Multiple factor analysis: principal component analysis for multitable and multiblock data sets
Multiple factor analysis: principal component analysis for multitable and multiblock data sets
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DOI：
10.1002/wics.1246
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发表时间：
2013-03-01
影响因子：
3.2
通讯作者：
Valentin, Domininique
中科院分区：
文献类型：
--
作者：
Abdi, Herve;Williams, Lynne J.;Valentin, Domininique
多因子分析（英语：Multiple factor analysis，缩写为MFA）是主成分分析（英语：Principal component analysis，缩写为PCA）的一种扩展，用于处理多个数据表，这些数据表测量在相同观测值上收集的变量集，或者（在双MFA中）多个数据表，其中相同的变量在不同的观测值集上测量。MFA分为两个步骤：首先，它计算每个数据表的PCA，并通过将其所有元素除以从其PCA获得的第一奇异值来“规范化”每个数据表。其次，所有规范化的数据表被聚合到一个大数据表中，该表通过（非规范化的）PCA进行分析，该PCA为变量的观测和负载提供一组因子得分。此外，MFA为每个数据表提供了一组反映该数据表特定“观点”的观测的部分因子得分。有趣的是，公共因子得分可以通过将原始归一化数据表替换为从这些表中的每个表的PCA获得的归一化因子得分来获得。在本文中，我们介绍了MFA，回顾了最近的扩展，并用一个详细的例子来说明它。(C)2013 Wiley Periodicals，Inc.
Multiple factor analysis (MFA, also called multiple factorial analysis) is an extension of principal component analysis (PCA) tailored to handle multiple data tables that measure sets of variables collected on the same observations, or, alternatively, (in dual-MFA) multiple data tables where the same variables are measured on different sets of observations. MFA proceeds in two steps: First it computes a PCA of each data table and 'normalizes' each data table by dividing all its elements by the first singular value obtained from its PCA. Second, all the normalized data tables are aggregated into a grand data table that is analyzed via a (non-normalized) PCA that gives a set of factor scores for the observations and loadings for the variables. In addition, MFA provides for each data table a set of partial factor scores for the observations that reflects the specific 'view-point' of this data table. Interestingly, the common factor scores could be obtained by replacing the original normalized data tables by the normalized factor scores obtained from the PCA of each of these tables. In this article, we present MFA, review recent extensions, and illustrate it with a detailed example. (C) 2013 Wiley Periodicals, Inc.