Time Series Classification

Persistent homology (PH) -- the conventional method in topological data analysis -- is computationally expensive, requires further vectorization of its signatures before machine learning (ML) can be applied, and captures information along only the spatial axis. For time series data, we propose Euler Characteristic Surfaces (ECS) as an alternative topological signature based on the Euler characteristic ($χ$) -- a fundamental topological invariant. The ECS provides a computationally efficient, spatiotemporal, and inherently discretized feature representation that can serve as direct input to ML models. We prove a stability theorem guaranteeing that the ECS remains stable under small perturbations of the input time series. We first demonstrate that ECS effectively captures the nontrivial topological differences between the limit cycle and the strange attractor in the Rössler system. We then develop an ECS-based classification framework and apply it to five benchmark biomedical datasets (four ECG, one EEG) from the UCR/UEA archive. On $\textit{ECG5000}$, our single-feature ECS classifier achieves $98\%$ accuracy with $O(n+R\cdot T)$ complexity, compared to $62\%$ reported by a recent PH-based method. An AdaBoost extension raises accuracy to $98.6\%$, matching the best deep learning results while retaining full interpretability. Strong results are also obtained on $\textit{TwoLeadECG}$ ($94.1\%$) and $\textit{Epilepsy2}$ ($92.6\%$).

Time series classification (TSC) performance depends not only on architectural design but also on the diversity of input representations. In this work, we propose a scalable multi-scale convolutional framework that systematically integrates structured multi-representation inputs for univariate time series. We introduce two architectures: MRMS-Net, a hierarchical multi-scale convolutional network optimized for robustness and calibration, and LMRMS-Net, a lightweight variant designed for efficiency-aware deployment. In addition, we adapt LiteMV -- originally developed for multivariate inputs -- to operate on multi-representation univariate signals, enabling cross-representation interaction. We evaluate all models across 142 benchmark datasets under a unified experimental protocol. Critical Difference (CD) analysis confirms statistically significant performance differences among the top models. Results show that LiteMV achieves the highest mean accuracy, MRMS-Net provides superior probabilistic calibration (lowest NLL), and LMRMS-Net offers the best efficiency-accuracy tradeoff. Pareto analysis further demonstrates that multi-representation multi-scale modeling yields a flexible design space that can be tuned for accuracy-oriented, calibration-oriented, or resource-constrained settings. These findings establish scalable multi-representation multi-scale learning as a principled and practical direction for modern TSC. Reference implementation of MRMS-Net and LMRMS-Net is available at: https://github.com/alagoz/mrmsnet-tsc

Deep learning models achieve high accuracy in time series classification, yet understanding their class-level decision behaviour remains challenging. Explanations for time series must respect temporal dependencies and identify patterns that recur across instances. Existing approaches face three limitations: model-agnostic XAI methods developed for images and tabular data do not readily extend to time series, global explanation synthesis for time series remains underexplored, and most existing global approaches are model-specific. We propose L2GTX, a model-agnostic framework that generates class-wise global explanations by aggregating local explanations from a representative set of instances. L2GTX extracts clusters of parameterised temporal event primitives, such as increasing or decreasing trends and local extrema, together with their importance scores from instance-level explanations produced by LOMATCE. These clusters are merged across instances to reduce redundancy, and an instance-cluster importance matrix is used to estimate global relevance. Under a user-defined instance selection budget, L2GTX selects representative instances that maximise coverage of influential clusters. Events from the selected instances are then aggregated into concise class-wise global explanations. Experiments on six benchmark time series datasets show that L2GTX produces compact and interpretable global explanations while maintaining stable global faithfulness measured as mean local surrogate fidelity.

We present a new method for generating plausible counterfactual explanations for time series classification problems. The approach performs gradient-based optimization directly in the input space. To enforce plausibility, we integrate soft-DTW (dynamic time warping) alignment with $k$-nearest neighbors from the target class, which effectively encourages the generated counterfactuals to adopt a realistic temporal structure. The overall optimization objective is a multi-faceted loss function that balances key counterfactual properties. It incorporates losses for validity, sparsity, and proximity, alongside the novel soft-DTW-based plausibility component. We conduct an evaluation of our method against several strong reference approaches, measuring the key properties of the generated counterfactuals across multiple dimensions. The results demonstrate that our method achieves competitive performance in validity while significantly outperforming existing approaches in distributional alignment with the target class, indicating superior temporal realism. Furthermore, a qualitative analysis highlights the critical limitations of existing methods in preserving realistic temporal structure. This work shows that the proposed method consistently generates counterfactual explanations for time series classifiers that are not only valid but also highly plausible and consistent with temporal patterns.

