51. Parameter Estimation in Finite Mixture Models by Regularized Optimal Transport: A Unified Framework for Hard and Soft Clustering
- Author
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Papadakis, Nicolas, Dessein, Arnaud, Deledalle, Charles-Alban, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Représentations musicales (Repmus), Sciences et Technologies de la Musique et du Son (STMS), Institut de Recherche et Coordination Acoustique/Musique (IRCAM)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche et Coordination Acoustique/Musique (IRCAM)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), ANR-16-CE33-0010,GOTMI,Generalized Optimal Transport Models for Image processing(2016), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Papadakis, Nicolas, and Generalized Optimal Transport Models for Image processing - - GOTMI2016 - ANR-16-CE33-0010 - AAPG2016 - VALID
- Subjects
FOS: Computer and information sciences ,Computer Science - Learning ,[INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing ,[INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing ,Statistics - Machine Learning ,Machine Learning (stat.ML) ,[STAT.OT]Statistics [stat]/Other Statistics [stat.ML] ,[STAT.OT] Statistics [stat]/Other Statistics [stat.ML] ,Machine Learning (cs.LG) - Abstract
In this short paper, we formulate parameter estimation for finite mixture models in the context of discrete optimal transportation with convex regularization. The proposed framework unifies hard and soft clustering methods for general mixture models. It also generalizes the celebrated $k$\nobreakdash-means and expectation-maximization algorithms in relation to associated Bregman divergences when applied to exponential family mixture models.
- Published
- 2017