A Greedy EM Algorithm for Gaussian Mixture Learning
Neural Processing Letters
Mixtures of Rectangles: Interpretable Soft Clustering
ICML '01 Proceedings of the Eighteenth International Conference on Machine Learning
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Mixture models constitute a popular type of probabilistic neuralnetworks which model the density of a dataset using a convexcombination of statistical distributions, with the Gaussiandistribution being the one most commonly used. In this work wepropose a new probability density function, called theΠ-sigmoid, from its ability to form the shape of the letter"Π" by appropriately combining two sigmoid functions. Wedemonstrate its modeling properties and the different shapes thatcan take for particular values of its parameters. We then presentthe Π-sigmoid mixture model and propose a maximum likelihoodestimation method to estimate the parameters of such a mixturemodel using the Generalized Expectation Maximization algorithm. Weassess the performance of the proposed method using syntheticdatasets and also on image segmentation and illustrate itssuperiority over Gaussian mixture models.