Mode estimation using pessimistic scale space tracking

Abstract

Abstract. Estimation of the mode of a distribution over � from discrete samples is introduced and three methods for its solution are developed and evaluated. The first solution is based on Fréchet’s definition of central tendencies. We show that algorithms based on this approach have only limited success due to the non-differentiability of the Fréchet measures. The second solution is based on tracking maxima through a Scale Space built from the samples. We show that this is more accurate than the Fréchet approach, but that tracking to very fine scales is unwarranted and undesirable. For our third method we analyze the reliability of the information across scale using an exact bootstrap analysis. This leads to a modified version of the Scale Space approach where unreliable information is downgraded (pessimistically) so that tracking into such regions does not occur. This modification improves the accuracy of mode estimation. We conclude with demonstrations on high-dimensional real and synthetic data, which confirm the technique’s accuracy and utility.