This paper examines several network-based volatility models for oil prices, capturing spillovers among OPEC oil-exporting countries by embedding novel network structures into ARCH-type models. We apply a network-based log-ARCH framework that incorporates weight matrices derived from time-series clustering and model-implied distances into the conditional variance equation. These weight matrices are constructed from return data and standard multivariate GARCH model outputs (CCC, DCC, and GO-GARCH), enabling a comparative analysis of volatility transmission across specifications. Through a rolling-window forecast evaluation, the network-based models demonstrate competitive forecasting performance relative to traditional specifications and uncover intricate spillover effects. These results provide a deeper understanding of the interconnectedness within the OPEC network, with important implications for financial risk assessment, market integration, and coordinated policy among oil-producing economies.
The widespread use of sensors in modern power grids has led to the accumulation of large amounts of voltage and current waveform data, especially during fault events. However, the lack of labeled datasets poses a significant challenge for fault classification and analysis. This paper explores the application of unsupervised clustering techniques for fault diagnosis in high-voltage power systems. A dataset provided by the Reseau de Transport d'Electricite (RTE) is analyzed, with frequency domain features extracted using the Fast Fourier Transform (FFT). The K-Means algorithm is then applied to identify underlying patterns in the data, enabling automated fault categorization without the need for labeled training samples. The resulting clusters are evaluated in collaboration with power system experts to assess their alignment with real-world fault characteristics. The results demonstrate the potential of unsupervised learning for scalable and data-driven fault analysis, providing a robust approach to detecting and classifying power system faults with minimal prior assumptions.
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 of time series based on their underlying dynamics is keeping attracting researchers due to its impacts on assisting complex system modelling. Most current time series clustering methods handle only scalar time series, treat them as white noise, or rely on domain knowledge for high-quality feature construction, where the autocorrelation pattern/feature is mostly ignored. Instead of relying on heuristic feature/metric construction, the system identification approach allows treating vector time series clustering by explicitly considering their underlying autoregressive dynamics. We first derive a clustering algorithm based on a mixture autoregressive model. Unfortunately it turns out to have significant computational problems. We then derive a `small-noise' limiting version of the algorithm, which we call k-LMVAR (Limiting Mixture Vector AutoRegression), that is computationally manageable. We develop an associated BIC criterion for choosing the number of clusters and model order. The algorithm performs very well in comparative simulations and also scales well computationally.
Diabetes is one of the most prevalent diseases worldwide, characterized by persistently high blood sugar levels, capable of damaging various internal organs and systems. Diabetes patients require routine check-ups, resulting in a time series of laboratory records, such as hemoglobin A1c, which reflects each patient's health behavior over time and informs their doctor's recommendations. Clustering patients into groups based on their entire time series data assists doctors in making recommendations and choosing treatments without the need to review all records. However, time series clustering of this type of dataset introduces some challenges; patients visit their doctors at different time points, making it difficult to capture and match trends, peaks, and patterns. Additionally, two aspects must be considered: differences in the levels of laboratory results and differences in trends and patterns. To address these challenges, we introduce a new clustering algorithm called Time and Trend Traveling Time Series Clustering (4TaStiC), using a base dissimilarity measure combined with Euclidean and Pearson correlation metrics. We evaluated this algorithm on artificial datasets, comparing its performance with that of seven existing methods. The results show that 4TaStiC outperformed the other methods on the targeted datasets. Finally, we applied 4TaStiC to cluster a cohort of 1,989 type 2 diabetes patients at Siriraj Hospital. Each group of patients exhibits clear characteristics that will benefit doctors in making efficient clinical decisions. Furthermore, the proposed algorithm can be applied to contexts outside the medical field.
Time series clustering is an unsupervised learning method for classifying time series data into groups with similar behavior. It is used in applications such as healthcare, finance, economics, energy, and climate science. Several time series clustering methods have been introduced and used for over four decades. Most of them focus on measuring either Euclidean distances or association dissimilarities between time series. In this work, we propose a new dissimilarity measure called ranked Pearson correlation dissimilarity (RDPC), which combines a weighted average of a specified fraction of the largest element-wise differences with the well-known Pearson correlation dissimilarity. It is incorporated into hierarchical clustering. The performance is evaluated and compared with existing clustering algorithms. The results show that the RDPC algorithm outperforms others in complicated cases involving different seasonal patterns, trends, and peaks. Finally, we demonstrate our method by clustering a random sample of customers from a Thai electricity consumption time series dataset into seven groups with unique characteristics.
