Data fusion modeling can identify common features across diverse data sources
while accounting for source-specific variability. Here we introduce the concept
of a \textit{coupled generator decomposition} and demonstrate how it
generalizes sparse principal component analysis (SPCA) for data fusion.
Leveraging data from a multisubject, multimodal (electro- and
magnetoencephalography (EEG and MEG)) neuroimaging experiment, we demonstrate
the efficacy of the framework in identifying common features in response to
face perception stimuli, while accommodating modality- and subject-specific
variability. Through split-half cross-validation of EEG/MEG trials, we
investigate the optimal model order and regularization strengths for models of
varying complexity, comparing these to a group-level model assuming shared
brain responses to stimuli. Our findings reveal altered $\sim170ms$ fusiform
face area activation for scrambled faces, as opposed to real faces,
particularly evident in the multimodal, multisubject model. Model parameters
were inferred using stochastic optimization in PyTorch, demonstrating
comparable performance to conventional quadratic programming inference for SPCA
but with considerably faster execution. We provide an easily accessible toolbox
for coupled generator decomposition that includes data fusion for SPCA,
archetypal analysis and directional archetypal analysis. Overall, our approach
offers a promising new avenue for data fusion.

数据融合建模可识别不同数据源的共同特征并考虑源特异性变异。在多主体、多模态（脑电图和脑磁图）的神经影像实验中，我们引入了 “耦合生成器分解” 的概念，并演示了如何将其推广为数据融合的稀疏主成分分析（SPCA）方法。通过对脑电图和脑磁图试验进行分半交叉验证，我们研究了不同复杂度模型的最佳模型顺序和正则化强度，并将其与假设刺激下共享脑反应的群体水平模型进行比较。我们的发现表明，对于打乱的脸部，与真实脸部相比，大约 170ms 后颞叶面区的激活性有所改变，特别在多模态、多主体模型中更为明显。我们通过在 PyTorch 中使用随机优化进行模型参数推断，证明了其与 SPCA 的传统二次规划推断具有可比性，但执行速度要快得多。我们提供了一个易于访问的工具箱，包括了耦合生成器分解、原型分析和定向原型分析的数据融合方法。总体而言，我们的方法为数据融合提供了一个有希望的新途径。