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標題: 具遺失訊息下混合因子分析器之自動學習
Automated learning of mixtures of factor analyzers with missing information
作者: 林瑩婷
Ying-Ting Lin
關鍵字: 自動學習;ECM演算法;因子分析;最大概似估計;遺失訊息;模型選擇;automatic learning;ECM algorithms;factor analysis;maximum likelihood estimation;missing values;model selection
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The mixtures of factor analyzers (MFA) model is a powerful tool which provides a unified approach to dimensionality reduction and model-based clustering of heterogeneous data. In seeking the most appropriate number of factors ($q$) of a MFA model with the number of components ($g$) fixed a priori, a two-stage procedure is commonly performed by first carrying out parameter estimation over a set of prespecified numbers of factors, and then selecting the best $q$ according to certain penalized likelihood criteria. When the dimensionality of data grows higher, such a procedure can be computationally prohibitive. To overcome this obstacle, we develop an automated learning scheme to effectively merge parameter estimation and selection of $q$ into a one-stage algorithm. The proposed new learning procedure that allows for much less computational cost is called the automated MFA (AMFA) algorithm, and our development is also extended to accommodate missing values. In addition, we explicitly derive the score vector and the empirical information matrix for inferring standard errors associated with the estimated parameters. The potential and applicability of the proposed method are demonstrated through a number of real datasets with genuine and synthetic missing values.
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