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One of the popular measures of central tendency that provides betterrepresentation and interesting insights of the data compared to the othermeasures like mean and median is the metric mode. If the analytical form of thedensity function is known, mode is an argument of the maximum value of thedensity function and one can apply the optimization techniques to find mode. Inmany of the practical applications, the analytical form of the density is notknown and only the samples from the distribution are available. Most of thetechniques proposed in the literature for estimating the mode from the samplesassume that all the samples are available beforehand. Moreover, some of thetechniques employ computationally expensive operations like sorting. In thiswork we provide a computationally effective, on-line iterative algorithm thatestimates the mode of a unimodal smooth density given only the samplesgenerated from the density. Asymptotic convergence of the proposed algorithmusing an ordinary differential equation (ODE) based analysis is provided. Wealso prove the stability of estimates by utilizing the concept ofregularization. Experimental results further demonstrate the effectiveness ofthe proposed algorithm.

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