Self-supervised foundation models have achieved remarkable success across domains, including time series. However, the potential of non-contrastive methods, a paradigm that has driven significant advances in computer vision, remains underexplored for time series. In this work, we adapt DINOv2-style self-distillation to pretrain a time series foundation model, building on the Mantis tokenizer and transformer encoder architecture as our backbone. Through a student-teacher framework, our method Utica learns representations that capture both temporal invariance via augmented crops and fine-grained local structure via patch masking. Our approach achieves state-of-the-art classification performance on both UCR and UEA benchmarks. These results suggest that non-contrastive methods are a promising and complementary pretraining strategy for time series foundation models.

Developing foundation models for time series classification is of high practical relevance, as such models can serve as universal feature extractors for diverse downstream tasks. Although early models such as Mantis have shown the promise of this approach, a substantial performance gap remained between frozen and fine-tuned encoders. In this work, we introduce methods that significantly strengthen zero-shot feature extraction for time series. First, we introduce Mantis+, a variant of Mantis pre-trained entirely on synthetic time series. Second, through controlled ablation studies, we refine the architecture and obtain MantisV2, an improved and more lightweight encoder. Third, we propose an enhanced test-time methodology that leverages intermediate-layer representations and refines output-token aggregation. In addition, we show that performance can be further improved via self-ensembling and cross-model embedding fusion. Extensive experiments on UCR, UEA, Human Activity Recognition (HAR) benchmarks, and EEG datasets show that MantisV2 and Mantis+ consistently outperform prior time series foundation models, achieving state-of-the-art zero-shot performance.

Normalization and scaling are fundamental preprocessing steps in time series modeling, yet their role in Transformer-based models remains underexplored from a theoretical perspective. In this work, we present the first formal analysis of how different normalization strategies, specifically instance-based and global scaling, impact the expressivity of Transformer-based architectures for time series representation learning. We propose a novel expressivity framework tailored to time series, which quantifies a model's ability to distinguish between similar and dissimilar inputs in the representation space. Using this framework, we derive theoretical bounds for two widely used normalization methods: Standard and Min-Max scaling. Our analysis reveals that the choice of normalization strategy can significantly influence the model's representational capacity, depending on the task and data characteristics. We complement our theory with empirical validation on classification and forecasting benchmarks using multiple Transformer-based models. Our results show that no single normalization method consistently outperforms others, and in some cases, omitting normalization entirely leads to superior performance. These findings highlight the critical role of preprocessing in time series learning and motivate the need for more principled normalization strategies tailored to specific tasks and datasets.

Time series data are prone to noise in various domains, and training samples may contain low-predictability patterns that deviate from the normal data distribution, leading to training instability or convergence to poor local minima. Therefore, mitigating the adverse effects of low-predictability samples is crucial for time series analysis tasks such as time series forecasting (TSF) and time series classification (TSC). While many deep learning models have achieved promising performance, few consider how to identify and penalize low-predictability samples to improve model performance from the training perspective. To fill this gap, we propose a general Amortized Predictability-aware Training Framework (APTF) for both TSF and TSC. APTF introduces two key designs that enable the model to focus on high-predictability samples while still learning appropriately from low-predictability ones: (i) a Hierarchical Predictability-aware Loss (HPL) that dynamically identifies low-predictability samples and progressively expands their loss penalty as training evolves, and (ii) an amortization model that mitigates predictability estimation errors caused by model bias, further enhancing HPL's effectiveness. The code is available at https://github.com/Meteor-Stars/APTF.

This paper proposes a few-shot classification framework based on Large Language Models (LLMs) to predict whether the next day will have spikes in real-time electricity prices. The approach aggregates system state information, including electricity demand, renewable generation, weather forecasts, and recent electricity prices, into a set of statistical features that are formatted as natural-language prompts and fed to an LLM along with general instructions. The model then determines the likelihood that the next day would be a spike day and reports a confidence score. Using historical data from the Texas electricity market, we demonstrate that this few-shot approach achieves performance comparable to supervised machine learning models, such as Support Vector Machines and XGBoost, and outperforms the latter two when limited historical data are available. These findings highlight the potential of LLMs as a data-efficient tool for classifying electricity price spikes in settings with scarce data.

