Generalized version of the support vector machine for binary classification problems: supporting hyperplane machine

TL;DR

This paper introduces a generalized support vector machine framework for binary classification that incorporates arbitrary transformations of input data, providing new formulations, detailed derivations, and an implementation example.

Contribution

It presents a novel generalized SVM approach with flexible data transformations, including detailed formulations and an Octave implementation.

Findings

Derived primal and dual problem formulations

Provided a detailed computational example

Implemented the method in Octave

Abstract

In this paper there is proposed a generalized version of the SVM for binary classification problems in the case of using an arbitrary transformation x -> y. An approach similar to the classic SVM method is used. The problem is widely explained. Various formulations of primal and dual problems are proposed. For one of the most important cases the formulae are derived in detail. A simple computational example is demonstrated. The algorithm and its implementation is presented in Octave language.