Fourier Transform Approach to Machine Learning I: Fourier Regression

TL;DR

This paper introduces a Fourier transform-based supervised learning algorithm that uses iterative band filtering and convergence criteria, avoiding ill-conditioned matrices and improving robustness to noisy data.

Contribution

It presents a novel Fourier regression method that unifies training and evaluation, eliminating least squares and enhancing stability and noise resistance.

Findings

Effective on noisy data

Avoids ill-conditioned matrices

Converges to optimal model

Abstract

We propose a supervised learning algorithm for machine learning applications. Contrary to the model developing in the classical methods, which treat training, validation, and test as separate steps, in the presented approach, there is a unified training and evaluating procedure based on an iterative band filtering by the use of a fast Fourier transform. The presented approach does not apply the method of least squares, thus, basically typical ill-conditioned matrices do not occur at all. The optimal model results from the convergence of the performance metric, which automatically prevents the usual underfitting and overfitting problems. The algorithm capability is investigated for noisy data, and the obtained result demonstrates a reliable and powerful machine learning approach beyond the typical limits of the classical methods.