Time Series Clustering
Momentum
2 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.
Latest papers 19
Functional data are intrinsically infinite-dimensional, and often exhibit phase variation, where corresponding events occur at different times across observations. Existing linear dimension reduction methods struggle with nonlinear amplitude variation, while functional autoencoders without an explicit warp entangle temporal misalignment with shape. We propose the Amplitude--Phase Functional Autoencoders (AP-FAE), an unsupervised framework for functional data that spans both univariate and multivariate cases, with emphasis on the multivariate setting, and factorizes the latent space into separate amplitude and phase embeddings derived from all channels. A smooth functional decoder reconstructs channel-specific amplitude functions in canonical time, and a shared monotone, endpoint-preserving warp captures phase variation. We prove a bound linking amplitude recovery to registration, reconstruction, and noise errors, and validate it numerically. Across synthetic data and six real-world benchmarks, AP-FAE outperforms state-of-the-art baselines on most clustering and alignment metrics and on all reconstruction metrics. Clustering with amplitude embeddings alone consistently surpasses joint amplitude--phase clustering, confirming the benefit of explicit disentanglement. Code is available at https://anonymous.4open.science/r/APFAE-418C/}{https://anonymous.4open.science/r/APFAE-418C/.
CLUES-WEASEL: No additional clues required to choose your time series clustering algorithm
Time series data is very common in many real-world applications and in numerous domains, with increasing interest for automated information extraction using machine learning. One of these subfields is time series clustering, which consists in identifying clusters among a set of time series in an unsupervised fashion. Most time series clustering algorithms suffer from the same balancing act: they trade clustering performance for faster runtimes or vice versa. We present a novel time series clustering algorithm that we call CLUES-WEASEL, which stands for CLustering with the UnsupervisEd Second version of Word ExtrAction for time SEries cLassification. CLUES-WEASEL extracts features using the unsupervised version of the transformation step of WEASEL 2.0, which is a time series classification algorithm, then reduces these features using principal component analysis, and finally performs clustering with the -means algorithm using these reduced extracted features. Through extensive experiments, we prove that CLUES-WEASEL is significantly better than any other existing time series clustering algorithm while being (much) faster than any state-of-the-art one. We also show that the architecture of CLUES-WEASEL can work well with other time series feature extraction algorithms. Our findings highlight the relevance of CLUES-WEASEL for time series clustering.
STCAD: Scalable Trajectory Clustering and Anomaly Detection on Terabyte-Scale AIS Data
We present a scalable framework for unsupervised clustering of maritime trajectories derived from terabyte-scale Automatic Identification System (AIS) archives. Variable-length trajectories are encoded with a custom BERT-based model trained via masked token modeling and clustered using CURE hierarchical clustering, producing physically interpretable trajectory groups without requiring a predefined number of clusters. An intrinsic unsupervised anomaly detection method based on reconstruction loss and clustering noise assignment identifies irregular navigation patterns. The framework is demonstrated on a national-scale AIS dataset comprising billions of messages spanning one year, yielding stable trajectory clusters and a clear separation between nominal and anomalous vessel behavior.
MINT: Tensor Decomposition on Stacked Recurrence Matrices for Time Series Data Mining
Recurrence plots are a time series data mining primitive applied to a variety of domains (e.g. star light curves, sound waveforms, CCT telemetry). This work proposes tensorized self-similarity matrices as a primitive for univariate time series datasets () of time series of length with a subsequence window of length , and whose tensor-based nature is naturally extensible to multivariate datasets. The proposed method to compute this primitive computes dot plots of size from these datasets, where the subsequent tensor is mined using tensor decomposition methods to mine for co-clustered patterns. We demonstrate our results in mass rapid transit, electricity demand, wind turbine, and car traffic data, finding the MINT pipeline effectively co-clusters cross-sensor patterns in highly regular datasets containing motifs at regular intervals.
