Statistical Inference Using Mean Shift Denoising

TL;DR

This paper explores the use of the mean shift algorithm as a denoising tool, analyzing its effects on data distribution and demonstrating improvements in clustering, hypothesis testing, and anomaly detection.

Contribution

It introduces a novel framework viewing mean shift as a distribution operator, providing theoretical insights and practical benefits for data analysis tasks.

Findings

Mean shift concentrates data around high-density regions.

Denoising with mean shift improves clustering performance.

Enhances power of two-sample tests and aids anomaly detection.

Abstract

In this paper, we study how the mean shift algorithm can be used to denoise a dataset. We introduce a new framework to analyze the mean shift algorithm as a denoising approach by viewing the algorithm as an operator on a distribution function. We investigate how the mean shift algorithm changes the distribution and show that data points shifted by the mean shift concentrate around high density regions of the underlying density function. By using the mean shift as a denoising method, we enhance the performance of several clustering techniques, improve the power of two-sample tests, and obtain a new method for anomaly detection.