Time series domain adaptation aims to transfer the complex temporal dependence from the labeled source domain to the unlabeled target domain. Recent advances leverage the stable causal mechanism over observed variables to model the domain-invariant temporal dependence. However, modeling precise causal structures in high-dimensional data, such as videos, remains challenging. Additionally, direct causal edges may not exist among observed variables (e.g., pixels). These limitations hinder the applicability of existing approaches to real-world scenarios. To address these challenges, we find that the high-dimension time series data are generated from the low-dimension latent variables, which motivates us to model the causal mechanisms of the temporal latent process. Based on this intuition, we propose a latent causal mechanism identification framework that guarantees the uniqueness of the reconstructed latent causal structures. Specifically, we first identify latent variables by utilizing sufficient changes in historical information. Moreover, by enforcing the sparsity of the relationships of latent variables, we can achieve identifiable latent causal structures. Built on the theoretical results, we develop the Latent Causality Alignment (LCA) model that leverages variational inference, which incorporates an intra-domain latent sparsity constraint for latent structure reconstruction and an inter-domain latent sparsity constraint for domain-invariant structure reconstruction. Experiment results on eight benchmarks show a general improvement in the domain-adaptive time series classification and forecasting tasks, highlighting the effectiveness of our method in real-world scenarios. Codes are available at https://github.com/DMIRLAB-Group/LCA.
The increasing computational demands of transformer models in time series classification necessitate effective optimization strategies for energy-efficient deployment. Our study presents a systematic investigation of optimization techniques, focusing on structured pruning and quantization methods for transformer architectures. Through extensive experimentation on three distinct datasets (RefrigerationDevices, ElectricDevices, and PLAID), we quantitatively evaluate model performance and energy efficiency across different transformer configurations. Our experimental results demonstrate that static quantization reduces energy consumption by 29.14% while maintaining classification performance, and L1 pruning achieves a 63% improvement in inference speed with minimal accuracy degradation. Our findings provide valuable insights into the effectiveness of optimization strategies for transformer-based time series classification, establishing a foundation for efficient model deployment in resource-constrained environments.
Recent advancements in transformer-based models have greatly improved time series analysis, providing robust solutions for tasks such as forecasting, anomaly detection, and classification. A crucial element of these models is positional encoding, which allows transformers to capture the intrinsic sequential nature of time series data. This survey systematically examines existing techniques for positional encoding in transformer-based time series models. We investigate a variety of methods, including fixed, learnable, relative, and hybrid approaches, and evaluate their effectiveness in different time series classification tasks. Furthermore, we outline key challenges and suggest potential research directions to enhance positional encoding strategies. By delivering a comprehensive overview and quantitative benchmarking, this survey intends to assist researchers and practitioners in selecting and designing effective positional encoding methods for transformer-based time series models.
Recently, there has been a significant advancement in designing Self-Supervised Learning (SSL) frameworks for time series data to reduce the dependency on data labels. Among these works, hierarchical contrastive learning-based SSL frameworks, which learn representations by contrasting data embeddings at multiple resolutions, have gained considerable attention. Due to their ability to gather more information, they exhibit better generalization in various downstream tasks. However, when the time series data length is significant long, the computational cost is often significantly higher than that of other SSL frameworks. In this paper, to address this challenge, we propose an efficient way to train hierarchical contrastive learning models. Inspired by the fact that each resolution's data embedding is highly dependent, we introduce importance-aware resolution selection based training framework to reduce the computational cost. In the experiment, we demonstrate that the proposed method significantly improves training time while preserving the original model's integrity in extensive time series classification performance evaluations. Our code could be found here, https://github.com/KEEBVIN/IARS
We propose a new method to extract discriminant and explainable features from a particular machine learning model, i.e., a combination of the scattering transform and the multiclass logistic regression. Although this model is well-known for its ability to learn various signal classes with high classification rate, it remains elusive to understand why it can generate such successful classification, mainly due to the nonlinearity of the scattering transform. In order to uncover the meaning of the scattering transform coefficients selected by the multiclass logistic regression (with the Lasso penalty), we adopt zeroth-order optimization algorithms to search an input pattern that maximizes the class probability of a class of interest given the learned model. In order to do so, it turns out that imposing sparsity and smoothness of input patterns is important. We demonstrate the effectiveness of our proposed method using a couple of synthetic time-series classification problems.
