Olsen Anders S, Høegh Rasmus M T, Hinrich Jesper L, Madsen Kristoffer H, Mørup Morten
Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark.
WS Audiology, Lynge, Denmark.
Front Neurosci. 2022 Jul 29;16:911034. doi: 10.3389/fnins.2022.911034. eCollection 2022.
Metastable microstates in electro- and magnetoencephalographic (EEG and MEG) measurements are usually determined using modified -means accounting for polarity invariant states. However, hard state assignment approaches assume that the brain traverses microstates in a discrete rather than continuous fashion. We present multimodal, multisubject directional archetypal analysis as a scale and polarity invariant extension to archetypal analysis using a loss function based on the Watson distribution. With this method, EEG/MEG microstates are modeled using subject- and modality-specific that are representative, distinct topographic maps between which the brain continuously traverses. Archetypes are specified as convex combinations of unit norm input data based on a shared generator matrix, thus assuming that the timing of neural responses to stimuli is consistent across subjects and modalities. The input data is reconstructed as convex combinations of archetypes using a subject- and modality-specific continuous archetypal mixing matrix. We showcase the model on synthetic data and an openly available face perception event-related potential data set with concurrently recorded EEG and MEG. In synthetic and unimodal experiments, we compare our model to conventional Euclidean multisubject archetypal analysis. We also contrast our model to a directional clustering model with discrete state assignments to highlight the advantages of modeling state trajectories rather than hard assignments. We find that our approach successfully models scale and polarity invariant data, such as microstates, accounting for intersubject and intermodal variability. The model is readily extendable to other modalities ensuring component correspondence while elucidating spatiotemporal signal variability.
在脑电图（EEG）和脑磁图（MEG）测量中，亚稳态微状态通常使用考虑极性不变状态的修正均值来确定。然而，硬状态分配方法假设大脑以离散而非连续的方式遍历微状态。我们提出了多模态、多主体方向原型分析，作为使用基于沃森分布的损失函数对原型分析进行尺度和极性不变扩展。通过这种方法，EEG/MEG微状态使用特定于主体和模态的原型进行建模，这些原型是具有代表性的、不同的地形图，大脑在这些地形图之间连续遍历。原型被指定为基于共享生成矩阵的单位范数输入数据的凸组合，因此假设对刺激的神经反应时间在不同主体和模态之间是一致的。输入数据使用特定于主体和模态的连续原型混合矩阵重建为原型的凸组合。我们在合成数据和一个公开可用的与面部感知事件相关的电位数据集（同时记录了EEG和MEG）上展示了该模型。在合成和单模态实验中，我们将我们的模型与传统的欧几里得多主体原型分析进行了比较。我们还将我们的模型与具有离散状态分配的方向聚类模型进行了对比，以突出建模状态轨迹而非硬分配的优势。我们发现我们的方法成功地对尺度和极性不变的数据（如微状态）进行了建模，同时考虑了主体间和模态间变异性。该模型易于扩展到其他模态，确保成分对应，同时阐明时空信号变异性。