Wiring diagram extraction and gluing: a case study in classifying figure skating jumps using 3D dataset
Hasse clustering is an algorithm that extracts common patterns in sequential data and represents them in graphical forms. As the number of expected clusters grows, however, the algorithm can become infeasible to run due to combinatorial complexity. In this article, we describe a theory of gluing wiring diagrams, allowing iterative applications of Hasse clustering to achieve the same result as a single application. We test our theory in the context of classifying videos of figure skating jumps.
Contrastive Representation Learning of Longitudinal Disease Trajectories on Temporal Graphs
Understanding disease trajectories from longitudinal clinical data remains challenging due to complex temporal dynamics and heterogeneous patient cohorts. Here, we present a contrastive representation learning framework that models multivariate disease trajectories as temporal graphs and learns representations using contrastive graph neural networks. Nodes represent patient observations over time, while edges capture temporal continuity and structural similarity between trajectories. Structure-aware random walks guide contrastive learning to generate embeddings that preserve temporal context and trajectory topology. The resulting representations enable robust clustering of patients with similar disease progression patterns and reveal latent structure in longitudinal data.
CASC: Causal Adversarial Subspace Clustering for Multivariate Spatiotemporal Data
Deep subspace clustering plays a critical role in applications involving multivariate spatiotemporal data, such as sea ice monitoring, disease spread analysis, and tracking neuro-degeneration over time. Despite recent advances, existing methods primarily rely on geometric self-expressiveness, assume static subspace structures, and often fail to capture causal dependencies, local spatial interactions, and long-range temporal dynamics inherent in complex spatiotemporal systems. To address these limitations, we propose a novel Causal Adversarial Subspace Clustering (CASC) framework for discovering evolving latent regimes in high-dimensional spatiotemporal data. CASC integrates a U-Net-inspired deep adversarial clustering architecture with stacked FAConvLSTM layers to preserve spatial and temporal structure while learning robust latent representations. A graph attention transformer-based self-expressive network is introduced to jointly model local spatial relationships, global dependencies, and long-range temporal interactions. Furthermore, we propose two new learning objectives: (1) a Causal Subspace Preservation Loss that aligns self-expression coefficients with latent causal relationships, encouraging clusters to reflect underlying causal processes rather than simple feature similarity, and (2) a Dynamic Temporal Subspace Evolution Loss that captures evolving subspace structures and temporal regime transitions in nonstationary environments. Together, these components transform deep subspace clustering from a correlation-driven paradigm into a causal-temporal regime discovery framework.
Clustering algorithms for multivariate wind farm SCADA data filtering
During wind farm operation, Supervisory Control and Data Acquisition (SCADA) systems record numerous anomalies, transients, and specific operational modes, leading to large datasets. However, for a wide range of applications, only measurements corresponding to normal operation are required and, therefore, the SCADA data must be filtered. For this purpose, several methods have been proposed to automate and replace manual filtering conducted by experts via visual inspection of the data. In this paper, we compare the filtering accuracy of multiple clustering algorithms against manual filtering, introducing evaluation metrics that are suitable for unlabeled data and robust across potential applications. Based on the results, we provide recommendations for generalizing model calibration to different datasets and discuss potential use cases for each model. The models are applied to the SCADA data of three turbines of an existing offshore wind farm, using 10-minute statistics across multiple data channels. In addition to the anomalies and operational modes typically recorded, the dataset presents a large number of non-evident outliers due to several field tests. Overall, the results highlight the importance of extending the analysis beyond the power curve, both in feature selection and in the design of evaluation metrics. In most cases, cluster-based methods are able to detect both evident and subtle outliers, achieving higher accuracy than manual filtering. However, the accuracy and the amount of data retained vary considerably depending on the model, and expert involvement remains necessary, though to a reduced extent compared to manual filtering.
