V4 has been reported to retain higher-order information (e.g., color and shape) and attention in visual processing (Fries et al., 2001; Orban, 2008), while PFC is considered to

Clustering multivariate time series data is a crucial task in many domains, as it enables the identification of meaningful patterns and groups in time-evolving data. Traditional approaches, such as crisp clustering, rely on the assumption that clusters are sufficiently separated with little overlap. However, real-world data often defy this assumption, exhibiting overlapping distributions or overlapping clouds of points and blurred boundaries between clusters. Fuzzy clustering offers a compelling alternative by allowing partial membership in multiple clusters, making it well-suited for these ambiguous scenarios. Despite its advantages, current fuzzy clustering methods primarily focus on univariate time series, and for multivariate cases, even datasets of moderate dimensionality become computationally prohibitive. This challenge is further exacerbated when dealing with time series of varying lengths, leaving a clear gap in addressing the complexities of modern datasets. This work introduces a novel fuzzy clustering approach based on common principal component analysis to address the aforementioned shortcomings. Our method has the advantage of efficiently handling high-dimensional multivariate time series by reducing dimensionality while preserving critical temporal features. Extensive numerical results show that our proposed clustering method outperforms several existing approaches in the literature. An interesting application involving brain signals from different drivers recorded from a simulated driving experiment illustrates the potential of the approach.

Discovering dominant patterns and exploring dynamic behaviors especially critical state transitions and tipping points in high-dimensional time-series data are challenging tasks in study of real-world complex systems, which demand interpretable data representations to facilitate comprehension of both spatial and temporal information within the original data space. Here, we proposed a general and analytical ultralow-dimensionality reduction method for dynamical systems named spatial-temporal principal component analysis (stPCA) to fully represent the dynamics of a high-dimensional time-series by only a single latent variable without distortion, which transforms high-dimensional spatial information into one-dimensional temporal information based on nonlinear delay-embedding theory. The dynamics of this single variable is analytically solved and theoretically preserves the temporal property of original high-dimensional time-series, thereby accurately and reliably identifying the tipping point before an upcoming critical transition. Its applications to real-world datasets such as individual-specific heterogeneous ICU records demonstrated the effectiveness of stPCA, which quantitatively and robustly provides the early-warning signals of the critical/tipping state on each patient.

This article considers a novel and widely applicable approach to modeling high-dimensional dependent data when a large number of explanatory variables are available and the signal-to-noise ratio is low. We postulate that a $p$-dimensional response series is the sum of a linear regression with many observable explanatory variables and an error term driven by some latent common factors and an idiosyncratic noise. The common factors have dynamic dependence whereas the covariance matrix of the idiosyncratic noise can have diverging eigenvalues to handle the situation of low signal-to-noise ratio commonly encountered in applications. The regression coefficient matrix is estimated using penalized methods when the dimensions involved are high. We apply factor modeling to the regression residuals, employ a high-dimensional white noise testing procedure to determine the number of common factors, and adopt a projected Principal Component Analysis when the signal-to-noise ratio is low. We establish asymptotic properties of the proposed method, both for fixed and diverging numbers of regressors, as $p$ and the sample size $T$ approach infinity. Finally, we use simulations and empirical applications to demonstrate the efficacy of the proposed approach in finite samples.

Approximate variational inference has shown to be a powerful tool for modeling unknown complex probability distributions. Recent advances in the field allow us to learn probabilistic models of sequences that actively exploit spatial and temporal structure. We apply a Stochastic Recurrent Network (STORN) to learn robot time series data. Our evaluation demonstrates that we can robustly detect anomalies both off- and on-line.