# An Online Sample Based Method for Mode Estimation using ODE Analysis of Stochastic Approximation Algorithms

## TL;DR

This paper introduces an online, sample-based iterative algorithm for estimating the mode of a unimodal density, using ODE analysis to prove convergence and stability, suitable for real-time applications with unknown density functions.

## Contribution

It presents a novel, computationally efficient online mode estimation method that does not require prior knowledge of the density's analytical form or batch processing.

## Key findings

- Algorithm converges asymptotically to the true mode.
- Proven stability of the mode estimates via regularization.
- Experimental results confirm effectiveness in practical scenarios.

## Abstract

One of the popular measures of central tendency that provides better representation and interesting insights of the data compared to the other measures like mean and median is the metric mode. If the analytical form of the density function is known, mode is an argument of the maximum value of the density function and one can apply the optimization techniques to find mode. In many of the practical applications, the analytical form of the density is not known and only the samples from the distribution are available. Most of the techniques proposed in the literature for estimating the mode from the samples assume that all the samples are available beforehand. Moreover, some of the techniques employ computationally expensive operations like sorting. In this work we provide a computationally effective, on-line iterative algorithm that estimates the mode of a unimodal smooth density given only the samples generated from the density. Asymptotic convergence of the proposed algorithm using an ordinary differential equation (ODE) based analysis is provided. We also prove the stability of estimates by utilizing the concept of regularization. Experimental results further demonstrate the effectiveness of the proposed algorithm.