Distance Density Analysis and Multivariate Mode Detection

Abstract

Finding the mode of the distribution for a sample of points is a very interesting task. In one dimensional problems this can easily be done by estimating the kernel density. Unfortunately this method does not work well in higher dimensions. This thesis presents a new approach to solve this problem. A method is presented which finds the mode by analyzing the distribution of the distances between each point and the rest of the sample. The idea is that if the i-th sample point, x_i, is in a high-density region, most of these distances should be small, whereas if x_i is an outlier, most of these distances should be large. By running simulations for different distributions this thesis shows that the new method works better than the existing ones in higher dimensions.