The effectiveness of neural network models largely relies on learning meaningful latent patterns from data, where self-supervised learning of informative representations can enhance model performance and generalisability. However, self-supervised representation learning for spatially characterised time series, which are ubiquitous in transportation domain, poses unique challenges due to the necessity of maintaining fine-grained spatio-temporal similarities in the latent space. In this study, we introduce two structure-preserving regularisers for the contrastive learning of spatial time series: one regulariser preserves the topology of similarities between instances, and the other preserves the graph geometry of similarities across spatial and temporal dimensions. To balance the contrastive learning objective and the need for structure preservation, we propose a dynamic weighting mechanism that adaptively manages this trade-off and stabilises training. We validate the proposed method through extensive experiments, including multivariate time series classification to demonstrate its general applicability, as well as macroscopic and microscopic traffic prediction to highlight its particular usefulness in encoding traffic interactions. Across all tasks, our method preserves the similarity structures more effectively and improves state-of-the-art task performances. This method can be integrated with an arbitrary neural network model and is particularly beneficial for time series data with spatial or geographical features. Furthermore, our findings suggest that well-preserved similarity structures in the latent space indicate more informative and useful representations. This provides insights to design more effective neural networks for data-driven transportation research. Our code is made openly accessible with all resulting data at https://github.com/yiru-jiao/spclt
The successful application of modern machine learning for time series classification is often hampered by limitations in quality and quantity of available training data. To overcome these limitations, available domain expert knowledge in the form of parametrised mechanistic dynamical models can be used whenever it is available and time series observations may be represented as an element from a given class of parametrised dynamical models. This makes the learning process interpretable and allows the modeller to deal with sparsely and irregularly sampled data in a natural way. However, the internal processes of a dynamical model are often only partially observed. This can lead to ambiguity regarding which particular model realization best explains a given time series observation. This problem is well-known in the literature, and a dynamical model with this issue is referred to as structurally unidentifiable. Training a classifier that incorporates knowledge about a structurally unidentifiable dynamical model can negatively influence classification performance. To address this issue, we employ structural identifiability analysis to explicitly relate parameter configurations that are associated with identical system outputs. Using the derived relations in classifier training, we demonstrate that this method significantly improves the classifier's ability to generalize to unseen data on a number of example models from the biomedical domain. This effect is especially pronounced when the number of training instances is limited. Our results demonstrate the importance of accounting for structural identifiability, a topic that has received relatively little attention from the machine learning community.
Medical time series has been playing a vital role in real-world healthcare systems as valuable information in monitoring health conditions of patients. Accurate classification for medical time series, e.g., Electrocardiography (ECG) signals, can help for early detection and diagnosis. Traditional methods towards medical time series classification rely on handcrafted feature extraction and statistical methods; with the recent advancement of artificial intelligence, the machine learning and deep learning methods have become more popular. However, existing methods often fail to fully model the complex spatial dynamics under different scales, which ignore the dynamic multi-resolution spatial and temporal joint inter-dependencies. Moreover, they are less likely to consider the special baseline wander problem as well as the multi-view characteristics of medical time series, which largely hinders their prediction performance. To address these limitations, we propose a Multi-resolution Spatiotemporal Graph Learning framework, MedGNN, for medical time series classification. Specifically, we first propose to construct multi-resolution adaptive graph structures to learn dynamic multi-scale embeddings. Then, to address the baseline wander problem, we propose Difference Attention Networks to operate self-attention mechanisms on the finite difference for temporal modeling. Moreover, to learn the multi-view characteristics, we utilize the Frequency Convolution Networks to capture complementary information of medical time series from the frequency domain. In addition, we introduce the Multi-resolution Graph Transformer architecture to model the dynamic dependencies and fuse the information from different resolutions. Finally, we have conducted extensive experiments on multiple medical real-world datasets that demonstrate the superior performance of our method. Our Code is available.
