This article investigates the use of Machine Learning and Deep Learning models in multivariate time series analysis within financial markets. It compares small and big data approaches, focusing on their distinct challenges and the benefits of scaling. Traditional methods such as SVMs are contrasted with modern architectures like ConvTimeNet. The results show the importance of using and understanding Big Data in depth in the analysis and prediction of financial time series.
Domain adaptation is challenging for time series classification due to the highly dynamic nature. This study tackles the most difficult subtask when both target labels and source data are inaccessible, namely, source-free domain adaptation. To reuse the classification backbone pre-trained on source data, time series reconstruction is a sound solution that aligns target and source time series by minimizing the reconstruction errors of both. However, simply fine-tuning the source pre-trained reconstruction model on target data may lose the learnt priori, and it struggles to accommodate domain varying temporal patterns in a single encoder-decoder. Therefore, this paper tries to disentangle the composition of domain transferability by using a compositional architecture for time series reconstruction. Here, the preceding component is a U-net frozen since pre-trained, the output of which during adaptation is the initial reconstruction of a given target time series, acting as a coarse step to prompt the subsequent finer adaptation. The following pipeline for finer adaptation includes two parallel branches: The source replay branch using a residual link to preserve the output of U-net, and the offset compensation branch that applies an additional autoencoder (AE) to further warp U-net's output. By deploying a learnable factor on either branch to scale their composition in the final output of reconstruction, the data transferability is disentangled and the learnt reconstructive capability from source data is retained. During inference, aside from the batch-level optimization in the training, we search at test time stability-aware rescaling of source replay branch to tolerate instance-wise variation. The experimental results show that such compositional architecture of time series reconstruction leads to SOTA performance on 3 widely used benchmarks.
In recent years, modeling and analysis of interval-valued time series have garnered increasing attention in econometrics, finance, and statistics. However, these studies have predominantly focused on statistical inference in the forecasting of univariate and multivariate interval-valued time series, overlooking another important aspect: classification. In this paper, we introduce a classification approach that treats intervals as unified entities, applicable to both univariate and multivariate interval-valued time series. Specifically, we first extend the point-valued time series imaging methods to interval-valued scenarios using the $D_K$-distance, enabling the imaging of interval-valued time series. Then, we employ suitable deep learning model for classification on the obtained imaging dataset, aiming to achieve classification for interval-valued time series. In theory, we derived a sharper excess risk bound for deep multiclassifiers based on offset Rademacher complexity. Finally, we validate the superiority of the proposed method through comparisons with various existing point-valued time series classification methods in both simulation studies and real data applications.
Unsupervised Domain Adaptation (UDA) leverages labeled source data to train models for unlabeled target data. Given the prevalence of multivariate time series (MTS) data across various domains, the UDA task for MTS classification has emerged as a critical challenge. However, for MTS data, correlations between variables often vary across domains, whereas most existing UDA works for MTS classification have overlooked this essential characteristic. To bridge this gap, we introduce a novel domain shift, {\em correlation shift}, measuring domain differences in multivariate correlation. To mitigate correlation shift, we propose a scalable and parameter-efficient \underline{C}orrelation \underline{A}dapter for M\underline{TS} (CATS). Designed as a plug-and-play technique compatible with various Transformer variants, CATS employs temporal convolution to capture local temporal patterns and a graph attention module to model the changing multivariate correlation. The adapter reweights the target correlations to align the source correlations with a theoretically guaranteed precision. A correlation alignment loss is further proposed to mitigate correlation shift, bypassing the alignment challenge from the non-i.i.d. nature of MTS data. Extensive experiments on four real-world datasets demonstrate that (1) compared with vanilla Transformer-based models, CATS increases over $10\%$ average accuracy while only adding around $1\%$ parameters, and (2) all Transformer variants equipped with CATS either reach or surpass state-of-the-art baselines.
