Abstract
A commonly used tool for estimating the parameters of a mixture model is the Expectation–Maximization (EM) algorithm, which is an iterative procedure that can serve as a maximum-likelihood estimator. The EM algorithm has well-documented drawbacks, such as the need for good initial values and the possibility of being trapped in local optima. Nevertheless, because of its appealing properties, EM plays an important role in estimating the parameters of mixture models. To overcome these initialization problems with EM, in this paper, we propose the Rough-Enhanced-Bayes mixture estimation (REBMIX) algorithm as a more effective initialization algorithm. Three different strategies are derived for dealing with the unknown number of components in the mixture model. These strategies are thoroughly tested on artificial datasets, density–estimation datasets and image–segmentation problems and compared with state-of-the-art initialization methods for the EM. Our proposal shows promising results in terms of clustering and density-estimation performance as well as in terms of computational efficiency. All the improvements are implemented in the rebmix R package.
Highlights
The Expectation–Maximization (EM) algorithm was introduced in [1]
We have proposed the use of the Rough-Enhanced-Bayes mixture estimation (REBMIX) algorithm as an initialization technique for the EM
The proposed strategies were thoroughly tested on artificially created datasets (Section 5.1), density-estimation tasks (Section 5.2), and image-segmentation tasks (Section 5.3)
Summary
The Expectation–Maximization (EM) algorithm was introduced in [1]. Today, after a little more than 40 years, it is still one of the most popular algorithms for statistical pattern recognition. DA-EM in [2], to modifications of the EM algorithm for different purposes: image matching [3]; parameter estimation [4,5]; malaria diagnoses [6]; mixture simplification [7]; and audio-visual scene analysis [8]. EM’s popularity has risen due to its use in estimating mixture-model (MM) parameters [9,10]. The parameters of MM can be used multi-purposely. Their use is interesting for density-estimation tasks [7,11] and clustering tasks [6,12,13]. In the context of MM parameter estimation, the EM algorithm can be seen as a clustering algorithm that maximizes the missing data log-likelihood function as the objective function. EM has many appealing properties, such as Mathematics 2020, 8, 373; doi:10.3390/math8030373 www.mdpi.com/journal/mathematics
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