Fourier Transform Approach to Machine Learning II: Fourier Clustering

TL;DR

This paper introduces a Fourier-based clustering method that smooths data density functions to identify cluster centers as local maxima, improving clustering accuracy and overcoming initialization issues.

Contribution

It presents a novel Fourier transform approach for clustering that enhances performance and provides a global optimization framework.

Findings

High accuracy in cluster centroid detection

Effective removal of initialization problems

Demonstrated robustness across datasets

Abstract

We propose a Fourier-based approach for optimization of several clustering algorithms. Mathematically, clusters data can be described by a density function represented by the Dirac mixture distribution. The density function can be smoothed by applying the Fourier transform and a Gaussian filter. The determination of the optimal standard deviation of the Gaussian filter will be accomplished by the use of a convergence criterion related to the correlation between the smoothed and the original density functions. In principle, the optimal smoothed density function exhibits local maxima, which correspond to the cluster centroids. Thus, the complex task of finding the centroids of the clusters is simplified by the detection of the peaks of the smoothed density function. A multiple sliding windows procedure is used to detect the peaks. The remarkable accuracy of the proposed algorithm demonstrates its capability as a reliable general method for enhancement of the clustering performance, its global optimization and also removing the initialization problem in many clustering methods.