by considering benchmark datasets.(c) 2022 Elsevier Ltd. All rights reserved.