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}.
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}.
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).
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.
This paper investigates the lack of research on activation functions for neural network models in time series tasks. It highlights the need to identify essential properties of these activations to improve their effectiveness in specific domains. To this end, the study comprehensively analyzes properties, such as bounded, monotonic, nonlinearity, and periodicity, for activation in time series neural networks. We propose a new activation that maximizes the coverage of these properties, called LeakySineLU. We empirically evaluate the LeakySineLU against commonly used activations in the literature using 112 benchmark datasets for time series classification, obtaining the best average ranking in all comparative scenarios.
Interpreting complex time series forecasting models is challenging due to the temporal dependencies between time steps and the dynamic relevance of input features over time. Existing interpretation methods are limited by focusing mostly on classification tasks, evaluating using custom baseline models instead of the latest time series models, using simple synthetic datasets, and requiring training another model. We introduce a novel interpretation method called Windowed Temporal Saliency Rescaling (WinTSR) addressing these limitations. WinTSR explicitly captures temporal dependencies among the past time steps and efficiently scales the feature importance with this time importance. We benchmark WinTSR against 10 recent interpretation techniques with 5 state-of-the-art deep-learning models of different architectures, including a time series foundation model. We use 3 real-world datasets for both time-series classification and regression. Our comprehensive analysis shows that WinTSR significantly outranks the other local interpretation methods in overall performance. Finally, we provide a novel and open-source framework to interpret the latest time series transformers and foundation models.
Recently, time series classification has attracted the attention of a large number of researchers, and hundreds of methods have been proposed. However, these methods often ignore the spatial correlations among dimensions and the local correlations among features. To address this issue, the causal and local correlations based network (CaLoNet) is proposed in this study for multivariate time series classification. First, pairwise spatial correlations between dimensions are modeled using causality modeling to obtain the graph structure. Then, a relationship extraction network is used to fuse local correlations to obtain long-term dependency features. Finally, the graph structure and long-term dependency features are integrated into the graph neural network. Experiments on the UEA datasets show that CaLoNet can obtain competitive performance compared with state-of-the-art methods.
Large language models (LLMs) have demonstrated their effectiveness in multivariate time series classification (MTSC). Effective adaptation of LLMs for MTSC necessitates informative data representations. Existing LLM-based methods directly encode embeddings for time series within the latent space of LLMs from scratch to align with semantic space of LLMs. Despite their effectiveness, we reveal that these methods conceal three inherent bottlenecks: (1) they struggle to encode temporal and channel-specific information in a lossless manner, both of which are critical components of multivariate time series; (2) it is much difficult to align the learned representation space with the semantic space of the LLMs; (3) they require task-specific retraining, which is both computationally expensive and labor-intensive. To bridge these gaps, we propose TableTime, which reformulates MTSC as a table understanding task. Specifically, TableTime introduces the following strategies: (1) convert multivariate time series into a tabular form, thus minimizing information loss to the greatest extent; (2) represent tabular time series in text format to achieve natural alignment with the semantic space of LLMs; (3) design a reasoning framework that integrates contextual text information, neighborhood assistance, multi-path inference and problem decomposition to enhance the reasoning ability of LLMs and realize zero-shot classification. Extensive experiments performed on 10 publicly representative datasets from UEA archive verify the superiorities of the TableTime.
Time series classification is a relevant step supporting decision-making processes in various domains, and deep neural models have shown promising performance. Despite significant advancements in deep learning, the theoretical understanding of how and why complex architectures function remains limited, prompting the need for more interpretable models. Recently, the Kolmogorov-Arnold Networks (KANs) have been proposed as a more interpretable alternative. While KAN-related research is significantly rising, to date, the study of KAN architectures for time series classification has been limited. In this paper, we aim to conduct a comprehensive and robust exploration of the KAN architecture for time series classification on the UCR benchmark. More specifically, we look at a) how reference architectures for forecasting transfer to classification, at the b) hyperparameter and implementation influence on the classification performance in view of finding the one that performs best on the selected benchmark, the c) complexity trade-offs and d) interpretability advantages. Our results show that (1) Efficient KAN outperforms MLP in performance and computational efficiency, showcasing its suitability for tasks classification tasks. (2) Efficient KAN is more stable than KAN across grid sizes, depths, and layer configurations, particularly with lower learning rates. (3) KAN maintains competitive accuracy compared to state-of-the-art models like HIVE-COTE2, with smaller architectures and faster training times, supporting its balance of performance and transparency. (4) The interpretability of the KAN model aligns with findings from SHAP analysis, reinforcing its capacity for transparent decision-making.
