Time-series clustering is a core analytical technique for data exploration and as a subroutine in downstream tasks. Although deep learning methods have surged recently, studies show that traditional algorithms, such as k -Shape, still achieve state-of-the-art performance, revealing an illusion of progress. k -Shape alternates between (i) cluster assignment using the Shape-based distance (SBD) and (ii) centroid update while preserving scale and temporal alignment. However, its cubic-time centroid computation limits scalability to long sequences. Despite advances in univariate time-series (UTS) clustering, multivariate (MTS) clustering remains underexplored—multiple channels complicate inter-channel dependency modeling and amplify the accuracy–runtime trade-off. To overcome these challenges, we introduce FASA and its multivariate extension MUFASA: scalable, accurate, and parameter-light methods. FASA derives a closed-form solution that minimizes within-cluster SBD distance in linear time, while MUFASA (i) introduces SBD-D, a distance measure identifying a global temporal alignment across channels, and (ii) introduces a centroid update that jointly estimates all channels to capture temporal and inter-channel dependencies efficiently. To demonstrate the effectiveness, we conduct the most comprehensive evaluation to date in the MTS clustering area—covering seven MTS distances and 21 clustering algorithms on 30 UEA MTS datasets—and benchmark FASA on 128 UCR UTS datasets against eight baselines. Results show that (i) SBD-D matches the accuracy of elastic distances while being on average two to four orders of magnitude faster, and (ii) MUFASA outperforms all scalable traditional, deep learning, and foundation models in accuracy while matching non-scalable ones at much lower runtime. Notably, FASA matches k -Shape's accuracy while exhibiting better scalability, especially with increasing length. Overall, MUFASA and FASA deliver efficient and accurate solutions for MTS and UTS clustering, respectively, paving the way for future progress in time-series analytics.

Time-series anomaly detection is critical across various domains. Despite advances in neural networks and foundation models, recent studies show that traditional data mining methods remain highly competitive due to their effectiveness and scalability. However, these approaches suffer from distinct limitations: discord-based methods fail in the presence of repeated anomalies, whereas clustering-based techniques, though mitigating this issue, struggle to capture fine-grained deviations. Moreover, both approaches rely on distance computation, whose effectiveness fundamentally depends on data normalization, with z-score serving as the de facto standard. However, we observe that while normalization reduces scale bias and can enhance anomaly detectability, it may also suppress amplitude-driven anomalies, making the choice of an appropriate normalization scheme both critical and non-trivial. To address these challenges, we propose HYDRA, a multi-level hierarchical and unsupervised approach that integrates the strengths of distance-based methods while reducing reliance on explicit normalization. HYDRA (i) employs a lightweight approximate nearest-neighbor detector with graph-based selection to identify representative subsequences; (ii) constructs multi-resolution representations of the time series and aggregates anomaly evidence from fine to coarse scales; and (iii) introduces a hierarchical ensemble mechanism that fuses level-wise scores to improve robustness against contamination and scale imbalance. This design allows HYDRA to detect diverse anomaly types, from short, isolated discords to long, persistent deviations, allowing it to detect patterns overlooked by single-scale methods. Extensive evaluation on 40 univariate and multivariate time-series anomaly detection datasets from the TSB-AD benchmark demonstrates that HYDRA achieves state-of-the-art performance, ranking first among 40 competing algorithms, while maintaining scalability to ultra-long sequences. We open-source our code at https://github.com/thedatumorg/HYDRA to facilitate reproducibility.

Predictive maintenance (PdM) is a key application of the industrial IoT, using sensor-acquired time-series data to forecast equipment failures that cost billions of dollars annually. Time-series anomaly detection (TSAD) offers a promising route to PdM, yet prior work is constrained by: i) reliance on private datasets or case studies, requiring extensive domain-specific engineering; ii) evaluation of only a small number of algorithms, limiting comparative insight; iii) use of a single implementation strategy per algorithm, hindering potential improvements; iv) emphasis on supervised solutions, necessitating annotated data that are costly or unavailable in practice; and v) neglect of runtime and online applicability, raising questions about deployability. To address these limitations, we present an extensive experimental study with rigorous statistical analysis conducted within a common evaluation framework. Our objectives are to: i) provide insights into the accuracy, robustness, and behavior of TSAD techniques in an online PdM setting across four implementation strategies; ii) analyze effectiveness–runtime trade-offs; and iii) rate dataset difficulty and characterize the forms exhibited by anomalies preceding machine breakdowns. Our findings indicate that most industrial cases benefit from an initial calibration phase for operational data collection. Well-established traditional TSAD methods deliver the best trade-off among effectiveness, runtime efficiency, and the ability to predict individual failure types; pre-trained LLMs are still statistically outperformed in this context, suggesting that there is still room for improvement in that direction. Our study serves as a significant step towards disseminating TSAD for PdM and we open source our work to support future research.

