EM Algorithms for Weighted-Data Clustering with Application to Audio-Visual Scene Analysis
This work addresses clustering for heterogeneous data like audio-visual scenes, but it is incremental as it extends existing mixture models with weight handling.
The paper tackles the problem of clustering weighted data by proposing a new weighted-data Gaussian mixture model and deriving two EM algorithms, one with fixed weights and another with random weights following a gamma distribution, achieving validation against state-of-the-art techniques and demonstrating effectiveness in audio-visual scene analysis.
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.