In this study, we employ k-means clustering algorithm of polyspectral means to analyze 49 stocks in the Indian stock market. We have used spectral and bispectral information obtained from the data, by using spectral and bispectral means with different weight functions that will give us varying insights into the temporal patterns of the stocks. In particular, the higher order polyspectral means can provide significantly more information than what we can gather from power spectra, and can also unveil nonlinear trends in a time series. Through rigorous analysis, we identify five distinctive clusters, uncovering nuanced market structures. Notably, one cluster emerges as that of a conglomerate powerhouse, featuring ADANI, BIRLA, TATA, and unexpectedly, government-owned bank SBI. Another cluster spotlights the IT sector with WIPRO and TCS, while a third combines private banks, government entities, and RELIANCE. The final cluster comprises publicly traded companies with dispersed ownership. Such clustering of stocks sheds light on intricate financial relationships within the stock market, providing valuable insights for investors and analysts navigating the dynamic landscape of the Indian stock market.
The air transportation local share, defined as the proportion of local passengers relative to total passengers, serves as a critical metric reflecting how economic growth, carrier strategies, and market forces jointly influence demand composition. This metric is particularly useful for examining industry structure changes and large-scale disruptive events such as the COVID-19 pandemic. This research offers an in-depth analysis of local share patterns on more than 3900 Origin and Destination (O&D) pairs across the U.S. air transportation system, revealing how economic expansion, the emergence of low-cost carriers (LCCs), and strategic shifts by legacy carriers have collectively elevated local share. To efficiently identify the local share characteristics of thousands of O&Ds and to categorize the O&Ds that have the same behavior, a range of time series clustering methods were used. Evaluation using visualization, performance metrics, and case-based examination highlighted distinct patterns and trends, from magnitude-based stratification to trend-based groupings. The analysis also identified pattern commonalities within O&D pairs, suggesting that macro-level forces (e.g., economic cycles, changing demographics, or disruptions such as COVID-19) can synchronize changes between disparate markets. These insights set the stage for predictive modeling of local share, guiding airline network planning and infrastructure investments. This study combines quantitative analysis with flexible clustering to help stakeholders anticipate market shifts, optimize resource allocation strategies, and strengthen the air transportation system's resilience and competitiveness.
Time series clustering poses a significant challenge with diverse applications across domains. A prominent drawback of existing solutions lies in their limited interpretability, often confined to presenting users with centroids. In addressing this gap, our work presents $k$-Graph, an unsupervised method explicitly crafted to augment interpretability in time series clustering. Leveraging a graph representation of time series subsequences, $k$-Graph constructs multiple graph representations based on different subsequence lengths. This feature accommodates variable-length time series without requiring users to predetermine subsequence lengths. Our experimental results reveal that $k$-Graph outperforms current state-of-the-art time series clustering algorithms in accuracy, while providing users with meaningful explanations and interpretations of the clustering outcomes.
This paper discusses an approach to inertial parameter estimation for the case of cargo carrying spacecraft that is based on causal learning, i.e. learning from the responses of the spacecraft, under actuation. Different spacecraft configurations (inertial parameter sets) are simulated under different actuation profiles, in order to produce an optimised time-series clustering classifier that can be used to distinguish between them. The actuation is comprised of finite sequences of constant inputs that are applied in order, based on typical actuators available. By learning from the system's responses across multiple input sequences, and then applying measures of time-series similarity and F1-score, an optimal actuation sequence can be chosen either for one specific system configuration or for the overall set of possible configurations. This allows for both estimation of the inertial parameter set without any prior knowledge of state, as well as validation of transitions between different configurations after a deployment event. The optimisation of the actuation sequence is handled by a reinforcement learning model that uses the proximal policy optimisation (PPO) algorithm, by repeatedly trying different sequences and evaluating the impact on classifier performance according to a multi-objective metric.