Time Series Classification (TSC) is highly vulnerable to backdoor attacks, posing significant security threats. Existing methods primarily focus on data poisoning during the training phase, designing sophisticated triggers to improve stealthiness and attack success rate (ASR). However, in practical scenarios, attackers often face restrictions in accessing training data. Moreover, it is a challenge for the model to maintain generalization ability on clean test data while remaining vulnerable to poisoned inputs when data is inaccessible. To address these challenges, we propose TrojanTime, a novel two-step training algorithm. In the first stage, we generate a pseudo-dataset using an external arbitrary dataset through target adversarial attacks. The clean model is then continually trained on this pseudo-dataset and its poisoned version. To ensure generalization ability, the second stage employs a carefully designed training strategy, combining logits alignment and batch norm freezing. We evaluate TrojanTime using five types of triggers across four TSC architectures in UCR benchmark datasets from diverse domains. The results demonstrate the effectiveness of TrojanTime in executing backdoor attacks while maintaining clean accuracy. Finally, to mitigate this threat, we propose a defensive unlearning strategy that effectively reduces the ASR while preserving clean accuracy.
In this paper, we introduce Neural Mapper for Vector Quantized Time Series Generator (NM-VQTSG), a novel method aimed at addressing fidelity challenges in vector quantized (VQ) time series generation. VQ-based methods, such as TimeVQVAE, have demonstrated success in generating time series but are hindered by two critical bottlenecks: information loss during compression into discrete latent spaces and deviations in the learned prior distribution from the ground truth distribution. These challenges result in synthetic time series with compromised fidelity and distributional accuracy. To overcome these limitations, NM-VQTSG leverages a U-Net-based neural mapping model to bridge the distributional gap between synthetic and ground truth time series. To be more specific, the model refines synthetic data by addressing artifacts introduced during generation, effectively aligning the distributions of synthetic and real data. Importantly, NM-VQTSG can be used for synthetic time series generated by any VQ-based generative method. We evaluate NM-VQTSG across diverse datasets from the UCR Time Series Classification archive, demonstrating its capability to consistently enhance fidelity in both unconditional and conditional generation tasks. The improvements are evidenced by significant improvements in FID, IS, and conditional FID, additionally backed up by visual inspection in a data space and a latent space. Our findings establish NM-VQTSG as a new method to improve the quality of synthetic time series. Our implementation is available on \url{https://github.com/ML4ITS/TimeVQVAE}.
1D-CNNs are used for time series classification in various domains with a high degree of accuracy. Most implementations collect the incoming data samples in a buffer before performing inference on it. On edge devices, which are typically constrained and single-threaded, such an implementation may interfere with time-critical tasks. One such task is that of sample acquisition. In this work, we propose an inference scheme that interleaves the convolution operations between sample intervals, which allows us to reduce the inference latency. Furthermore, our scheme is well-suited for storing data in ring buffers, yielding a small memory footprint. We demonstrate these improvements by comparing our approach to TFLite's inference method, giving a 10% reduction in the inference delay while almost halving the memory usage. Our approach is feasible on common consumer devices, which we show using an AVR-based Arduino board and an ARM-based Arduino board.
Time series classification (TSC) is fundamental in numerous domains, including finance, healthcare, and environmental monitoring. However, traditional TSC methods often struggle with the inherent complexity and variability of time series data. Building on our previous work with the linear law-based transformation (LLT) - which improved classification accuracy by transforming the feature space based on key data patterns - we introduce adaptive law-based transformation (ALT). ALT enhances LLT by incorporating variable-length shifted time windows, enabling it to capture distinguishing patterns of various lengths and thereby handle complex time series more effectively. By mapping features into a linearly separable space, ALT provides a fast, robust, and transparent solution that achieves state-of-the-art performance with only a few hyperparameters.
