EM Algorithms for Weighted-Data Clustering with Application to Audio-Visual Scene Analysis

Israel Dejene Gebru 1 Xavier Alameda-Pineda 2 Florence Forbes 3 Radu Horaud 1
1 PERCEPTION - Interpretation and Modelling of Images and Videos
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
3 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : Data clustering has received a lot of attention and numerous methods, algorithms and software packages are available. Among these techniques, parametric finite-mixture models play a central role due to their interesting mathematical properties and to the existence of maximum-likelihood estimators based on expectation-maximization (EM). In this paper we propose a new mixture model that associates a weight with each observed point. We introduce the weighted-data Gaussian mixture and we derive two EM algorithms. The first one considers a fixed weight for each observation. The second one treats each weight as a random variable following a gamma distribution. We propose a model selection method based on a minimum message length criterion, provide a weight initialization strategy, and validate the proposed algorithms by comparing them with several state of the art parametric and non-parametric clustering techniques. We also demonstrate the effectiveness and robustness of the proposed clustering technique in the presence of heterogeneous data, namely audio-visual scene analysis.
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Israel Dejene Gebru, Xavier Alameda-Pineda, Florence Forbes, Radu Horaud. EM Algorithms for Weighted-Data Clustering with Application to Audio-Visual Scene Analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence, Institute of Electrical and Electronics Engineers, 2016, 38 (12), pp.2402 - 2415. ⟨10.1109/TPAMI.2016.2522425⟩. ⟨hal-01261374⟩

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