Time series, as one of the most fundamental representations of sequential data, has been extensively studied across diverse disciplines, including computer science, biology, geology, astronomy, and environmental sciences. The advent of advanced sensing, storage, and networking technologies has resulted in high-dimensional time-series data, however, posing significant challenges for analyzing latent structures over extended temporal scales. Time-series clustering, an established unsupervised learning strategy that groups similar time series together, helps unveil hidden patterns in these complex datasets. In this survey, we trace the evolution of time-series clustering methods from classical approaches to recent advances in neural networks. While previous surveys have focused on specific methodological categories, we bridge the gap between traditional clustering methods and emerging deep learning-based algorithms, presenting a comprehensive, unified taxonomy for this research area. This survey highlights key developments and provides insights to guide future research in time-series clustering.
Temporal Neural Networks (TNNs), a special class of spiking neural networks, draw inspiration from the neocortex in utilizing spike-timings for information processing. Recent works proposed a microarchitecture framework and custom macro suite for designing highly energy-efficient application-specific TNNs. These recent works rely on manual hardware design, a labor-intensive and time-consuming process. Further, there is no open-source functional simulation framework for TNNs. This paper introduces TNNGen, a pioneering effort towards the automated design of TNNs from PyTorch software models to post-layout netlists. TNNGen comprises a novel PyTorch functional simulator (for TNN modeling and application exploration) coupled with a Python-based hardware generator (for PyTorch-to-RTL and RTL-to-Layout conversions). Seven representative TNN designs for time-series signal clustering across diverse sensory modalities are simulated and their post-layout hardware complexity and design runtimes are assessed to demonstrate the effectiveness of TNNGen. We also highlight TNNGen's ability to accurately forecast silicon metrics without running hardware process flow.
Gravitational-wave observatories like LIGO are large-scale, terrestrial instruments housed in infrastructure that spans a multi-kilometer geographic area and which must be actively controlled to maintain operational stability for long observation periods. Despite exquisite seismic isolation, they remain susceptible to seismic noise and other terrestrial disturbances that can couple undesirable vibrations into the instrumental infrastructure, potentially leading to control instabilities or noise artifacts in the detector output. It is, therefore, critical to characterize the seismic state of these observatories to identify a set of temporal patterns that can inform the detector operators in day-to-day monitoring and diagnostics. On a day-to-day basis, the operators monitor several seismically relevant data streams to diagnose operational instabilities and sources of noise using some simple empirically-determined thresholds. It can be untenable for a human operator to monitor multiple data streams in this manual fashion and thus a distillation of these data-streams into a more human-friendly format is sought. In this paper, we present an end-to-end machine learning pipeline for features-based multivariate time series clustering to achieve this goal and to provide actionable insights to the detector operators by correlating found clusters with events of interest in the detector.
Time series data has become increasingly prevalent across numerous domains, driving a growing demand for time series machine learning techniques. Among these, time series clustering (TSCL) stands out as one of the most popular machine learning tasks. TSCL serves as a powerful exploratory analysis tool and is also employed as a preprocessing step or subroutine for various tasks, including anomaly detection, segmentation, and classification. The most popular TSCL algorithms are either fast (in terms of run time) but perform poorly on benchmark problems, or perform well on benchmarks but scale poorly. We present a new TSCL algorithm, the $k$-means (K) accelerated (A) Stochastic subgradient (S) Barycentre (B) Average (A) (KASBA) clustering algorithm. KASBA is a $k$-means clustering algorithm that uses the Move-Split-Merge (MSM) elastic distance at all stages of clustering, applies a randomised stochastic subgradient gradient descent to find barycentre centroids, links each stage of clustering to accelerate convergence and exploits the metric property of MSM distance to avoid a large proportion of distance calculations. It is a versatile and scalable clusterer designed for real-world TSCL applications. It allows practitioners to balance run time and clustering performance. We demonstrate through extensive experimentation that KASBA produces significantly better clustering than the faster state of the art clusterers and is offers orders of magnitude improvement in run time over the most performant $k$-means alternatives.
Time series data analysis is prevalent across various domains, including finance, healthcare, and environmental monitoring. Traditional time series clustering methods often struggle to capture the complex temporal dependencies inherent in such data. In this paper, we propose the Variational Mixture Graph Autoencoder (VMGAE), a graph-based approach for time series clustering that leverages the structural advantages of graphs to capture enriched data relationships and produces Gaussian mixture embeddings for improved separability. Comparisons with baseline methods are included with experimental results, demonstrating that our method significantly outperforms state-of-the-art time-series clustering techniques. We further validate our method on real-world financial data, highlighting its practical applications in finance. By uncovering community structures in stock markets, our method provides deeper insights into stock relationships, benefiting market prediction, portfolio optimization, and risk management.
