The "K-Product" Criterion for Gaussian Mixture Estimation

A global algorithm to estimate the expectations of the components of an observed univariate mixture

“…The performance criteria are the observed frequencies for e r to be smaller than 0.1 (top), smaller than 0.2 (middle) and greater than 0.5 (bottom) of components is known. We proposed a method based on the minimization of the "K -product" criterion first introduced in Paul et al (2006). We have shown that the global minimum of this criterion can be reached with a linear least square minimization followed by a roots finding algorithm.…”

“…In this contribution, we propose a non-iterative algorithm which mainly consists in calculating the minimum of the "K -Product" (KP) criterion we first introduced in Paul et al (2006): if {z n } n∈{1,...,N } is a set of N observations in R 1 which originate from a K -component mixture and if {x k } k∈{1,...,K } is any vector of R K , we define the KP criterion as the sum of all the K -terms products K k=1 (z n − x k ) 2 [see (2) below]. The main motivation for using such a criterion is that, though it provides a slightly biased estimation of the component expectations, its global minimum can be reached by first solving a system of K linear equations then calculating the roots of some polynomial of order K .…”

Blind Frequency Estimation for Short 16 QAM Radio Burst

“…It is nevertheless necessary to evaluate i m values and, for that purpose, we propose to introduce an iterative weighted least mean squares algorithm, so called K-products [24], due to the particular form of equation (4.). At each step of this algorithm, we freeze …”

“…For that, two competitive cost functions are compared. The first one is based on the clustering K-means algorithm [18,21,22], the second one is a new approach so called Kproducts [24] that exhibits interesting properties compared to K-means.…”