Ceulemans Eva, Kiers Henk A L
Katholieke Universiteit Leuven, Belgium.
Br J Math Stat Psychol. 2006 May;59(Pt 1):133-50. doi: 10.1348/000711005X64817.
Several three-mode principal component models can be considered for the modelling of three-way, three-mode data, including the Candecomp/Parafac, Tucker3, Tucker2, and Tucker1 models. The following question then may be raised: given a specific data set, which of these models should be selected, and at what complexity (i.e. with how many components)? We address this question by proposing a numerical model selection heuristic based on a convex hull. Simulation results show that this heuristic performs almost perfectly, except for Tucker3 data arrays with at least one small mode and a relatively large amount of error.
对于三向、三模式数据的建模，可以考虑几种三模式主成分模型，包括Candecomp/Parafac模型、Tucker3模型、Tucker2模型和Tucker1模型。接下来可能会提出以下问题：对于给定的特定数据集，应该选择这些模型中的哪一个，以及模型的复杂度应该是多少（即包含多少个成分）？我们通过提出一种基于凸包的数值模型选择启发式方法来解决这个问题。仿真结果表明，除了至少有一个小模式且误差相对较大的Tucker3数据阵列外，这种启发式方法的性能几乎完美。