The zero-shot evaluation of time series foundation models (TSFMs) for classification typically uses a frozen encoder followed by a task-specific classifier. However, this practice violates the training-free premise of zero-shot deployment and introduces evaluation bias due to classifier-dependent training choices. To address this issue, we propose TIC-FM, an in-context learning framework that treats the labeled training set as context and predicts labels for all test instances in a single forward pass, without parameter updates. TIC-FM pairs a time series encoder and a lightweight projection adapter with a split-masked latent memory Transformer. We further provide theoretical justification that in-context inference can subsume trained classifiers and can emulate gradient-based classifier training within a single forward pass. Experiments on 128 UCR datasets show strong accuracy, with consistent gains in the extreme low-label situation, highlighting training-free transfer for time series classification.The source code is publicly available at https://github.com/fangjuntao/TIC-FM.

We address the problem of classifying trajectories or sequences generated by nonlinear dynamical systems, where each class corresponds to a distinct dynamical system. We propose Dynafit, a kernel-based method that learns a distance metric between training data and the underlying dynamics. New observations are assigned to the class whose dynamics best fit the observations according to the learned metric.The learning algorithm approximates the Koopman operator, which globally linearizes the dynamics in a (potentially infinite-dimensional) feature space associated with a kernel function. The distance metric is computed in the feature space independently of its dimensionality by exploiting the kernel trick commonly used in machine learning. The kernel function can be tailored to incorporate prior knowledge of the dynamics when available. We consider a classical test example, the logistic map as a discrete dynamical system, and derive analytically the kernel function from the polynomial Koopman basis that exactly linearizes the dynamics. Dynafit is applicable to a wide range of classification tasks involving nonlinear dynamical systems and sensors. We illustrate its effectiveness through three examples: chaos detection in the logistic map, recognition of handwritten dynamical patterns, and classification of visual dynamic textures.

Modeling continuous-time dynamics from sparse and irregularly-sampled time series remains a fundamental challenge. Neural controlled differential equations provide a principled framework for such tasks, yet their performance is highly sensitive to the choice of control path constructed from discrete observations. Existing methods commonly employ fixed interpolation schemes, which impose simplistic geometric assumptions that often misrepresent the underlying data manifold, particularly under high missingness. We propose FlowPath, a novel approach that learns the geometry of the control path via an invertible neural flow. Rather than merely connecting observations, FlowPath constructs a continuous and data-adaptive manifold, guided by invertibility constraints that enforce information-preserving and well-behaved transformations. This inductive bias distinguishes FlowPath from prior unconstrained learnable path models. Empirical evaluations on 18 benchmark datasets and a real-world case study demonstrate that FlowPath consistently achieves statistically significant improvements in classification accuracy over baselines using fixed interpolants or non-invertible architectures. These results highlight the importance of modeling not only the dynamics along the path but also the geometry of the path itself, offering a robust and generalizable solution for learning from irregular time series.

The proliferation of Internet-of-Things (IoT) devices has led to an unprecedented volume of multivariate time series (MTS) data, requiring efficient and accurate processing for timely decision-making in resource-constrained edge environments. Hyperdimensional (HD) computing, with its inherent efficiency and parallelizability, has shown promise in classification tasks but struggles to capture complex temporal patterns, while Transformers excel at sequence modeling but incur high computational and memory overhead. We introduce BiHDTrans, an efficient neurosymbolic binary hyperdimensional Transformer that integrates self-attention into the HD computing paradigm, unifying the representational efficiency of HD computing with the temporal modeling power of Transformers. Empirically, BiHDTrans outperforms state-of-the-art (SOTA) HD computing models by at least 14.47% and achieves 6.67% higher accuracy on average than SOTA binary Transformers. With hardware acceleration on FPGA, our pipelined implementation leverages the independent and identically distributed properties of high-dimensional representations, delivering 39.4 times lower inference latency than SOTA binary Transformers. Theoretical analysis shows that binarizing in holographic high-dimensional space incurs significantly less information distortion than directly binarizing neural networks, explaining BiHDTrans's superior accuracy. Furthermore, dimensionality experiments confirm that BiHDTrans remains competitive even with a 64% reduction in hyperspace dimensionality, surpassing SOTA binary Transformers by 1-2% in accuracy with 4.4 times less model size, as well as further reducing the latency by 49.8% compare to the full-dimensional baseline. Together, these contributions bridge the gap between the expressiveness of Transformers and the efficiency of HD computing, enabling accurate, scalable, and low-latency MTS classification.