Recent advances in data collection technology, accompanied by the ever-rising volume and velocity of streaming data, underscore the vital need for time series analytics. In this regard, time-series anomaly detection has been an important activity, entailing various applications in fields such as cyber security, financial markets, law enforcement, and health care. While traditional literature on anomaly detection is centered on statistical measures, the increasing number of machine learning algorithms in recent years call for a structured, general characterization of the research methods for time-series anomaly detection. In this paper, we present a process-centric taxonomy for time-series anomaly detection methods, systematically categorizing traditional statistical approaches and contemporary machine learning techniques. Beyond this taxonomy, we conduct a meta-analysis of the existing literature to identify broad research trends. Given the absence of a one-size-fits-all anomaly detector, we also introduce emerging trends for time-series anomaly detection. Furthermore, we review commonly used evaluation measures and benchmarks, followed by an analysis of benchmark results to provide insights into the impact of different design choices on model performance. Through these contributions, we aim to provide a holistic perspective on time-series anomaly detection and highlight promising avenues for future investigation.

Despite decades of research on time-series anomaly detection, the effectiveness of existing anomaly detectors remains constrained to specific domains-a model that performs well on one dataset may fail on another. Consequently, developing automated solutions for anomaly detection remains a pressing challenge. However, the AutoML community has predominantly focused on supervised learning solutions, which are impractical for anomaly detection due to the lack of labeled data and the absence of a well-defined objective function for model evaluation. While recent studies have evaluated standalone anomaly detectors, no study has ever evaluated automated solutions for selecting or generating scores in an automated manner. In this study, we (i) provide a systematic review and taxonomy of automated solutions for time-series anomaly detection, categorizing them into selection, ensembling, and generation methods; (ii) introduce TSB-AutoAD, a comprehensive benchmark encompassing 20 standalone methods and 70 variants; and (iii) conduct the most extensive evaluation in this area to date. Our benchmark includes state-of-the-art methods across all three categories, evaluated on TSB-AD, a recently curated heterogeneous testbed from nine domains. Our findings reveal a significant gap, where over half of the existing solutions do not statistically outperform a simple random choice. Foundation models that claim to offer generalized, one-size-fits-all solutions have yet to deliver on this promise. While naive ensembling achieves high accuracy, it comes at a substantial computational overhead. Conversely, methods leveraging historical datasets enable fast inference but suffer under out-of-distribution conditions. To address this trade-off, we propose a selective ensembling solution, which combines model selection with ensembling to offer a lightweight, practical balance between accuracy and efficiency. We open-source TSB-AutoAD and highlight the need for more robust and efficient solutions.

Despite the recent focus on time-series anomaly detection, the effectiveness of the proposed anomaly detectors is restricted to specific domains. A model that performs well on one dataset may not perform well on another. Therefore, how to develop automated solutions for anomaly detection for a particular dataset has emerged as a pressing issue. However, there is a noticeable gap in the literature regarding providing a comprehensive review of the ongoing efforts toward automated solutions for selecting or generating scores in an automated manner. Conducting a meta-analysis of proposed methods is challenging due to: (i) their evaluation across limited datasets; (ii) different assumptions on application scenarios; and (iii) the absence of evaluations for out-of-distribution performance. Motivated by the limitations above, we introduce the EasyAD, a modular web engine designed to facilitate the exploration of the first comprehensive benchmark for automated time-series anomaly detection. The EasyAD engine enables rigorous statistical analysis of 20 automated methods and 70 of their variants across the TSB-AD benchmark, a recently curated, heterogeneous dataset spanning nine application domains. The engine supports a two-dimensional evaluation framework, incorporating both accuracy and runtime performance. Our engine allows users to assess the performance of various methods per dataset and per instance, which offers fine-grained analysis per time series. Furthermore, the engine accommodates the processing of user-uploaded data, enabling users to experiment with different model selection strategies on their own datasets.