Multivariate Time Series Classification (MTSC) enables the analysis if complex temporal data, and thus serves as a cornerstone in various real-world applications, ranging from healthcare to finance. Since the relationship among variables in MTS usually contain crucial cues, a large number of graph-based MTSC approaches have been proposed, as the graph topology and edges can explicitly represent relationships among variables (channels), where not only various MTS graph representation learning strategies but also different Graph Neural Networks (GNNs) have been explored. Despite such progresses, there is no comprehensive study that fairly benchmarks and investigates the performances of existing widely-used graph representation learning strategies/GNN classifiers in the application of different MTSC tasks. In this paper, we present the first benchmark which systematically investigates the effectiveness of the widely-used three node feature definition strategies, four edge feature learning strategies and five GNN architecture, resulting in 60 different variants for graph-based MTSC. These variants are developed and evaluated with a standardized data pipeline and training/validation/testing strategy on 26 widely-used suspensor MTSC datasets. Our experiments highlight that node features significantly influence MTSC performance, while the visualization of edge features illustrates why adaptive edge learning outperforms other edge feature learning methods. The code of the proposed benchmark is publicly available at \url{https://github.com/CVI-yangwn/Benchmark-GNN-for-Multivariate-Time-Series-Classification}.
Early Warning Signals (EWSs) are vital for implementing preventive measures before a disease turns into a pandemic. While new diseases exhibit unique behaviors, they often share fundamental characteristics from a dynamical systems perspective. Moreover, measurements during disease outbreaks are often corrupted by different noise sources, posing challenges for Time Series Classification (TSC) tasks. In this study, we address the problem of having a robust EWS for disease outbreak prediction using a best-performing deep learning model in the domain of TSC. We employed two simulated datasets to train the model: one representing generated dynamical systems with randomly selected polynomial terms to model new disease behaviors, and another simulating noise-induced disease dynamics to account for noisy measurements. The model's performance was analyzed using both simulated data from different disease models and real-world data, including influenza and COVID-19. Results demonstrate that the proposed model outperforms previous models, effectively providing EWSs of impending outbreaks across various scenarios. This study bridges advancements in deep learning with the ability to provide robust early warning signals in noisy environments, making it highly applicable to real-world crises involving emerging disease outbreaks.
Deep Learning systems excel in complex tasks but often lack transparency, limiting their use in critical applications. Counterfactual explanations, a core tool within eXplainable Artificial Intelligence (XAI), offer insights into model decisions by identifying minimal changes to an input to alter its predicted outcome. However, existing methods for time series data are limited by univariate assumptions, rigid constraints on modifications, or lack of validity guarantees. This paper introduces Multi-SpaCE, a multi-objective counterfactual explanation method for multivariate time series. Using non-dominated ranking genetic algorithm II (NSGA-II), Multi-SpaCE balances proximity, sparsity, plausibility, and contiguity. Unlike most methods, it ensures perfect validity, supports multivariate data and provides a Pareto front of solutions, enabling flexibility to different end-user needs. Comprehensive experiments in diverse datasets demonstrate the ability of Multi-SpaCE to consistently achieve perfect validity and deliver superior performance compared to existing methods.
We present ORACLE, the first hierarchical deep-learning model for real-time, context-aware classification of transient and variable astrophysical phenomena. ORACLE is a recurrent neural network with Gated Recurrent Units (GRUs), and has been trained using a custom hierarchical cross-entropy loss function to provide high-confidence classifications along an observationally-driven taxonomy with as little as a single photometric observation. Contextual information for each object, including host galaxy photometric redshift, offset, ellipticity and brightness, is concatenated to the light curve embedding and used to make a final prediction. Training on $\sim$0.5M events from the Extended LSST Astronomical Time-Series Classification Challenge, we achieve a top-level (Transient vs Variable) macro-averaged precision of 0.96 using only 1 day of photometric observations after the first detection in addition to contextual information, for each event; this increases to $>$0.99 once 64 days of the light curve has been obtained, and 0.83 at 1024 days after first detection for 19-way classification (including supernova sub-types, active galactic nuclei, variable stars, microlensing events, and kilonovae). We also compare ORACLE with other state-of-the-art classifiers and report comparable performance for the 19-way classification task, in addition to delivering accurate top-level classifications much earlier. The code and model weights used in this work are publicly available at our associated GitHub repository (https://github.com/uiucsn/ELAsTiCC-Classification).