Time series analysis has emerged as an important tool for improving patient diagnosis and management in healthcare applications. However, these applications commonly face two critical challenges: time misalignment and data sparsity. Traditional approaches address these issues through a two-step process of imputation followed by prediction. We propose MAGIC (Multi-tAsk Gaussian Process for Imputation and Classification), a novel unified framework that simultaneously performs class-informed missing value imputation and label prediction within a hierarchical multi-task Gaussian process coupled with functional logistic regression. To handle intractable likelihood components, MAGIC employs Taylor expansion approximations with bounded error analysis, and parameter estimation is performed using EM algorithm with block coordinate optimization supported by convergence analysis. We validate MAGIC through two healthcare applications: prediction of post-traumatic headache improvement following mild traumatic brain injury and prediction of in-hospital mortality within 48 hours after ICU admission. In both applications, MAGIC achieves superior predictive accuracy compared to existing methods. The ability to generate real-time and accurate predictions with limited samples facilitates early clinical assessment and treatment planning, enabling healthcare providers to make more informed treatment decisions.

Handling missing data in time series classification remains a significant challenge in various domains. Traditional methods often rely on imputation, which may introduce bias or fail to capture the underlying temporal dynamics. In this paper, we propose TANDEM (Temporal Attention-guided Neural Differential Equations for Missingness), an attention-guided neural differential equation framework that effectively classifies time series data with missing values. Our approach integrates raw observation, interpolated control path, and continuous latent dynamics through a novel attention mechanism, allowing the model to focus on the most informative aspects of the data. We evaluate TANDEM on 30 benchmark datasets and a real-world medical dataset, demonstrating its superiority over existing state-of-the-art methods. Our framework not only improves classification accuracy but also provides insights into the handling of missing data, making it a valuable tool in practice.

Differentiable logic networks (DLNs) have shown promising results in tabular domains by combining accuracy, interpretability, and computational efficiency. In this work, we apply DLNs to the domain of TSC for the first time, focusing on univariate datasets. To enable DLN application in this context, we adopt feature-based representations relying on Catch22 and TSFresh, converting sequential time series into vectorized forms suitable for DLN classification. Unlike prior DLN studies that fix the training configuration and vary various settings in isolation via ablation, we integrate all such configurations into the hyperparameter search space, enabling the search process to select jointly optimal settings. We then analyze the distribution of selected configurations to better understand DLN training dynamics. We evaluate our approach on 51 publicly available univariate TSC benchmarks. The results confirm that classification DLNs maintain their core strengths in this new domain: they deliver competitive accuracy, retain low inference cost, and provide transparent, interpretable decision logic, thus aligning well with previous DLN findings in the realm of tabular classification and regression tasks.

Sleep stage classification is critical for diagnosing and managing disorders like sleep apnea and insomnia. However, conventional methods like polysomnography are costly and impractical for long-term, home-based monitoring. This study presents an energy-efficient approach for detecting four sleep stages (wake, rapid eye movement (REM), light sleep, deep sleep) using a single-lead electrocardiogram (ECG) signal. We evaluate various machine learning and deep learning models, introducing two windowing strategies: (1) a 5-minute window with 30-second steps for machine learning and (2) a 30-second window with 10-second steps for deep learning, enabling 10-second temporal resolution for real-time predictions. While deep learning models like MobileNet-v1 achieve high accuracy (92%) and F1-score (91%), their energy demands make them unsuitable for wearables. To address this, we design SleepLiteCNN, optimized for ECG-based sleep staging, achieving 89% accuracy and 89% F1-score while minimizing energy use. Applying 8-bit quantization further reduces energy consumption to 5.48 microJ per inference, with 90% accuracy and F1-score. Additionally, field-programmable gate array (FPGA) deployment shows significant reductions in resource usage. This approach provides a practical, energy-efficient solution for continuous ECG-based sleep monitoring in resource-constrained wearable devices.

In physical human-robot collaboration (pHRC) settings, humans and robots collaborate directly in shared environments. Robots must analyze interactions with objects to ensure safety and facilitate meaningful workflows. One critical aspect is human/object detection, where the contacted object is identified. Past research introduced binary machine learning classifiers to distinguish between soft and hard objects. This study improves upon those results by evaluating three-class human/object detection models, offering more detailed contact analysis. A dataset was collected using the Franka Emika Panda robot manipulator, exploring preprocessing strategies for time-series analysis. Models including LSTM, GRU, and Transformers were trained on these datasets. The best-performing model achieved 91.11% accuracy during real-time testing, demonstrating the feasibility of multi-class detection models. Additionally, a comparison of preprocessing strategies suggests a sliding window approach is optimal for this task.

