# A Learning Framework of Nonparallel Hyperplanes Classifier

## TL;DR

This paper introduces a new machine learning framework for classification tasks that improves speed and performance using nonparallel hyperplanes.

## Contribution

The framework extends TWSVM into multiclass classification and reduces computational cost by using absolute value in the decision function.

## Key findings

- The framework is fast and shows good generalization on artificial and benchmark datasets.
- Replacing Euclidean distance with absolute value improves consistency and reduces computational cost.
- The framework includes linear and nonlinear cases with hinge loss as an example.

## Abstract

A novel learning framework of nonparallel hyperplanes support vector machines (NPSVMs) is proposed for binary classification and multiclass classification. This framework not only includes twin SVM (TWSVM) and its many deformation versions but also extends them into multiclass classification problem when different parameters or loss functions are chosen. Concretely, we discuss the linear and nonlinear cases of the framework, in which we select the hinge loss function as example. Moreover, we also give the primal problems of several extension versions of TWSVM's deformation versions. It is worth mentioning that, in the decision function, the Euclidean distance is replaced by the absolute value |w
T
x + b|, which keeps the consistency between the decision function and the optimization problem and reduces the computational cost particularly when the kernel function is introduced. The numerical experiments on several artificial and benchmark datasets indicate that our framework is not only fast but also shows good generalization.