Time-series clustering is a key task in time series analysis, enabling unsupervised data exploration and often serving as a subroutine for other tasks. Despite decades of active cross-disciplinary research, benchmarking of time-series clustering methods has received limited attention. Existing studies have (i) excluded popular methods and entire method classes; (ii) used a narrow range of distance measures; (iii) evaluated only a few datasets; (iv) lacked statistical validation; (v) had poor reproducibility; or (vi) relied on questionable evaluation setups. The rise of deep learning-especially foundation models claiming broad generalization-further emphasizes the need for comprehensive evaluation, as their role in time-series clustering remains largely untested. To address these gaps, we evaluate 84 time-series clustering methods across 10 method classes from data mining, machine learning, and deep learning. Our analysis spans 128 time-series datasets and uses rigorous statistical methods. Within a fair comparison framework, we (i) identify the top-performing method in each class; (ii) highlight previously overlooked, high-performing classes; (iii) challenge assumptions about elastic distance measures; (iv) refute the claimed superiority of deep learning methods, including foundation models; (v) expose reproducibility issues; (vi) analyze performance variation across dataset properties; and (vii) assess scalability. Our findings reveal an illusion of progress: no method significantly outperforms the decade-old k-Shape method. Still, we highlight a deep learning-based approach with notable promise. Our results provide a strong benchmark for advancing time-series clustering, and we have open-sourced our work to support future research.

Effective analysis of time series data presents significant challenges due to the complex temporal dependencies and cross-channel interactions in multivariate data. Inspired by the way human analysts visually inspect time series to uncover hidden patterns, we ask: can incorporating visual representations enhance automated time-series analysis? Recent advances in multimodal large language models have demonstrated impressive generalization and visual understanding capability, yet their application to time series remains constrained by the modality gap between continuous numerical data and discrete natural language. To bridge this gap, we introduce MLLM4TS, a novel framework that leverages multimodal large language models for general time-series analysis by integrating a dedicated vision branch. Each time-series channel is rendered as a horizontally stacked color-coded line plot in one composite image to capture spatial dependencies across channels, and a temporal-aware visual patch alignment strategy then aligns visual patches with their corresponding time segments. MLLM4TS fuses fine-grained temporal details from the numerical data with global contextual information derived from the visual representation, providing a unified foundation for multimodal time-series analysis. Extensive experiments on standard benchmarks demonstrate the effectiveness of MLLM4TS across both predictive tasks (e.g., classification) and generative tasks (e.g., anomaly detection and forecasting). These results underscore the potential of integrating visual modalities with pretrained language models to achieve robust and generalizable time-series analysis.

Distance measures are fundamental to time series analysis and have been extensively studied for decades. Until now, research efforts mainly focused on univariate time series, leaving multivariate cases largely under-explored. Furthermore, the existing experimental studies on multivariate distances have critical limitations: (a) focusing only on lock-step and elastic measures while ignoring categories such as sliding and kernel measures; (b) considering only one normalization technique; and (c) placing limited focus on statistical analysis of findings. Motivated by these shortcomings, we present the most complete evaluation of multivariate distance measures to date. Our study examines 30 standalone measures across 8 categories, 2 channel-dependency models, and considers 13 normalizations. We perform a comprehensive evaluation across 30 datasets and 3 downstream tasks, accompanied by rigorous statistical analysis. To ensure fairness, we conduct a thorough investigation of parameters for methods in both a supervised and an unsupervised manner. Our work verifies and extends earlier findings, showing that insights from univariate distance measures also apply to the multivariate case: (a) alternative normalization methods outperform Z-score, and for the first time, we demonstrate statistical differences in certain categories for the multivariate case; (b) multiple lock-step measures are better suited than Euclidean distance, when it comes to multivariate time series; and (c) newer elastic measures outperform the widely adopted Dynamic Time Warping distance, especially with proper parameter tuning in the supervised setting. Moreover, our results reveal that (a) sliding measures offer the best trade-off between accuracy and runtime; (b) current normalization techniques fail to significantly enhance accuracy on multivariate time series and, surprisingly, do not outperform the no normalization case, indicating a lack of appropriate solutions for normalizing multivariate time series; and (c) independent consideration of time series channels is beneficial only for elastic measures. In summary, we offer guidelines to aid in designing and selecting preprocessing strategies and multivariate distance measures for our community.

