Fitting a Gaussian Mixture Model Through the Gini Index

A linear combination of Gaussian components is known as a Gaussian mixture model. It is widely used in data mining and pattern recognition. In this paper, we propose a method to estimate the parameters of the density function given by a Gaussian mixture model. Our proposal is based on the Gini index, a methodology to measure the inequality degree between two probability distributions, and consists in minimizing the Gini index between an empirical distribution for the data and a Gaussian mixture model. We will show several simulated examples and real data examples, observing some of the properties of the proposed method.