Multivariate time series classification is a crucial task in data mining, attracting growing research interest due to its broad applications. While many existing methods focus on discovering discriminative patterns in time series, real-world data does not always present such patterns, and sometimes raw numerical values can also serve as discriminative features. Additionally, the recent success of Transformer models has inspired many studies. However, when applying to time series classification, the self-attention mechanisms in Transformer models could introduce classification-irrelevant features, thereby compromising accuracy. To address these challenges, we propose a novel method, VSFormer, that incorporates both discriminative patterns (shape) and numerical information (value). In addition, we extract class-specific prior information derived from supervised information to enrich the positional encoding and provide classification-oriented self-attention learning, thereby enhancing its effectiveness. Extensive experiments on all 30 UEA archived datasets demonstrate the superior performance of our method compared to SOTA models. Through ablation studies, we demonstrate the effectiveness of the improved encoding layer and the proposed self-attention mechanism. Finally, We provide a case study on a real-world time series dataset without discriminative patterns to interpret our model.
We build upon time-series classification by leveraging the capabilities of Vision Language Models (VLMs). We find that VLMs produce competitive results after two or less epochs of fine-tuning. We develop a novel approach that incorporates graphical data representations as images in conjunction with numerical data. This approach is rooted in the hypothesis that graphical representations can provide additional contextual information that numerical data alone may not capture. Additionally, providing a graphical representation can circumvent issues such as limited context length faced by LLMs. To further advance this work, we implemented a scalable end-to-end pipeline for training on different scenarios, allowing us to isolate the most effective strategies for transferring learning capabilities from LLMs to Time Series Classification (TSC) tasks. Our approach works with univariate and multivariate time-series data. In addition, we conduct extensive and practical experiments to show how this approach works for time-series classification and generative labels.
Matrix-product states (MPS) have proven to be a versatile ansatz for modeling quantum many-body physics. For many applications, and particularly in one-dimension, they capture relevant quantum correlations in many-body wavefunctions while remaining tractable to store and manipulate on a classical computer. This has motivated researchers to also apply the MPS ansatz to machine learning (ML) problems where capturing complex correlations in datasets is also a key requirement. Here, we develop and apply an MPS-based algorithm, MPSTime, for learning a joint probability distribution underlying an observed time-series dataset, and show how it can be used to tackle important time-series ML problems, including classification and imputation. MPSTime can efficiently learn complicated time-series probability distributions directly from data, requires only moderate maximum MPS bond dimension $\chi_{\rm max}$, with values for our applications ranging between $\chi_{\rm max} = 20-160$, and can be trained for both classification and imputation tasks under a single logarithmic loss function. Using synthetic and publicly available real-world datasets, spanning applications in medicine, energy, and astronomy, we demonstrate performance competitive with state-of-the-art ML approaches, but with the key advantage of encoding the full joint probability distribution learned from the data, which is useful for analyzing and interpreting its underlying structure. This manuscript is supplemented with the release of a publicly available code package MPSTime that implements our approach. The effectiveness of the MPS-based ansatz for capturing complex correlation structures in time-series data makes it a powerful foundation for tackling challenging time-series analysis problems across science, industry, and medicine.
Due to the superior ability of global dependency, transformer and its variants have become the primary choice in Masked Time-series Modeling (MTM) towards time-series classification task. In this paper, we experimentally analyze that existing transformer-based MTM methods encounter with two under-explored issues when dealing with time series data: (1) they encode features by performing long-dependency ensemble averaging, which easily results in rank collapse and feature homogenization as the layer goes deeper; (2) they exhibit distinct priorities in fitting different frequency components contained in the time-series, inevitably leading to spectrum energy imbalance of encoded feature. To tackle these issues, we propose an auxiliary content-aware balanced decoder (CBD) to optimize the encoding quality in the spectrum space within masked modeling scheme. Specifically, the CBD iterates on a series of fundamental blocks, and thanks to two tailored units, each block could progressively refine the masked representation via adjusting the interaction pattern based on local content variations of time-series and learning to recalibrate the energy distribution across different frequency components. Moreover, a dual-constraint loss is devised to enhance the mutual optimization of vanilla decoder and our CBD. Extensive experimental results on ten time-series classification datasets show that our method nearly surpasses a bunch of baselines. Meanwhile, a series of explanatory results are showcased to sufficiently demystify the behaviors of our method.