Robust learning from incomplete data via parameterized t mixture models through eigenvalue decomposition
| Autor: | Wan-Yu Wang, 王婉諭 |
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| Rok vydání: | 2012 |
| Druh dokumentu: | 學位論文 ; thesis |
| Popis: | 100 Celeux and Govaert (1995, Pattern Recognition, 28, pp. 781-793) introduced a family of Gaussian mixture (GMIX) models in which the within-group covariance matrices are structured parsimoniously in a geometrically interpretable way as originally introduced by Banfield and Raftery (1993, Biometrics, 49, pp. 803-821). In this thesis, we extend their ideas to present a novel class of multivariate t mixture (TMIX) models with fourteen parsimonious covariance structures for the unsupervised learning of heterogeneous multivariate data with possible missing values. We establish computationally flexible EM-type algorithms for parameter estimation of these models under a missing at random (MAR) mechanism. For ease of computation and theoretical developments, two auxiliary indicator matrices are incorporated into the estimating procedure for exactly extracting the location of observed and missing components of each observation. The practical usefulness of the proposed methodology is illustrated with real examples and simulation studies with varying proportions of missing values. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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