Classification Rules for Heterogeneous Incomplete Multivariate Normal Populations Through Eigenvalue Decomposition
碩士 === 國立中興大學 === 應用數學系所 === 101 === We study the problem of classification under fourteen eigen-decomposed covariance structures for the supervised learning of heterogeneous multivariate data with possible missing values. The new classification rules are built under assumption of multivariate norma...
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Other Authors: | |
Format: | Others |
Language: | zh-TW |
Published: |
2013
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Online Access: | http://ndltd.ncl.edu.tw/handle/69959568166140625519 |
Summary: | 碩士 === 國立中興大學 === 應用數學系所 === 101 === We study the problem of classification under fourteen eigen-decomposed covariance structures for the supervised learning of heterogeneous multivariate data with possible missing values. The new classification rules are built under assumption of multivariate normality for populations with parameters obtained by the maximum likelihood estimates. Under the missing at random (MAR) mechanism, we develop computationally feasible EM-type algorithms coupled with the F–G diagonalization routine for carrying out estimation of parameters and imputation of missing values. To facilitate the implementation, 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 several real data sets. Experimental results show that some parsimonious models may provide better performances than over-parameterized ones, especially when the percentage of missing values is high.
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