Symbolic approximations are dimensionality reduction techniques that convert time series into sequences of discrete symbols, enhancing interpretability while reducing computational and storage costs. To construct symbolic representations, first numeric representations approximate and capture properties of raw time series, followed by a discretization step that converts these numeric dimensions into symbols. Despite decades of development, existing approaches have several key limitations that often result in unsatisfactory performance: they (i) rely on data-agnostic numeric approximations, disregarding intrinsic properties of the time series; (ii) decompose dimensions into equal-sized subspaces, assuming independence among dimensions; and (iii) allocate a uniform encoding budget for discretizing each dimension or subspace, assuming balanced importance. To address these shortcomings, we propose SPARTAN, a novel data-adaptive symbolic approximation method that intelligently allocates the encoding budget according to the importance of the constructed uncorrelated dimensions. Specifically, SPARTAN (i) leverages intrinsic dimensionality reduction properties to derive non-overlapping, uncorrelated latent dimensions; (ii) adaptively distributes the budget based on the importance of each dimension by solving a constrained optimization problem; and (iii) prevents false dismissals in similarity search by ensuring a lower bound on the true distance in the original space. To demonstrate SPARTAN's robustness, we conduct the most comprehensive study to date, comparing SPARTAN with seven state-of-the-art symbolic methods across four tasks: classification, clustering, indexing, and anomaly detection. Rigorous statistical analysis across hundreds of datasets shows that SPARTAN outperforms competing methods significantly on all tasks in terms of downstream accuracy, given the same budget. Notably, SPARTAN achieves up to a 2x speedup compared to the most accurate rival. Overall, SPARTAN effectively improves the symbolic representation quality without storage or runtime overheads, paving the way for future advancements.

Anomaly detection is a fundamental task for time-series analytics with important implications for the downstream performance of many applications. Despite increasing academic interest and the large number of methods proposed in the literature, recent benchmarks and evaluation studies demonstrated that no overall best anomaly detection methods exist when applied to very heterogeneous time series datasets. Therefore, the only scalable and viable solution to solve anomaly detection over very different time series collected from diverse domains is to propose a model selection method that will select, based on time series characteristics, the best anomaly detection methods to run. Existing AutoML solutions are, unfortunately, not directly applicable to time series anomaly detection, and no evaluation of time series-based approaches for model selection exists. Towards that direction, this paper studies the performance of time series classification methods used as model selection for anomaly detection. In total, we evaluate 234 model configurations derived from 16 base classifiers across more than 1980 time series, and we propose the first extensive experimental evaluation of time series classification as model selection for anomaly detection. Our results demonstrate that model selection methods outperform every single anomaly detection method while being in the same order of magnitude regarding execution time. This evaluation is the first step to demonstrate the accuracy and efficiency of time series classification algorithms for anomaly detection, and represents a strong baseline that can then be used to guide the model selection step in general AutoML pipelines.

Identifying patterns or clusters in streaming time-series data is crucial for decision-making, and underpins applications such as anomaly detection, forecasting, and data quality monitoring. While numerous clustering algorithms have been proposed, many remain unexplored in the time-series domain, and others are unsuitable for streaming scenarios. Moreover, many effective methods require prior knowledge of the number of clusters, a significant limitation when dealing with evolving data streams. To address these challenges, we propose BURST, a principled and general-purpose framework that enables the application of partition-based clustering methods in streaming time-series settings. At its core, BURST integrates AutoKC, a novel, adaptive algorithm for automatically estimating the number of clusters, enhancing robustness to evolving time-series streams. Experimental analyses show that BURST is a robust strategy for real-time time-series clustering, effectively generalizing across different partitioning methods, and achieving state-of-the-art performance compared to existing algorithms.

