A global difference measure for the reduction of Gaussian inverse Wishart mixtures

• The paper presents an evaluation criterion for GIW mixtures.
• The authors propose a weighted KL difference for merging.
• The NISD measure is derived for evaluating the performance of algorithms.

This paper presents an evaluation criterion, called a global difference measure, for the reduction of Gaussian inverse Wishart (GIW) mixtures. It is a deviation between the original and reduced GIW mixture, in other words, a numerical way describing the performance of the reduction algorithm instead of just a previous curve analysis (i.e., visual inspection of the resulting mixture intensity functions). In this paper, the global difference measure is obtained by solving the normalized integrated squared distance (NISD). Additionally, a weighted Kullback–Leibler (KL) difference for the reduction of GIW is proposed, which makes a small modification to an existing algorithm introduced by Granström et al. (2012) [1]. The weighted KL difference is derived by considering the weights of components. This is ignored in the existing literatures. Both the proposed evaluation criterion and algorithm are tested on simulation examples, and the results show that the proposed evaluation criterion can depict correctly the result of the curve analysis.