Terminal Dimension Reduction for Time Series with Applications
Terminal embeddings have emerged as a powerful tool for dimension reduction. Given a set of points , a terminal embedding is a mapping that preserves the pairwise distance between any pair of points and up to small distortion under this mapping. Terminal embeddings have been particularly fruitful for constructing -means and -median coresets, where the objective is to find a typically weighted subset of such that for any candidate solution, the cost of the clustering objective on approximates the cost of the clustering objective on up to small distortion. Unfortunately, these techniques have not been extended to more complicated structures such as clustering time-series data under common straight-line interpolation between measurements. The main issue is that terminal embeddings, arguably the central technique in this line of research, cannot be linear and are thus not immediately suitable to preserve linear structures. In this work, we develop a generalization of terminal embeddings to affine line-segments that overcomes this issue. We showcase their applicability by using our lines-preserving terminal embeddings to obtain the first dimension-free coresets for clustering time-series under the Fréchet distance. The underlying dimension reduction uses Johnson-Lindenstrauss (JL) embeddings, and our experiments indicate that terminal embeddings perform similarly to JL and favorably against PCA for synthetic and real-world time-series, while only terminal embeddings extend pairwise distance preservation to the full ambient space.
FMMVCC: Fuzzy Mamba-based Multi-View Contrastive Clustering for Univariate Time Series
In many realistic scenarios, large volumes of time series data are generated with limited or expensive annotations. This limitation makes supervised learning methods difficult to apply and leads to the use of unsupervised approaches capable of discovering meaningful structures directly from raw data. Clustering therefore plays a crucial role in organizing time series into groups that share similar temporal patterns, enabling exploratory analysis and downstream tasks without requiring manual labeling. However, existing deep clustering methods often struggle to capture long-range temporal dependencies or rely on architectures with high computational cost. This paper introduces FMMVCC, a Mamba-based deep clustering framework for time series that leverages state space sequence modeling to efficiently learn temporal representations with linear complexity. Additionally, it utilizes multi-view self-supervised learning with temporal masking and augmentations. Experimental evaluation in 15 benchmark datasets proves that FMMVCC consistently outperforms state-of-the-art baselines, achieving the best overall performance in 29 of 60 total metric evaluations and the highest average rank in all tested scenarios.
NEST: Tackling Dataset-Level Distribution Shifts via Regime-Oriented Mixture-of-Experts
Accurate long-term forecasting in complex systems is frequently compromised by dataset-level distribution shifts, where diverse underlying behavioral modes and evolving system states drive the dynamic multivariate time-series. While existing methods predominantly focus on local temporal shifts, they fail to explicitly model the global structural challenge where datasets are composites of distinct operational regimes. In this paper, we propose NEST, a specialized framework designed to model and recompose these evolving structures through a two-phase dense MoE architecture. NEST first facilitates structural specialization by partitioning the dataset into distinct operational regimes through unsupervised clustering in a principled moment-entropy space. We introduce a regime-oriented router mechanism that generates initial expert weights based on temporal content, subsequently refined through geometric modulation to regime centroids. Crucially, rather than acting as monolithic predictors, individual experts function as specialized kernels that capture regime-specific dynamics by evolving unique variate-attention patterns. Extensive evaluations on diverse benchmarks, including heterogeneous network traffic and physical phenomena, demonstrate that NEST consistently achieves state-of-the-art performance. Our code and datasets are available at https://github.com/Aaralshin/NEST
Robust State-Conditional Feature-Weighted Jump Models for Temporal Clustering
We propose a robust feature-weighted jump model for time-dependent clustering. A penalty is used to encourage smoothness of transitions over time, while robustness is achieved through the use of a Tukey's biweight loss function. An additional parameter controls the variability of feature weights across states, allowing the model to assign state-specific relevance to each feature. We illustrate in simulation how the method accurately recovers the true cluster sequence and reliably identifies relevant features, outperforming competing approaches, particularly in the presence of outliers. We conclude with two empirical applications, one on the number of conflict-related homicides in Kosovo in the period 1998-2000, and another on macroeconomic performance of twelve European countries in the period 1949-2024.