This study explores the potential of using wrist-worn inertial sensors to automate the labeling of ARAT (Action Research Arm Test) items. While the ARAT is commonly used to assess upper limb motor function, its limitations include subjectivity and time consumption of clinical staff. By using IMU (Inertial Measurement Unit) sensors and MiniROCKET as a time series classification technique, this investigation aims to classify ARAT items based on sensor recordings. We test common preprocessing strategies to efficiently leverage included information in the data. Afterward, we use the best preprocessing to improve the classification. The dataset includes recordings of 45 participants performing various ARAT items. Results show that MiniROCKET offers a fast and reliable approach for classifying ARAT domains, although challenges remain in distinguishing between individual resembling items. Future work may involve improving classification through more advanced machine-learning models and data enhancements.
We introduce ALT, an open-source Python package created for efficient and accurate time series classification (TSC). The package implements the adaptive law-based transformation (ALT) algorithm, which transforms raw time series data into a linearly separable feature space using variable-length shifted time windows. This adaptive approach enhances its predecessor, the linear law-based transformation (LLT), by effectively capturing patterns of varying temporal scales. The software is implemented for scalability, interpretability, and ease of use, achieving state-of-the-art performance with minimal computational overhead. Extensive benchmarking on real-world datasets demonstrates the utility of ALT for diverse TSC tasks in physics and related domains.
Reservoir computing (RC) is attracting attention as a machine-learning technique for edge computing. In time-series classification tasks, the number of features obtained using a reservoir depends on the length of the input series. Therefore, the features must be converted to a constant-length intermediate representation (IR), such that they can be processed by an output layer. Existing conversion methods involve computationally expensive matrix inversion that significantly increases the circuit size and requires processing power when implemented in hardware. In this article, we propose a simple but effective IR, namely, dot-product-based reservoir representation (DPRR), for RC based on the dot product of data features. Additionally, we propose a hardware-friendly delayed-feedback reservoir (DFR) consisting of a nonlinear element and delayed feedback loop with DPRR. The proposed DFR successfully classified multivariate time series data that has been considered particularly difficult to implement efficiently in hardware. In contrast to conventional DFR models that require analog circuits, the proposed model can be implemented in a fully digital manner suitable for high-level syntheses. A comparison with existing machine-learning methods via field-programmable gate array implementation using 12 multivariate time-series classification tasks confirmed the superior accuracy and small circuit size of the proposed method.
Time series classification (TSC) is an important task in time series analysis. Existing TSC methods mainly train on each single domain separately, suffering from a degradation in accuracy when the samples for training are insufficient in certain domains. The pre-training and fine-tuning paradigm provides a promising direction for solving this problem. However, time series from different domains are substantially divergent, which challenges the effective pre-training on multi-source data and the generalization ability of pre-trained models. To handle this issue, we introduce Augmented Series and Image Contrastive Learning for Time Series Classification (AimTS), a pre-training framework that learns generalizable representations from multi-source time series data. We propose a two-level prototype-based contrastive learning method to effectively utilize various augmentations in multi-source pre-training, which learns representations for TSC that can be generalized to different domains. In addition, considering augmentations within the single time series modality are insufficient to fully address classification problems with distribution shift, we introduce the image modality to supplement structural information and establish a series-image contrastive learning to improve the generalization of the learned representations for TSC tasks. Extensive experiments show that after multi-source pre-training, AimTS achieves good generalization performance, enabling efficient learning and even few-shot learning on various downstream TSC datasets.
