A variational Expectation–Maximization algorithm for temporal data clustering
The problem of temporal data clustering is addressed using a dynamic Gaussian mixture model. In addition to the missing clusters used in the classical Gaussian mixture model, the proposed approach assumes that the means of the Gaussian densities are latent variables distributed according to random w...
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| Published in: | Computational statistics & data analysis Vol. 103; pp. 206 - 228 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
01.11.2016
Elsevier |
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| ISSN: | 0167-9473, 1872-7352 |
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| Abstract | The problem of temporal data clustering is addressed using a dynamic Gaussian mixture model. In addition to the missing clusters used in the classical Gaussian mixture model, the proposed approach assumes that the means of the Gaussian densities are latent variables distributed according to random walks. The parameters of the proposed algorithm are estimated by the maximum likelihood approach. However, the EM algorithm cannot be applied directly due to the complex structure of the model, and some approximations are required. Using a variational approximation, an algorithm called VEM-DyMix is proposed to estimate the parameters of the proposed model. Using simulated data, the ability of the proposed approach to accurately estimate the parameters is demonstrated. VEM-DyMix outperforms, in terms of clustering and estimation accuracy, other state-of-the-art algorithms. The experiments performed on real world data from two fields of application (railway condition monitoring and object tracking from videos) show the strong potential of the proposed algorithms. |
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| AbstractList | The problem of temporal data clustering is addressed using a dynamic Gaussian mixture model. In addition to the missing clusters used in the classical Gaussian mixture model, the proposed approach assumes that the means of the Gaussian densities are latent variables distributed according to random walks. The parameters of the proposed algorithm are estimated by the maximum likelihood approach. However, the EM algorithm cannot be applied directly due to the complex structure of the model, and some approximations are required. Using a variational approximation, an algorithm called VEM-DyMix is proposed to estimate the parameters of the proposed model. Using simulated data, the ability of the proposed approach to accurately estimate the parameters is demonstrated. VEM-DyMix outperforms, in terms of clustering and estimation accuracy, other state-of-the-art algorithms. The experiments performed on real world data from two fields of application (railway condition monitoring and object tracking from videos) show the strong potential of the proposed algorithms. |
| Author | El Assaad, Hani Aknin, Patrice Samé, Allou Govaert, Gérard |
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| Keywords | Kalman filter Dynamic latent variable model Mixture model Variational approximation Maximum likelihood Clustering EM algorithm Temporal data clustering DYNAMIC LATENT VARIABLE MODEL TEMPORAL DATA CLUSTERING CLUSTERING MODELE DE MELANGE ALGORITHME ESPERANCE-MAXIMISATION FILTRE DE KALMAN VARIATIONAL APPROXIMATION |
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| SubjectTerms | Algorithms Approximation Clustering Data Analysis, Statistics and Probability Dynamic latent variable model EM algorithm Estimates Gaussian Kalman filter Mathematical models Maximum likelihood Mixture model Parameter estimation Parameters Physics statistical analysis Temporal data clustering Variational approximation |
| Title | A variational Expectation–Maximization algorithm for temporal data clustering |
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