Efficient Time Series Clustering from Multiscale Reservoir Dynamics with Granular-Ball Anchoring Graph Optimization
Time-series clustering remains challenging due to the inherent trade-off between clustering effectiveness and computational efficiency. Similarity-based methods often suffer from quadratic complexity caused by pairwise distance computations, while deep learning-based approaches typically rely on costly iterative training and a large number of trainable parameters. In this paper, we propose MSRGC-Net, an efficient time-series clustering framework that integrates multiscale reservoir computing, granular-ball-based anchoring graph construction, and consensus learning. MSRGC-Net adopts a training-free reservoir computing paradigm to extract multiscale temporal representations from raw time series without backpropagation, significantly reducing computational overhead. To capture the intrinsic structure of the resulting representations, granular-ball computing is employed to adaptively model data distributions via density-consistent regions, yielding compact and robust anchor graph representations. Furthermore, a consensus-based anchoring graph optimization strategy is introduced to effectively align multiscale reservoir representations and integrate complementary information across temporal scales. Extensive experiments on widely used univariate and multivariate benchmark datasets demonstrate that MSRGC-Net consistently outperforms state-of-the-art methods in clustering performance while maintaining superior computational efficiency.
An Analytical Multiple Criteria Framework for Temporal and Dynamic Business-to-Business Customer Segmentation in Manufacturing
In sales and marketing, customer segmentation is an important tool for formulating strategies for customer treatment and supply chain management. Most segmentation implementations rely on limited criteria, such as recency, frequency, and monetary (RFM) modeling, which often fail to capture complex business interactions. In this work, we design and evaluate a dynamic multi-criteria decision-making (MCDM) method in a business-to-business (B2B) manufacturing context by 1) extending RFM to dimensions of stability and growth, 2) integrating an adaptive and analytical hierarchical process to match business objectives, and 3) evaluating multivariate time-series clustering models. We then measure customer stability, tracking between-segment transitions, and volatility over time, and apply a graph-based consensus model to further strengthen the analysis. We test the efficacy of the proposed method using a real-world manufacturing company dataset to segment more than 3,000 B2B customers, showing strong robustness to temporal shifts. The implementation enables domain experts with preferential analytics to devise their strategies, providing effective decision support for B2B customer segmentation.
Amortized Neural Clustering of Time Series based on Statistical Features
This paper introduces an algorithm-agnostic approach to feature-based time series clustering via amortized neural inference. By training neural networks to approximate the optimal partitioning rule from simulated data, the proposed framework reduces reliance on conventional clustering methods, such as -means, -medoids, or hierarchical clustering, and their associated objective functions and heuristics. Leveraging statistical features, such as autocorrelations and quantile autocorrelations, the approach learns a data-driven affinity structure from which clustering partitions can be recovered, without requiring explicit prior specification of cluster shapes or structures. In addition, one version of the method can automatically determine the number of clusters, avoiding ad-hoc selection procedures. Comprehensive empirical studies show that the proposed framework achieves competitive or superior clustering accuracy relative to traditional methods, even in challenging scenarios where competing techniques are provided with the true number of clusters. An application to financial time series of stock returns illustrates its practical utility. By reducing the need for algorithm selection and calibration, the proposed framework opens new possibilities for automated, adaptive, and data-driven clustering of temporal data across scientific and industrial domains.
Scalable inference of spatial regions and temporal signatures from time series
Regionalization aims to partition a spatial domain into contiguous regions that share similar characteristics, enabling more effective spatial analysis, policy making, and resource management. Existing approaches for spatial regionalization typically rely on static spatial snapshots rather than evolving time series. Meanwhile, most time series clustering methods ignore spatial structure or enforce spatial continuity through ad hoc regularization, constraining the number of inferred regions a priori either explicitly or implicitly. Utilizing the minimum description length principle from information theory, here we propose an efficient and fully nonparametric framework for the regionalization of spatial time series. Our method jointly infers a spatial partition along with a set of representative time series archetypes ("drivers") that best compress a spatiotemporal dataset, with a runtime log-linear in the number of time series. We demonstrate that this method can accurately recover planted regional structure and drivers in synthetic time series, and can extract meaningful structural regularities in large-scale empirical air quality and vegetation index records. Our method provides a principled and scalable framework for spatially contiguous partitioning, allowing interpretable temporal patterns and homogeneous regions to emerge directly from the data itself.
