Fuzzy clustering provides a natural framework for modeling partial memberships, particularly important in multivariate time series (MTS) where state boundaries are often ambiguous. For example, in EEG monitoring of driver alertness, neural activity evolves along a continuum (from unconscious to fully alert, with many intermediate levels of drowsiness) so crisp labels are unrealistic and partial memberships are essential. However, most existing algorithms are developed for static, low-dimensional data and struggle with temporal dependence, unequal sequence lengths, high dimensionality, and contamination by noise or artifacts. To address these challenges, we introduce RFCPCA, a robust fuzzy subspace-clustering method explicitly tailored to MTS that, to the best of our knowledge, is the first of its kind to simultaneously: (i) learn membership-informed subspaces, (ii) accommodate unequal lengths and moderately high dimensions, (iii) achieve robustness through trimming, exponential reweighting, and a dedicated noise cluster, and (iv) automatically select all required hyperparameters. These components enable RFCPCA to capture latent temporal structure, provide calibrated membership uncertainty, and flag series-level outliers while remaining stable under contamination. On driver drowsiness EEG, RFCPCA improves clustering accuracy over related methods and yields a more reliable characterization of uncertainty and outlier structure in MTS.

翻译：模糊聚类为部分隶属度建模提供了自然框架，这在状态边界通常模糊的多元时间序列（MTS）中尤为重要。例如，在驾驶员警觉性的脑电图监测中，神经活动沿连续统演变（从无意识到完全警觉，其间存在多个不同程度的困倦状态），因此硬标签不切实际，部分隶属度至关重要。然而，现有算法大多针对静态低维数据开发，难以处理时间依赖性、不等长序列、高维度以及噪声或伪影污染等问题。为解决这些挑战，我们提出了RFCPCA——一种专门针对MTS设计的鲁棒模糊子空间聚类方法。据我们所知，这是首个能同时实现以下功能的算法：（i）学习基于隶属度的子空间，（ii）适应不等长序列和中等高维度数据，（iii）通过修剪、指数重加权和专用噪声聚类实现鲁棒性，（iv）自动选择所有必需超参数。这些组件使RFCPCA能够捕捉潜在时间结构、提供校准的隶属度不确定性、标记序列级异常值，并在污染条件下保持稳定性。在驾驶员困倦脑电图数据上，RFCPCA相比相关方法提升了聚类精度，并对MTS中的不确定性和异常值结构给出了更可靠的特征描述。