# Incremental and Decremental Fuzzy Bounded Twin Support Vector Machine

## TL;DR

This paper introduces an incremental and decremental fuzzy twin support vector machine that efficiently handles large datasets and data streams, offering fast training and robust classification through innovative algorithms and approximations.

## Contribution

It presents a novel incremental/decremental FBTWSVM combining fuzzy membership, Fourier Gaussian approximation, and a DAG multi-class extension, with theoretical analysis and improved training speed.

## Key findings

- Fast training and retraining on benchmark datasets
- Robust classification performance maintained
- Effective handling of large datasets and data streams

## Abstract

In this paper we present an incremental variant of the Twin Support Vector Machine (TWSVM) called Fuzzy Bounded Twin Support Vector Machine (FBTWSVM) to deal with large datasets and learning from data streams. We combine the TWSVM with a fuzzy membership function, so that each input has a different contribution to each hyperplane in a binary classifier. To solve the pair of quadratic programming problems (QPPs) we use a dual coordinate descent algorithm with a shrinking strategy, and to obtain a robust classification with a fast training we propose the use of a Fourier Gaussian approximation function with our linear FBTWSVM. Inspired by the shrinking technique, the incremental algorithm re-utilizes part of the training method with some heuristics, while the decremental procedure is based on a scored window. The FBTWSVM is also extended for multi-class problems by combining binary classifiers using a Directed Acyclic Graph (DAG) approach. Moreover, we analyzed the theoretical foundations properties of the proposed approach and its extension, and the experimental results on benchmark datasets indicate that the FBTWSVM has a fast training and retraining process while maintaining a robust classification performance.