Soft-MSM: Differentiable Context-Aware Elastic Alignment for Time Series
Elastic distances like dynamic time warping (DTW) are central to time series machine learning because they compare sequences under local temporal misalignment. Soft-DTW is an adaptation of DTW that can be used as a gradient-based loss by replacing the hard minimum in its dynamic-programming recursion with a smooth relaxation. However, this approach does not directly extend to elastic distances whose transition costs depend on the local alignment context. Move-Split-Merge (MSM) is one such distance: it uses context-aware split and merge penalties and has often outperformed DTW in supervised and unsupervised time series machine learning tasks such as classification and clustering. We introduce Soft-MSM, a smooth relaxation of MSM and an elastic alignment loss with context-aware transition costs. Central to the formulation is a smooth gated surrogate for MSM's piecewise split/merge cost, which enables gradients through both the dynamic-programming recursion and the local transition structure. We derive the forward recursion, backward recursion, soft alignment matrix, closed-form gradient, limiting behaviour, and divergence-corrected formulation. Experiments on 112 UCR datasets show that Soft-MSM gives lower MSM barycentre loss than existing MSM barycentre methods, and yields significantly better clustering and nearest-centroid classification performance than Soft-DTW-based alternatives. An implementation is available in the open-source \texttt{aeon} toolkit.
Deep Clustering for Climate: Analyzing Teleconnections through Learned Categorical States
Understanding and representing complex climate variability is essential for both scientific analysis and predictive modeling. However, identifying meaningful climate regimes from raw variables is challenging, as they exhibit high noise and nonlinear dependencies. In this work, we explore the use of Masked Siamese Networks to discretize climate time series into semantically rich clusters. Focusing on daily minimum and maximum temperature, we show that the resulting representations: (i) yield clusters that reflect meaningful climate states under our modeling assumptions, offering a simplified representation for downstream use; (ii) enable sampling and analysis of specific climate scenarios; and (iii) exhibit statistical associations with El Niño events, underscoring their scientific relevance. Our findings highlight the potential of self-supervised discretization as a tool for climate data analysis and open avenues for incorporating richer climate indicators in future work.
CROCS: A Two-Stage Clustering Framework for Behaviour-Centric Consumer Segmentation with Smart Meter Data
With grid operators confronting rising uncertainty from renewable integration and a broader push toward electrification, Demand-Side Management (DSM) -- particularly Demand Response (DR) -- has attracted significant attention as a cost-effective mechanism for balancing modern electricity systems. Unprecedented volumes of consumption data from a continuing global deployment of smart meters enable consumer segmentation based on real usage behaviours, promising to inform the design of more effective DSM and DR programs. However, existing clustering-based segmentation methods insufficiently reflect the behavioural diversity of consumers, often relying on rigid temporal alignment, and faltering in the presence of anomalies, missing data, or large-scale deployments. To address these challenges, we propose a novel two-stage clustering framework -- Clustered Representations Optimising Consumer Segmentation (CROCS). In the first stage, each consumer's daily load profiles are clustered independently to form a Representative Load Set (RLS), providing a compact summary of their typical diurnal consumption behaviours. In the second stage, consumers are clustered using the Weighted Sum of Minimum Distances (WSMD), a novel set-to-set measure that compares RLSs by accounting for both the prevalence and similarity of those behaviours. Finally, community detection on the WSMD-induced graph reveals higher-order prototypes that embody the shared diurnal behaviours defining consumer groups, enhancing the interpretability of the resulting clusters. Extensive experiments on both synthetic and real Australian smart meter datasets demonstrate that CROCS captures intra-consumer variability, uncovers both synchronous and asynchronous behavioural similarities, and remains robust to anomalies and missing data, while scaling efficiently through natural parallelisation. These results...