From Linear to Spline-Based Classification:Developing and Enhancing SMPA for Noisy Non-Linear Datasets

TL;DR

The paper extends the Moving Points Algorithm (MPA) to enable non-linear classification by incorporating cubic splines, culminating in the Spline Moving Points Algorithm (SMPA). It critically evaluates linear MPA, explores random initialization and stabilization strategies, and introduces adaptive, spline-based updates to shape decision boundaries. Through synthetic experiments (moons and blobs) and rigorous evaluation against baselines, SMPA demonstrates competitive accuracy with low variance, though statistical significance over established classifiers remains inconclusive. The work highlights the potential of spline-based heuristic classifiers for non-linear datasets while outlining avenues for stability, efficiency, and scalability improvements in future research.

Abstract

Building upon the concepts and mechanisms used for the development in Moving Points Algorithm, we will now explore how non linear decision boundaries can be developed for classification tasks. First we will look at the classification performance of MPA and some minor developments in the original algorithm. We then discuss the concepts behind using cubic splines for classification with a similar learning mechanism and finally analyze training results on synthetic datasets with known properties.

Figures (1)

• Figure 1: Convergence graphs of MPA on different datasets, illustrating varying learning behaviors.