Deep learning-based electrocardiogram (ECG) classification has shown impressive performance but clinical adoption has been slowed by the lack of transparent and faithful explanations. Post hoc methods such as saliency maps may fail to reflect a model's true decision process. Prototype-based reasoning offers a more transparent alternative by grounding decisions in similarity to learned representations of real ECG segments, enabling faithful, case-based explanations. We introduce ProtoECGNet, a prototype-based deep learning model for interpretable, multi-label ECG classification. ProtoECGNet employs a structured, multi-branch architecture that reflects clinical interpretation workflows: it integrates a 1D CNN with global prototypes for rhythm classification, a 2D CNN with time-localized prototypes for morphology-based reasoning, and a 2D CNN with global prototypes for diffuse abnormalities. Each branch is trained with a prototype loss designed for multi-label learning, combining clustering, separation, diversity, and a novel contrastive loss that encourages appropriate separation between prototypes of unrelated classes while allowing clustering for frequently co-occurring diagnoses. We evaluate ProtoECGNet on all 71 diagnostic labels from the PTB-XL dataset, demonstrating competitive performance relative to state-of-the-art black-box models while providing structured, case-based explanations. To assess prototype quality, we conduct a structured clinician review of the final model's projected prototypes, finding that they are rated as representative and clear. ProtoECGNet shows that prototype learning can be effectively scaled to complex, multi-label time-series classification, offering a practical path toward transparent and trustworthy deep learning models for clinical decision support.
In recent years, the modeling and analysis of interval-valued time series have garnered significant attention in the fields of econometrics and statistics. However, the existing literature primarily focuses on regression tasks while neglecting classification aspects. In this paper, we propose an adaptive approach for interval-valued time series classification. Specifically, we represent interval-valued time series using convex combinations of upper and lower bounds of intervals and transform these representations into images based on point-valued time series imaging methods. We utilize a fine-grained image classification neural network to classify these images, to achieve the goal of classifying the original interval-valued time series. This proposed method is applicable to both univariate and multivariate interval-valued time series. On the optimization front, we treat the convex combination coefficients as learnable parameters similar to the parameters of the neural network and provide an efficient estimation method based on the alternating direction method of multipliers (ADMM). On the theoretical front, under specific conditions, we establish a margin-based multiclass generalization bound for generic CNNs composed of basic blocks involving convolution, pooling, and fully connected layers. Through simulation studies and real data applications, we validate the effectiveness of the proposed method and compare its performance against a wide range of point-valued time series classification methods.
The ever-growing amount of sensor data from machines, smart devices, and the environment leads to an abundance of high-resolution, unannotated time series (TS). These recordings encode the recognizable properties of latent states and transitions from physical phenomena that can be modelled as abstract processes. The unsupervised localization and identification of these states and their transitions is the task of time series state detection (TSSD). We introduce CLaP, a new, highly accurate and efficient algorithm for TSSD. It leverages the predictive power of time series classification for TSSD in an unsupervised setting by applying novel self-supervision techniques to detect whether data segments emerge from the same state or not. To this end, CLaP cross-validates a classifier with segment-labelled subsequences to quantify confusion between segments. It merges labels from segments with high confusion, representing the same latent state, if this leads to an increase in overall classification quality. We conducted an experimental evaluation using 391 TS from four benchmarks and found CLaP to be significantly more precise in detecting states than five state-of-the-art competitors. It achieves the best accuracy-runtime tradeoff and is scalable to large TS. We provide a Python implementation of CLaP, which can be deployed in TS analysis workflows.
Time series classification is usually regarded as a distinct task from tabular data classification due to the importance of temporal information. However, in this paper, by performing permutation tests that disrupt temporal information on the UCR time series classification archive, the most widely used benchmark for time series classification, we identify a significant proportion of datasets where temporal information has little to no impact on classification. Many of these datasets are tabular in nature or rely mainly on tabular features, leading to potentially biased evaluations of time series classifiers focused on temporal information. To address this, we propose UCR Augmented, a benchmark based on the UCR time series classification archive designed to evaluate classifiers' ability to extract and utilize temporal information. Testing classifiers from seven categories on this benchmark revealed notable shifts in performance rankings. Some previously overlooked approaches perform well, while others see their performance decline significantly when temporal information is crucial. UCR Augmented provides a more robust framework for assessing time series classifiers, ensuring fairer evaluations. Our code is available at https://github.com/YunruiZhang/Revisit-Time-Series-Classification-Benchmark.
