Quadratically constrained quadratic programming for classification using particle swarms and applications

TL;DR

This paper introduces a novel particle swarm optimization approach for solving quadratically constrained quadratic programming problems in classification, effectively determining optimal hyperplanes without traditional classifiers, and demonstrating competitive results on standard datasets.

Contribution

The work presents a new particle swarm-based method for classification that handles quadratic constraints and optimizes hyperplanes without relying on traditional classifiers.

Findings

Outperforms neural networks on benchmark datasets.

Achieves performance close to SVMs.

Uses distributed particle swarm optimization effectively.

Abstract

Particle swarm optimization is used in several combinatorial optimization problems. In this work, particle swarms are used to solve quadratic programming problems with quadratic constraints. The approach of particle swarms is an example for interior point methods in optimization as an iterative technique. This approach is novel and deals with classification problems without the use of a traditional classifier. Our method determines the optimal hyperplane or classification boundary for a data set. In a binary classification problem, we constrain each class as a cluster, which is enclosed by an ellipsoid. The estimation of the optimal hyperplane between the two clusters is posed as a quadratically constrained quadratic problem. The optimization problem is solved in distributed format using modified particle swarms. Our method has the advantage of using the direction towards optimal solution rather than searching the entire feasible region. Our results on the Iris, Pima, Wine, and Thyroid datasets show that the proposed method works better than a neural network and the performance is close to that of SVM.