关于设计的多路数据集上 ANOVA 同时成分分析 (ASCA+) 和 Tucker3 张量分解的互补性质,Journal of Chemometrics

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关于设计的多路数据集上 ANOVA 同时成分分析 (ASCA+) 和 Tucker3 张量分解的互补性质
Journal of Chemometrics ( IF 1.9 ) Pub Date : 2023-08-30 , DOI: 10.1002/cem.3514
Farnoosh Koleini ₁ , Siewert Hugelier ₂ , Mahsa Akbari Lakeh ₃ , Hamid Abdollahi ₃ , José Camacho ₄ , Paul J. Gemperline ₁

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方差分析 (ANOVA) 同步成分分析 (ASCA+) 和 Tucker3 张量分解的互补性在设计数据集上得到了证明。我们展示了如何使用 ASCA+ 来 (a) 识别统计上足够的 Tucker3 模型；(b) 确定统计上重要的三元组，使其更容易解释；(c) 消除不重要的三元组，使可视化和解释更加简单。对于具有至少两个因素的实验设计的多元数据集，数据矩阵可以折叠成多路张量。ASCA+可以用在展开矩阵上，Tucker3建模可以用在折叠矩阵（张量）上。据报道，有两种新颖的策略可以使用先前发布的数据集来确定 Tucker3 模型的统计显着性。通过逐步向 Tucker3 模型添加因子直至在残差中观察不到 ASCA+ 可检测结构，创建了一个统计上足够的模型。Tucker3 模型残差的 Bootstrap 分析用于确定载荷和核心矩阵各个元素的置信区间，结果表明 3 × 7 × 3 模型的 63 个核心值中有 21 个在 95% 置信水平下不显着。利用 Tucker3 模型 63 个三元组的相互正交性，从模型中删除了这 21 个因子（三元组）。据报道，ASCA+ 向后消除策略进一步将 Tucker3 3 × 7 × 3 模型简化为 36 个核心值和相关的三元组。ASCA+ 还用于识别对实验因素 A、B 或交互作用 A × B 具有选择性响应的单个因素（三元组），以改进模型可视化和解释。

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On the complementary nature of ANOVA simultaneous component analysis (ASCA+) and Tucker3 tensor decompositions on designed multi-way datasets

The complementary nature of analysis of variance (ANOVA) Simultaneous Component Analysis (ASCA+) and Tucker3 tensor decompositions is demonstrated on designed datasets. We show how ASCA+ can be used to (a) identify statistically sufficient Tucker3 models; (b) identify statistically important triads making their interpretation easier; and (c) eliminate non-significant triads making visualization and interpretation simpler. For multivariate datasets with an experimental design of at least two factors, the data matrix can be folded into a multi-way tensor. ASCA+ can be used on the unfolded matrix, and Tucker3 modeling can be used on the folded matrix (tensor). Two novel strategies are reported to determine the statistical significance of Tucker3 models using a previously published dataset. A statistically sufficient model was created by adding factors to the Tucker3 model in a stepwise manner until no ASCA+ detectable structure was observed in the residuals. Bootstrap analysis of the Tucker3 model residuals was used to determine confidence intervals for the loadings and the individual elements of the core matrix and showed that 21 out of 63 core values of the 3 × 7 × 3 model were not significant at the 95% confidence level. Exploiting the mutual orthogonality of the 63 triads of the Tucker3 model, these 21 factors (triads) were removed from the model. An ASCA+ backward elimination strategy is reported to further simplify the Tucker3 3 × 7 × 3 model to 36 core values and associated triads. ASCA+ was also used to identify individual factors (triads) with selective responses on experimental factors A, B, or interactions, A × B, for improved model visualization and interpretation.

更新日期：2023-08-30

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