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

• Published in: IEEE transactions on pattern analysis and machine intelligence Vol. 38; no. 12; pp. 2402 - 2415
• Main Authors: Gebru, Israel Dejene, Alameda-Pineda, Xavier, Forbes, Florence, Horaud, Radu
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.12.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Institute of Electrical and Electronics Engineers
• Subjects: Algorithm design and analysis; Algorithms; Audio data; audio-visual fusion; Bayes methods; Clustering; Clustering algorithms; Computer Science; Computer Vision and Pattern Recognition; Data analysis; expectation-maximization; Finite mixtures; Machine Learning; Maximum likelihood estimators; minimum message length; Mixture models; model selection; outlier detection; Probabilistic models; Probability distribution functions; Random variables; robust clustering; Robustness; Robustness (mathematics); Scene analysis; Software algorithms; Sound; speaker localization; Statistics; weighted-data clustering; robust clustering; minimum message length; finite mixtures; model selection; speaker localization; expectation-maximization; audio-visual fusion; weighted-data clustering; outlier detection
• ISSN: 0162-8828; 2160-9292; 1939-3539
• DOI: 10.1109/TPAMI.2016.2522425

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 nonparametric 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.