Crop type classification from optical satellite time series remains limited in its ability to generalize across growing seasons, particularly when crop phenology shifts due to inter-annual weather variability. This hampers deployment in operational settings where current-year labels are unavailable. In addition, uncertainty quantification is often overlooked, reducing the reliability of such approaches for practical crop monitoring. Inspired by ecophysiological principles, we introduce Thermal Time-based Temporal Sampling ($T^3S$), a simple, model-agnostic method that replaces calendar time with thermal time. By re-indexing satellite observations by cumulative growing degree days, $T^3S$ aligns phenologically equivalent growth stages across years, reducing temporal redundancy while concentrating on the most biologically informative periods. We evaluate $T^3S$ across three architecturally distinct backbones on (i) SwissCrop, a new country-scale, multi-year Sentinel-2 dataset with paired temperature data that we publicly release, and (ii) the cross-region TimeMatch benchmark spanning Denmark and France. Across these settings, $T^3S$ consistently improves cross-year and cross-region crop classification over several state-of-the-art baselines, including thermal positional encoding, with particularly strong gains in uncertainty calibration, robustness under label scarcity, and early-season prediction, while requiring no architectural modification.

Adapting vision models for time series analysis is compelling, yet all existing approaches are falling short of dedicated time series foundation models (TSFMs) in classification. In this work, we propose Time Vision Transformer (TiViT), the first framework that successfully unlocks the representational power of frozen Vision Transformers (ViTs) pretrained on large-scale image datasets for time series classification. TiViT achieves state-of-the-art performance without any finetuning by utilizing the hidden representations of OpenCLIP models. We explore the structure of TiViT representations and find that intermediate ViT layers with high intrinsic dimension are the most effective for time series classification. Furthermore, we assess the alignment between TiViT and TSFM representation spaces and identify a strong complementarity, with additional performance gains achieved through feature concatenation. Finally, we unfreeze the ViT backbone of TiViT for continual pretraining and contrastive alignment with TSFMs on time series, enhancing the performance of lightweight TiViT variants. Our findings reveal a new direction for the domain and task adaptation of vision foundation models. Code is available at https://github.com/ExplainableML/TiViT.

This paper introduces Fuzzy Attention Network-Based Transformer (FANTF), an approach for time series forecasting, classification, and anomaly detection. FANTF combines fuzzy logic concepts with transformer architectures through a novel fuzzy attention mechanism. The proposed mechanism is inspired by Type-2 fuzzy set theory. It uses a learnable Gaussian uncertainty perturbation to model uncertainty in attention relevance scores. This makes it possible for the model to accurately capture uncertainty in temporal relationships better than normal deterministic attention. Transformers capacity to record complex temporal patterns and multivariate connections is enhanced by FANTF. The approach is both architecture-agnostic and task-agnostic. The proposed fuzzy attention module can be used as a direct replacement for the standard attention layer. To evaluate its effectiveness, FANTF is integrated into five transformer backbones: Transformer, Informer, PatchTST, Crossformer, and iTransformer. The fuzzy attention mechanism produces softer and more diverse attention distributions. It provides uncertainty-aware interpretations through attention heatmap visualizations. Experimental evaluations on some real-life datasets reveal that FANTF enhances the forecasting performance, classification, and anomaly detection tasks over traditional transformer-based models. FANTF achieves statistically significant and competitive performance improvements over standard transformer-based baselines on most benchmark datasets (p < 0.05, Wilcoxon signed-rank test), observed under noisy and non-stationary time series conditions.

Time series forecasts are widely used to inform decisions under uncertainty. In many applications, these decisions involve classifying a time series based on outcomes that have yet to be observed. In this paper, we introduce Foreclassing, a new machine learning problem in which the class label of a time series is defined as a function of its future observations. We provide a mathematical formulation of Foreclassing and establish several theoretical results characterizing the problem. These results describe how additional future information affects Bayes classification risk, provide bounds on the classification error of learned Foreclassing models, and demonstrate how future observations used during training can yield finite-sample improvements over conventional classifiers. To provide a benchmark for future research, we propose ForeClassNet, a family of neural network models that jointly perform forecasting and classification while accounting for uncertainty in future outcomes. We investigate a variety of model architectures and evaluate their performance against conventional time series classifiers and forecasting-then-classify approaches. Experiments on datasets spanning weather, energy, and finance demonstrate the potential of Foreclassing to improve classification performance, probabilistic prediction, and downstream decision-making. Together, these theoretical and empirical contributions establish a foundation for future research on Foreclassing.

