Time series clustering promises to uncover hidden structural patterns in data with applications across healthcare, finance, industrial systems, and other critical domains. However, without validated ground truth information, researchers cannot objectively assess clustering quality or determine whether poor results stem from absent structures in the data, algorithmic limitations, or inappropriate validation methods, raising the question whether clustering is "more art than science" (Guyon et al., 2009). To address these challenges, we introduce CSTS (Correlation Structures in Time Series), a synthetic benchmark for evaluating the discovery of correlation structures in multivariate time series data. CSTS provides a clean benchmark that enables researchers to isolate and identify specific causes of clustering failures by differentiating between correlation structure deterioration and limitations of clustering algorithms and validation methods. Our contributions are: (1) a comprehensive benchmark for correlation structure discovery with distinct correlation structures, systematically varied data conditions, established performance thresholds, and recommended evaluation protocols; (2) empirical validation of correlation structure preservation showing moderate distortion from downsampling and minimal effects from distribution shifts and sparsification; and (3) an extensible data generation framework enabling structure-first clustering evaluation. A case study demonstrates CSTS's practical utility by identifying an algorithm's previously undocumented sensitivity to non-normal distributions, illustrating how the benchmark enables precise diagnosis of methodological limitations. CSTS advances rigorous evaluation standards for correlation-based time series clustering.
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.
This paper introduces an algorithm for the detection of change-points and the identification of the corresponding subsequences in transient multivariate time-series data (MTSD). The analysis of such data has become more and more important due to the increase of availability in many industrial fields. Labeling, sorting or filtering highly transient measurement data for training condition based maintenance (CbM) models is cumbersome and error-prone. For some applications it can be sufficient to filter measurements by simple thresholds or finding change-points based on changes in mean value and variation. But a robust diagnosis of a component within a component group for example, which has a complex non-linear correlation between multiple sensor values, a simple approach would not be feasible. No meaningful and coherent measurement data which could be used for training a CbM model would emerge. Therefore, we introduce an algorithm which uses a recurrent neural network (RNN) based Autoencoder (AE) which is iteratively trained on incoming data. The scoring function uses the reconstruction error and latent space information. A model of the identified subsequence is saved and used for recognition of repeating subsequences as well as fast offline clustering. For evaluation, we propose a new similarity measure based on the curvature for a more intuitive time-series subsequence clustering metric. A comparison with seven other state-of-the-art algorithms and eight datasets shows the capability and the increased performance of our algorithm to cluster MTSD online and offline in conjunction with mechatronic systems.