The improvement described in applying Gaussian mixtures (k weighted sums with weights summing to one) to heterogeneous population data employs the expectation-maximization (EM) algorithm in a greedy manner, solving the problem successively over values of k. The problem reduces to EM learning of two-component mixtures, the k+1 mixture becoming a weighted sum of the (“old”) k mixture and a new component, the old mixture being unchanged.

The approach is based on quite recent theory (2000) showing that, if the new components are allocated optimally (which is an open problem), the greedy approach works “almost as well” (defined precisely in the paper) as any k mixture. Component allocation builds on previous work, namely, rendering the k+1 likelihood independently of the mixing weight, and employing pre-stored, Gaussian matrices to simplify the parameter search, to which the authors present an additional proposal. A six-step algorithm summarizes all; the search computation complexity is quadratic in the training set size. A Matlab implementation available on the Internet is mentioned.

Experiments, using synthetic and real data, include results better than proffered by the theory, possibly due to the usual initialization difficulty in the non-greedy case, which the authors note. A final, brief discussion lists other approaches and the author’s future plans. The paper is well written, with surgically placed repetitions of important theory and practice points. EM (general and greedy) algorithm details are also outlined. The paper may have a slightly bloated introduction, and text on better-known information may squeeze out some paper-pertinent details; this might promote wider readership.