Quantifying similarities between time series in a meaningful way remains a challenge in time series analysis, despite many advances in the field. Most real-world solutions still rely on a few popular measures, such as Euclidean Distance (EuD), Longest Common Subsequence (LCSS), and Dynamic Time Warping (DTW). The strengths and weaknesses of these measures have been studied extensively, and incremental improvements have been proposed. In this study, however, we present a different similarity measure that fuses the notion of Dubuc's variation from fractal analysis with the Intersection-over-Union (IoU) measure which is widely used in object recognition (also known as the Jaccard Index). In this proof-of-concept paper, we introduce the Multiscale Dubuc Distance (MDD) measure and prove that it is a metric, possessing desirable properties such as the triangle inequality. We use 95 datasets from the UCR Time Series Classification Archive to compare MDD's performance with EuD, LCSS, and DTW. Our experiments show that MDD's overall success, without any case-specific customization, is comparable to DTW with optimized window sizes per dataset. We also highlight several datasets where MDD's performance improves significantly when its single parameter is customized. This customization serves as a powerful tool for gauging MDD's sensitivity to noise. Lastly, we show that MDD's running time is linear in the length of the time series, which is crucial for real-world applications involving very large datasets.
Over the past decade, multivariate time series classification has received great attention. Machine learning (ML) models for multivariate time series classification have made significant strides and achieved impressive success in a wide range of applications and tasks. The challenge of many state-of-the-art ML models is a lack of transparency and interpretability. In this work, we introduce M-CELS, a counterfactual explanation model designed to enhance interpretability in multidimensional time series classification tasks. Our experimental validation involves comparing M-CELS with leading state-of-the-art baselines, utilizing seven real-world time-series datasets from the UEA repository. The results demonstrate the superior performance of M-CELS in terms of validity, proximity, and sparsity, reinforcing its effectiveness in providing transparent insights into the decisions of machine learning models applied to multivariate time series data.
In time-series analysis, many recent works seek to provide a unified view and representation for time-series across multiple domains, leading to the development of foundation models for time-series data. Despite diverse modeling techniques, existing models are black boxes and fail to provide insights and explanations about their representations. In this paper, we present VQShape, a pre-trained, generalizable, and interpretable model for time-series representation learning and classification. By introducing a novel representation for time-series data, we forge a connection between the latent space of VQShape and shape-level features. Using vector quantization, we show that time-series from different domains can be described using a unified set of low-dimensional codes, where each code can be represented as an abstracted shape in the time domain. On classification tasks, we show that the representations of VQShape can be utilized to build interpretable classifiers, achieving comparable performance to specialist models. Additionally, in zero-shot learning, VQShape and its codebook can generalize to previously unseen datasets and domains that are not included in the pre-training process. The code and pre-trained weights are available at https://github.com/YunshiWen/VQShape.
Motion time series collected from mobile and wearable devices such as smartphones and smartwatches offer significant insights into human behavioral patterns, with wide applications in healthcare, automation, IoT, and AR/XR due to their low-power, always-on nature. However, given security and privacy concerns, building large-scale motion time series datasets remains difficult, preventing the development of pre-trained models for human activity analysis. Typically, existing models are trained and tested on the same dataset, leading to poor generalizability across variations in device location, device mounting orientation and human activity type. In this paper, we introduce UniMTS, the first unified pre-training procedure for motion time series that generalizes across diverse device latent factors and activities. Specifically, we employ a contrastive learning framework that aligns motion time series with text descriptions enriched by large language models. This helps the model learn the semantics of time series to generalize across activities. Given the absence of large-scale motion time series data, we derive and synthesize time series from existing motion skeleton data with all-joint coverage. Spatio-temporal graph networks are utilized to capture the relationships across joints for generalization across different device locations. We further design rotation-invariant augmentation to make the model agnostic to changes in device mounting orientations. Our model shows exceptional generalizability across 18 motion time series classification benchmark datasets, outperforming the best baselines by 340% in the zero-shot setting, 16.3% in the few-shot setting, and 9.2% in the full-shot setting.