Medical time series (MedTS) classification is crucial for improved diagnosis in healthcare, and yet it is challenging due to the varying granularity of patterns, intricate inter-channel correlation, information redundancy, and label scarcity. While existing transformer-based models have shown promise in time series analysis, they mainly focus on forecasting and fail to fully exploit the distinctive characteristics of MedTS data. In this paper, we introduce Sparseformer, a transformer specifically designed for MedTS classification. We propose a sparse token-based dual-attention mechanism that enables global modeling and token compression, allowing dynamic focus on the most informative tokens while distilling redundant features. This mechanism is then applied to the multi-granularity, cross-channel encoding of medical signals, capturing intra- and inter-granularity correlations and inter-channel connections. The sparsification design allows our model to handle heterogeneous inputs of varying lengths and channels directly. Further, we introduce an adaptive label encoder to address label space misalignment across datasets, equipping our model with cross-dataset transferability to alleviate the medical label scarcity issue. Our model outperforms 12 baselines across seven medical datasets under supervised learning. In the few-shot learning experiments, our model also achieves superior average results. In addition, the in-domain and cross-domain experiments among three diagnostic scenarios demonstrate our model's zero-shot learning capability. Collectively, these findings underscore the robustness and transferability of our model in various medical applications.
Time series classification (TSC) is a cornerstone of modern web applications, powering tasks such as financial data analysis, network traffic monitoring, and user behavior analysis. In recent years, deep neural networks (DNNs) have greatly enhanced the performance of TSC models in these critical domains. However, DNNs are vulnerable to backdoor attacks, where attackers can covertly implant triggers into models to induce malicious outcomes. Existing backdoor attacks targeting DNN-based TSC models remain elementary. In particular, early methods borrow trigger designs from computer vision, which are ineffective for time series data. More recent approaches utilize generative models for trigger generation, but at the cost of significant computational complexity. In this work, we analyze the limitations of existing attacks and introduce an enhanced method, FreqBack. Drawing inspiration from the fact that DNN models inherently capture frequency domain features in time series data, we identify that improper perturbations in the frequency domain are the root cause of ineffective attacks. To address this, we propose to generate triggers both effectively and efficiently, guided by frequency analysis. FreqBack exhibits substantial performance across five models and eight datasets, achieving an impressive attack success rate of over 90%, while maintaining less than a 3% drop in model accuracy on clean data.
Minimizing computational overhead in time-series classification, particularly in deep learning models, presents a significant challenge. This challenge is further compounded by adversarial attacks, emphasizing the need for resilient methods that ensure robust performance and efficient model selection. We introduce ReLATE, a framework that identifies robust learners based on dataset similarity, reduces computational overhead, and enhances resilience. ReLATE maintains multiple deep learning models in well-known adversarial attack scenarios, capturing model performance. ReLATE identifies the most analogous dataset to a given target using a similarity metric, then applies the optimal model from the most similar dataset. ReLATE reduces computational overhead by an average of 81.2%, enhancing adversarial resilience and streamlining robust model selection, all without sacrificing performance, within 4.2% of Oracle.
Multivariate Time Series Classification (MTSC) is crucial in extensive practical applications, such as environmental monitoring, medical EEG analysis, and action recognition. Real-world time series datasets typically exhibit complex dynamics. To capture this complexity, RNN-based, CNN-based, Transformer-based, and hybrid models have been proposed. Unfortunately, current deep learning-based methods often neglect the simultaneous construction of local features and global dependencies at different time scales, lacking sufficient feature extraction capabilities to achieve satisfactory classification accuracy. To address these challenges, we propose a novel Multiscale Periodic Time Series Network (MPTSNet), which integrates multiscale local patterns and global correlations to fully exploit the inherent information in time series. Recognizing the multi-periodicity and complex variable correlations in time series, we use the Fourier transform to extract primary periods, enabling us to decompose data into multiscale periodic segments. Leveraging the inherent strengths of CNN and attention mechanism, we introduce the PeriodicBlock, which adaptively captures local patterns and global dependencies while offering enhanced interpretability through attention integration across different periodic scales. The experiments on UEA benchmark datasets demonstrate that the proposed MPTSNet outperforms 21 existing advanced baselines in the MTSC tasks.
