Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/96609
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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摘要: 
混合因子分析器(MFA)為一種高效用的工具,它提供一個統整的方法處理具異質性資料之維度縮減與基於模型的分群。在固定群數的條件下,通常利用兩階段程序尋找MFA模型中的最適因子個數,其方法是對於所有可能的因子個數進行參數估計,再根據懲罰式概似準則來選擇模型的最佳因子個數。然而當資料的維度變高,這樣的計算程序可能會產生計算上負荷過高的問題。為了克服這個障礙,我們發展一階段自動學習方法有效率地整合參數估計和選擇因子個數,這個新的學習程序具較少的計算成本,稱為自動混合因子分析(AMFA)演算法,我們發展出的方法也被延伸運用在具遺失值的資料上。此外,我們明確地推導計分向量和經驗訊息矩陣來推論有關於配適參數估計值的標準差。最後,我們透過一些具真實與虛擬遺失值之資料來闡述所提出之方法的潛力與適用性。

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.
URI: http://hdl.handle.net/11455/96609
Rights: 同意授權瀏覽/列印電子全文服務,2021-07-24起公開。
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