Prescribed-parameter convolutional transforms achieve strong time series classification performance using fixed kernels, simple pooling operations, and a linear classifier. Their success raises a mechanistic question: which properties of the representation make this construction effective? We study the proportion of positive values (PPV), a pooling operator shared by ROCKET, MiniROCKET, and MultiROCKET. We establish exact invariance to circular translations under periodic boundaries and quantify departures from invariance under finite boundaries. A complementary analysis bounds the sensitivity of a smooth PPV surrogate. We then define the population pairwise geometry induced by a distribution of convolutional parameters and show how a finite random kernel bank concentrates around that geometry. This separates the role of the parameter distribution from the number of sampled kernels. Experiments on the UCR classification collection examine effective dimensionality, distance correlation with the input, and classification accuracy using PPV-only, unit-energy ROCKET kernels. Increasing kernel count produces diminishing representational gains. Increasing kernel length generally raises effective dimensionality and distance correlation, while the best test performance occurs at intermediate lengths and training accuracy remains close to perfect. Together, these results support an interpretation in which nonlinear pooling creates a richer but structured representation that can favour linear separation, while further representational richness need not improve generalisation.

While foundation models have revolutionized various domains, their application to time series classification remains rather under-explored, with existing literature predominantly focused on forecasting. To bridge this gap, we introduce Mantis, a transformer-based foundation model pre-trained exclusively on synthetic data via self-supervised contrastive learning. We demonstrate that effective tokenization is critical to unlocking the full potential of transformers, proposing a novel token generator unit. Furthermore, we introduce an enhanced test-time methodology that bridges the performance gap between Mantis and strong specialized approaches by leveraging intermediate-layer representations, self-ensembling, and cross-model embedding fusion. Extensive experiments demonstrate that Mantis establishes a new state-of-the-art, outperforming existing foundation models across four diverse dataset collections covering various application domains.

As with most other data domains, EEG data analysis relies on rich domain-specific preprocessing. Beyond such preprocessing, machine learners would hope to deal with such data as with any other time series data. For EEG classification many models have been developed with layer types and architectures we typically do not see in time series classification. Furthermore, typically separate models for each individual subject are learned, not one model for all of them. In this paper, we systematically study the differences between EEG classification models and generic time series classification models. We describe three different model setups to deal with EEG data from different subjects, subject-specific models (most EEG literature), subject-agnostic models and subject-conditional models. In experiments on three datasets, we demonstrate that off-the-shelf time series classification models trained per subject perform close to EEG classification models, but that do not quite reach the performance of domain-specific modeling. Additionally, we combine time-series models with subject embeddings to train one joint subject-conditional classifier on all subjects. The resulting models are competitive with dedicated EEG models in 2 out of 3 datasets, even outperforming all EEG methods on one of them.

The current trend in the literature on Time Series Classification is to develop increasingly accurate algorithms by combining multiple models in ensemble hybrids, representing time series in complex and expressive feature spaces, and extracting features from different representations of the same time series. As a consequence of this focus on predictive performance, the best time series classifiers are black-box models, which are not understandable from a human standpoint. Even the approaches that are regarded as interpretable, such as shapelet-based ones, rely on randomization to maintain computational efficiency. This poses challenges for interpretability, as the explanation can change from run to run. Given these limitations, we propose the Bag-Of-Receptive-Field (BORF), a fast, interpretable, and deterministic time series transform. Building upon the classical Bag-Of-Patterns, we bridge the gap between convolutional operators and discretization, enhancing the Symbolic Aggregate Approximation (SAX) with dilation and stride, which can more effectively capture temporal patterns at multiple scales. We propose an algorithmic speedup that reduces the time complexity associated with SAX-based classifiers, allowing the extension of the Bag-Of-Patterns to the more flexible Bag-Of-Receptive-Fields, represented as a sparse multivariate tensor. The empirical results from testing our proposal on more than 150 univariate and multivariate classification datasets demonstrate good accuracy and great computational efficiency compared to traditional SAX-based methods and state-of-the-art time series classifiers, while providing easy-to-understand explanations.