Interacting systems are prevalent in nature. It is challenging to accurately predict the dynamics of the system if its constituent components are analyzed independently. We develop a graph-based model that unveils the systemic interactions of time series observed at irregular time points, by using a directed acyclic graph to model the conditional dependencies (a form of causal notation) of the system components and learning this graph in tandem with a continuous-time model that parameterizes the solution curves of ordinary differential equations (ODEs). Our technique, a graph neural flow, leads to substantial enhancements over non-graph-based methods, as well as graph-based methods without the modeling of conditional dependencies. We validate our approach on several tasks, including time series classification and forecasting, to demonstrate its efficacy.
Contrastive learning (CL) has emerged as a promising approach for representation learning in time series data by embedding similar pairs closely while distancing dissimilar ones. However, existing CL methods often introduce false negative pairs (FNPs) by neglecting inherent characteristics and then randomly selecting distinct segments as dissimilar pairs, leading to erroneous representation learning, reduced model performance, and overall inefficiency. To address these issues, we systematically define and categorize FNPs in time series into semantic false negative pairs and temporal false negative pairs for the first time: the former arising from overlooking similarities in label categories, which correlates with similarities in non-stationarity and the latter from neglecting temporal proximity. Moreover, we introduce StatioCL, a novel CL framework that captures non-stationarity and temporal dependency to mitigate both FNPs and rectify the inaccuracies in learned representations. By interpreting and differentiating non-stationary states, which reflect the correlation between trends or temporal dynamics with underlying data patterns, StatioCL effectively captures the semantic characteristics and eliminates semantic FNPs. Simultaneously, StatioCL establishes fine-grained similarity levels based on temporal dependencies to capture varying temporal proximity between segments and to mitigate temporal FNPs. Evaluated on real-world benchmark time series classification datasets, StatioCL demonstrates a substantial improvement over state-of-the-art CL methods, achieving a 2.9% increase in Recall and a 19.2% reduction in FNPs. Most importantly, StatioCL also shows enhanced data efficiency and robustness against label scarcity.
Large language models (LLMs) have shown remarkable in-context learning (ICL) capabilities on textual data. We explore whether these capabilities can be extended to continuous vectors from diverse domains, obtained from black-box pretrained encoders. By aligning input data with an LLM's embedding space through lightweight projectors, we observe that LLMs can effectively process and learn from these projected vectors, which we term Vector-ICL. In particular, we find that pretraining projectors with general language modeling objectives enables Vector-ICL, while task-specific finetuning further enhances performance. In our experiments across various tasks and modalities, including text reconstruction, numerical function regression, text classification, summarization, molecule captioning, time-series classification, graph classification, and fMRI decoding, Vector-ICL often surpasses both few-shot ICL and domain-specific model or tuning. We further conduct analyses and case studies, indicating the potential of LLMs to process vector representations beyond traditional token-based paradigms.
Transfer learning is a common practice that alleviates the need for extensive data to train neural networks. It is performed by pre-training a model using a source dataset and fine-tuning it for a target task. However, not every source dataset is appropriate for each target dataset, especially for time series. In this paper, we propose a novel method of selecting and using multiple datasets for transfer learning for time series classification. Specifically, our method combines multiple datasets as one source dataset for pre-training neural networks. Furthermore, for selecting multiple sources, our method measures the transferability of datasets based on shapelet discovery for effective source selection. While traditional transferability measures require considerable time for pre-training all the possible sources for source selection of each possible architecture, our method can be repeatedly used for every possible architecture with a single simple computation. Using the proposed method, we demonstrate that it is possible to increase the performance of temporal convolutional neural networks (CNN) on time series datasets.
Multivariate time series classification is an important task with widespread domains of applications. Recently, deep neural networks (DNN) have achieved state-of-the-art performance in time series classification. However, they often require large expert-labeled training datasets which can be infeasible in practice. In few-shot settings, i.e. only a limited number of samples per class are available in training data, DNNs show a significant drop in testing accuracy and poor generalization ability. In this paper, we propose to address these problems from an optimization and a loss function perspective. Specifically, we propose a new learning framework named COSCO consisting of a sharpness-aware minimization (SAM) optimization and a Prototypical loss function to improve the generalization ability of DNN for multivariate time series classification problems under few-shot setting. Our experiments demonstrate our proposed method outperforms the existing baseline methods. Our source code is available at: https://github.com/JRB9/COSCO.