There is a long history of research into time series clustering using distance-based partitional clustering. Many of the most popular algorithms adapt k-means (also known as Lloyd's algorithm) to exploit time dependencies in the data by specifying a time series distance function. However, these algorithms are often presented with k-means configured in various ways, altering key parameters such as the initialisation strategy. This variability makes it difficult to compare studies because k-means is known to be highly sensitive to its configuration. To address this, we propose a standard Lloyd's-based model for TSCL that adopts an end-to-end approach, incorporating a specialised distance function not only in the assignment step but also in the initialisation and stopping criteria. By doing so, we create a unified structure for comparing seven popular Lloyd's-based TSCL algorithms. This common framework enables us to more easily attribute differences in clustering performance to the distance function itself, rather than variations in the k-means configuration.
This paper presents a machine learning approach to estimate the inertial parameters of a spacecraft in cases when those change during operations, e.g. multiple deployments of payloads, unfolding of appendages and booms, propellant consumption as well as during in-orbit servicing and active debris removal operations. The machine learning approach uses time series clustering together with an optimised actuation sequence generated by reinforcement learning to facilitate distinguishing among different inertial parameter sets. The performance of the proposed strategy is assessed against the case of a multi-satellite deployment system showing that the algorithm is resilient towards common disturbances in such kinds of operations.
In this paper, we propose a novel method of model-based time series clustering with mixtures of general state space models (MSSMs). Each component of MSSMs is associated with each cluster. An advantage of the proposed method is that it enables the use of time series models appropriate to the specific time series. This not only improves clustering and prediction accuracy but also enhances the interpretability of the estimated parameters. The parameters of the MSSMs are estimated using stochastic variational inference, a subtype of variational inference. The proposed method estimates the latent variables of an arbitrary state space model by using neural networks with a normalizing flow as a variational estimator. The number of clusters can be estimated using the Bayesian information criterion. In addition, to prevent MSSMs from converging to the local optimum, we propose several optimization tricks, including an additional penalty term called entropy annealing. To our best knowledge, the proposed method is the first computationally feasible one for time series clustering based on general (possibly nonlinear, non-Gaussian) state space models. Experiments on simulated datasets show that the proposed method is effective for clustering, parameter estimation, and estimating the number of clusters.
The detection of abnormal or critical system states is essential in condition monitoring. While much attention is given to promptly identifying anomalies, a retrospective analysis of these anomalies can significantly enhance our comprehension of the underlying causes of observed undesired behavior. This aspect becomes particularly critical when the monitored system is deployed in a vital environment. In this study, we delve into anomalies within the domain of Bio-Regenerative Life Support Systems (BLSS) for space exploration and analyze anomalies found in telemetry data stemming from the EDEN ISS space greenhouse in Antarctica. We employ time series clustering on anomaly detection results to categorize various types of anomalies in both uni- and multivariate settings. We then assess the effectiveness of these methods in identifying systematic anomalous behavior. Additionally, we illustrate that the anomaly detection methods MDI and DAMP produce complementary results, as previously indicated by research.
Time series clustering is fundamental in data analysis for discovering temporal patterns. Despite recent advancements, learning cluster-friendly representations is still challenging, particularly with long and complex time series. Deep temporal clustering methods have been trying to integrate the canonical k-means into end-to-end training of neural networks but fall back on surrogate losses due to the non-differentiability of the hard cluster assignment, yielding sub-optimal solutions. In addition, the autoregressive strategy used in the state-of-the-art RNNs is subject to error accumulation and slow training, while recent research findings have revealed that Transformers are less effective due to time points lacking semantic meaning, to the permutation invariance of attention that discards the chronological order and high computation cost. In light of these observations, we present LoSTer which is a novel dense autoencoder architecture for the long-sequence time series clustering problem (LSTC) capable of optimizing the k-means objective via the Gumbel-softmax reparameterization trick and designed specifically for accurate and fast clustering of long time series. Extensive experiments on numerous benchmark datasets and two real-world applications prove the effectiveness of LoSTer over state-of-the-art RNNs and Transformer-based deep clustering methods.