LA - A clustering algorithm with an automated selection of attributes, which is invariant to functional transformations of coordinates

Abstract

A clustering algorithm called LA is described. The algorithm is based on comparison of the n-dimensional density of the data points in various regions of the space of attributes p(x1,…,xn) with an expected homogeneous density obtained as a simple product of the corresponding one-dimensional densities pi(xi). The regions with a high value of the ratio p(x1,…,xn)/p1(x1)…pn(xn) are considered to contain clusters. A set of attributes which provides the most contrast clustering is selected automatically. The results obtained with the help of the LA algorithm are invariant to any clustering space coordinate reparametrizations, i. e. to one-dimensional monotonous functional transformations xʹ = f(x). Another valuable property of the algorithm is the weak dependence of the computational time on the number of data points.