Symbolic Approximation, a dimensionality reduction technique that transforms time series into discrete symbols, has gained increasing attention in various downstream applications. Despite decades of development, there is a noticeable absence of a comprehensive study in this domain, highlighting a need for more in-depth investigation and well-designed exploration tools. To address this gap, we propose SAIL, a modular web engine serving two purposes: (i) to provide the first comprehensive study on 7 state-of-the-art methods over 100+ time-series datasets, the largest study in this area; (ii) to evaluate the performance of a recently proposed solution, SPARTAN, that solves two core problems. First, SPARTAN exploits intrinsic dimensionality reduction to effectively model the underlying data distribution for approximation. Second, SPARTAN dynamically allocates alphabet sizes per segment, recognizing the non-uniform distribution of information in practice. Through its interactive interface, SAIL enables users to visualize and explore quantitative assessments across various methods, datasets, and analytical tasks. SAIL's exploration reveals that (i) while SAX variants outperform SAX by sacrificing storage, none surpass SAX under the same budget, reinforcing it as a strong baseline; SFA is the only existing method that consistently outperforms SAX within the same budget; and (ii) across diverse scenarios, SPARTAN outperforms competing methods in all evaluated tasks significantly, including classification, clustering, indexing, and anomaly detection, without incurring additional storage or runtime overhead. Overall, SAIL not only facilitates the most comprehensive studies in this field but also provides new insights and concrete solutions for future research. We release the SAIL web engine at https://saildemo.streamlit.app/.

Anomaly detection (AD) is a fundamental task for time-series analytics with important implications for the downstream performance of many applications. In contrast to other domains where AD mainly focuses on point-based anomalies (i.e., outliers in standalone observations), AD for time series is also concerned with range-based anomalies (i.e., outliers spanning multiple observations). Nevertheless, it is common to use traditional point-based information retrieval measures, such as Precision, Recall, and F-score, to assess the quality of methods by thresholding the anomaly score to mark each point as an anomaly or not. However, mapping discrete labels into continuous data introduces unavoidable shortcomings, complicating the evaluation of range-based anomalies. Notably, the choice of evaluation measure may significantly bias the experimental outcome. Despite over six decades of attention, there has never been a large-scale systematic quantitative and qualitative analysis of time-series AD evaluation measures. This paper extensively evaluates quality measures for time-series AD to assess their robustness under noise, misalignments, and different anomaly cardinality ratios. Our results indicate that measures producing quality values independently of a threshold (i.e., AUC-ROC and AUC-PR) are more suitable for time-series AD. Motivated by this observation, we first extend the AUC-based measures to account for range-based anomalies. Then, we introduce a new family of parameter-free and threshold-independent measures, Volume Under the Surface (VUS), to evaluate methods while varying parameters. We also introduce two optimized implementations for VUS that reduce significantly the execution time of the initial implementation. Our findings demonstrate that our four measures are significantly more robust in assessing the quality of time-series AD methods.

Modern data-intensive applications generate vast amounts of floating-point data, essential for fields like databases and machine learning. While many compression techniques focus on space efficiency, there is a lack of benchmarks evaluating both compression and query performance, especially in areas like in-situ query execution on compressed data and machine learning tasks such as distance measurement and k-nearest neighbors (k-NN) in Retrieval-Augmented Generation (RAG) systems. This paper addresses this gap by evaluating popular lossless floating-point compression methods on three key factors: compression efficiency, database operations performance, and machine learning query performance. We implemented these techniques in Rust and integrated them into an open-source library for use with columnar engines. Our comparison highlights trade-offs between compression efficiency and query performance, showing that no single approach excels in all areas, and some methods trade off compression for slower performance.

A variety of distance measures for multivariate time series has been proposed in recent literature. However, evaluations of such measures have been incomplete; comparisons are limited to subsets of similar measures, lacking a holistic view of the field with an appropriate taxonomy of measures. This paper presents a structured evaluation of multivariate time series distance measures. Through a novel taxonomy, measures are categorized based on how they handle the multiple variates; in an atomic or a holistic manner. Experimental evaluation of 12 measures shows that no single measure or approach is superior; the optimal choice depends on the data and the task at hand.

Anomaly detection is an important problem in data analytics with applications in many domains. In recent years, there has been an increasing interest in anomaly detection tasks applied to time series. In this tutorial, we take a holistic view of anomaly detection in time series, starting from the core definitions and taxonomies related to time series and anomaly types, to an extensive description of the anomaly detection methods proposed by different communities in the literature. We explore the literature and the proposed methods by demonstrating systems that help users understand the core computational steps of some methods and navigate benchmark results. Finally, we describe the problem of model selection for anomaly detection and discuss recent experimental results.