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Title: Revisiting factor analysis: Three types of its formulation Authors:  Kohei Adachi - Osaka University (Japan) [presenting]
Abstract: The main goal of factor analysis (FA) is to explain the variation of multiple observed variables by the factors called common and unique: the common factors serve for explaining the variation of all variables, while the unique factors have one-to-one correspondences to the variables. According to how the common and unique factors are treated, the FA procedures can be classified into three types. A classic one of them can be called a latent variable FA (LVFA), in which the factors are regarded as random latent variables. The remaining two types were recently proposed, in which the factors are treated as fixed parameter matrices. Those two types can be called matrix decomposition FA (MDFA) and constrained uniqueness FA (CUFA), respectively, as the former algorithm consists entirely of matrix-algebraic computations, and the latter is a constrained version of MDFA. Here, the constraint requires each unique factor to affect the corresponding variable in a completely exclusive manner, and CUFA can be regarded as equivalent to minimum rank FA. We compare the three types of FA theoretically and empirically.