As the quantities of data recorded by embedded edge sensors grow, so too does the need for intelligent local processing. Such data often comes in the form of time-series signals, based on which real-time predictions can be made locally using an AI model. However, a hardware-software approach capable of making low-latency predictions with low power consumption is required. In this paper, we present a hardware implementation of an event-graph neural network for time-series classification. We leverage an artificial cochlea model to convert the input time-series signals into a sparse event-data format that allows the event-graph to drastically reduce the number of calculations relative to other AI methods. We implemented the design on a SoC FPGA and applied it to the real-time processing of the Spiking Heidelberg Digits (SHD) dataset to benchmark our approach against competitive solutions. Our method achieves a floating-point accuracy of 92.7% on the SHD dataset for the base model, which is only 2.4% and 2% less than the state-of-the-art models with over 10% and 67% fewer model parameters, respectively. It also outperforms FPGA-based spiking neural network implementations by 19.3% and 4.5%, achieving 92.3% accuracy for the quantised model while using fewer computational resources and reducing latency.
In recent years, there has been increasing interest in developing foundation models for time series data that can generalize across diverse downstream tasks. While numerous forecasting-oriented foundation models have been introduced, there is a notable scarcity of models tailored for time series classification. To address this gap, we present Mantis, a new open-source foundation model for time series classification based on the Vision Transformer (ViT) architecture that has been pre-trained using a contrastive learning approach. Our experimental results show that Mantis outperforms existing foundation models both when the backbone is frozen and when fine-tuned, while achieving the lowest calibration error. In addition, we propose several adapters to handle the multivariate setting, reducing memory requirements and modeling channel interdependence.
Time-series classification is essential across diverse domains, including medical diagnosis, industrial monitoring, financial forecasting, and human activity recognition. The Rocket algorithm has emerged as a simple yet powerful method, achieving state-of-the-art performance through random convolutional kernels applied to time-series data, followed by non-linear transformation. Its architecture approximates a one-hidden-layer convolutional neural network while eliminating parameter training, ensuring computational efficiency. Despite its empirical success, fundamental questions about its theoretical foundations remain unexplored. We bridge theory and practice by formalizing Rocket's random convolutional filters within the compressed sensing framework, proving that random projections preserve discriminative patterns in time-series data. This analysis reveals relationships between kernel parameters and input signal characteristics, enabling more principled approaches to algorithm configuration. Moreover, we demonstrate that its non-linearity, based on the proportion of positive values after convolutions, expresses the inherent sparsity of time-series data. Our theoretical investigation also proves that Rocket satisfies two critical conditions: translation invariance and noise robustness. These findings enhance interpretability and provide guidance for parameter optimization in extreme cases, advancing both theoretical understanding and practical application of time-series classification.
As machine learning models become increasingly prevalent in time series applications, Explainable Artificial Intelligence (XAI) methods are essential for understanding their predictions. Within XAI, feature attribution methods aim to identify which input features contribute the most to a model's prediction, with their evaluation typically relying on perturbation-based metrics. Through systematic empirical analysis across multiple datasets, model architectures, and perturbation strategies, we reveal previously overlooked class-dependent effects in these metrics: they show varying effectiveness across classes, achieving strong results for some while remaining less sensitive to others. In particular, we find that the most effective perturbation strategies often demonstrate the most pronounced class differences. Our analysis suggests that these effects arise from the learned biases of classifiers, indicating that perturbation-based evaluation may reflect specific model behaviors rather than intrinsic attribution quality. We propose an evaluation framework with a class-aware penalty term to help assess and account for these effects in evaluating feature attributions, offering particular value for class-imbalanced datasets. Although our analysis focuses on time series classification, these class-dependent effects likely extend to other structured data domains where perturbation-based evaluation is common.