UCR Time Series Research Articles

Benchmarking Anomaly Detection Methods: Insights From the UCR Time Series Anomaly Archive

ABSTRACTAnomaly detection, vital for identifying deviations from normative data patterns, is particularly crucial in sensor‐driven real‐world applications, which predominantly involve temporal data in the form of time series. Traditional evaluation of anomaly detection methods has relied on public benchmark datasets. Yet, recent revelations have uncovered inherent flaws and inadequacies in these datasets, casting doubt on the perceived progress in the field. To address this challenge, the UCR Time Series Anomaly Archive has been recently proposed—a meticulously curated database comprising 250 time series—designed to provide a robust and error‐free benchmark for anomaly detection research. This paper comprehensively evaluates state‐of‐the‐art anomaly detection techniques using the UCR Time Series Anomaly Archive. Our findings demonstrate the efficacy of current methods in accurately detecting anomalies across an important portion of datasets without additional optimization, underscoring the archive's utility as a foundational baseline for future research and development in anomaly detection methodologies.

A New Composite Dissimilarity Measure for Planar Curves Based on Higher-Order Derivatives

With the rapid development of information technology, the problem of curve matching has appeared in many application domains, including sequence analysis, signals processing, speech recognition, etc. Many similarity measures have been studied for matching curves based on Euclidean distance, which shows fragility in portraying the morphological information of curve data. In this paper, we propose a novel weighted composite curve dissimilarity metric (WCDM). First, the WCDM measures the dissimilarity based on the higher-order semantic difference between curve shapes and location difference. These two differences are calculated using the curvature difference and Euclidean distance between the curves, respectively. Second, a new dynamic weighting function is defined by employing the relationship between the trends of the curves. This function aims at adjusting the contributions of the curvature difference and the Euclidean distance to compose the dissimilarity measure WCDM. Finally, to ascertain the rationality of the WCDM, its metric properties are studied and proved theoretically. Comparison experiments on clustering and classification tasks are carried out on curve sets transformed from UCR time series datasets, and an application analysis of the WCDM is conducted on spectral data. The experimental results indicate the effectiveness of the WCDM. Specifically, clustering and classification based on the WCDM are superior to those based on ED, DTW, Hausdorff, Fréchet, and LCSS on at least 8 out of 14 datasets across all evaluation indices. In particular, the Purity and ARI on the Beetlefly dataset are improved by more than 7.5%, while accuracy on the Beef, Chinatown, and OliveOil datasets increases by 13.32%, 10.08%, and 12.83%, respectively.

Clustering and Classification of Time Series Sound Data

This scientific article addresses two critical tasks in data analysis—time series classification and clustering, particularly focusing on heart sound recordings. One of the main challenges in analyzing time series lies in the difficulty of comparing different series due to their variability in length, shape, and amplitude. Various algorithms were employed to tackle these tasks, including the Long Short-Term Memory (LSTM), KNN, recurrent neural network for classification and the K-means and DBSCAN methods for clustering. The study emphasizes the effectiveness of these methods in solving classification and clustering problems involving time series data containing heart sound recordings. The results indicate that LSTM is a powerful tool for time series classification due to its ability to retain contextual information over time. In contrast, KNN demonstrated high accuracy and speed in classification, though its limitations became apparent with larger datasets. For clustering tasks, the K-means method proved to be more effective than DBSCAN, showing higher clustering quality based on metrics such as silhouette score, Rand score, and others. The data used in this research were obtained from the UCR Time Series Archive, which includes heart sound recordings from various categories: normal sounds, murmurs, additional heart sounds, artifacts, and extra systolic rhythms. The analysis of results demonstrated that the chosen classification and clustering methods could be effectively used for diagnosing heart diseases. Furthermore, this research opens up new opportunities for further improvement in data processing and analysis methods, particularly in developing new medical diagnostic tools. Thus, this work illustrates the effectiveness of machine learning algorithms for time series analysis and their significance in improving cardiovascular disease diagnosis.

Explainable time series anomaly detection using masked latent generative modeling

We present a novel time series anomaly detection method that achieves excellent detection accuracy while offering a superior level of explainability. Our proposed method, TimeVQVAE-AD, leverages masked generative modeling adapted from the cutting-edge time series generation method known as TimeVQVAE. The prior model is trained on the discrete latent space of a time–frequency domain. Notably, the dimensional semantics of the time–frequency domain are preserved in the latent space, enabling us to compute anomaly scores across different frequency bands, which provides a better insight into the detected anomalies. Additionally, the generative nature of the prior model allows for sampling likely normal states for detected anomalies, enhancing the explainability of the detected anomalies through counterfactuals. Our experimental evaluation on the UCR Time Series Anomaly archive demonstrates that TimeVQVAE-AD significantly surpasses the existing methods in terms of detection accuracy and explainability. We provide our implementation on GitHub: https://github.com/ML4ITS/TimeVQVAE-AnomalyDetection.

New two‐sample test utilizing interpoint distance discrepancy

In this paper, we propose a novel two‐sample test for multivariate sample space. The test statistic calculates the mean of absolute difference of average interpoint distance. We utilize a permutation procedure to establish the critical value for the test. Through comprehensive simulation studies, we compare the performance of our proposed test with that of the K‐nearest neighbour test and the energy test. The results demonstrate that our proposed test exhibits advantages over the other two tests, particularly in high‐dimensional sample spaces. This superiority is further validated by its application to UCR time series datasets.

Randomnet: clustering time series using untrained deep neural networks

Neural networks are widely used in machine learning and data mining. Typically, these networks need to be trained, implying the adjustment of weights (parameters) within the network based on the input data. In this work, we propose a novel approach, RandomNet, that employs untrained deep neural networks to cluster time series. RandomNet uses different sets of random weights to extract diverse representations of time series and then ensembles the clustering relationships derived from these different representations to build the final clustering results. By extracting diverse representations, our model can effectively handle time series with different characteristics. Since all parameters are randomly generated, no training is required during the process. We provide a theoretical analysis of the effectiveness of the method. To validate its performance, we conduct extensive experiments on all of the 128 datasets in the well-known UCR time series archive and perform statistical analysis of the results. These datasets have different sizes, sequence lengths, and they are from diverse fields. The experimental results show that the proposed method is competitive compared with existing state-of-the-art methods.

Finding Discriminative Subsequences Via a Coverage Measure and Mutual Information Selection Strategy for Multi-Class Time Series Classification

Time series classification (TSC) has attracted considerable attention from the data mining community over the past decades. One of the effective ways to handle this task is to find discriminative subsequences in time series to train a classifier. Obviously, how to measure the discriminative power of subsequences and find the optimal combination of subsequences is crucial to the accuracy of TSC. In this paper, we introduce a new method, CRMI, to find high-quality discriminative subsequences for multi-class time series classification (MC-TSC). Different from existing methods, there are two significant innovations in the work. At first, we propose a novel measure, named coverage ratio, to evaluate the discriminative power of a subsequence based on a coverage matrix which is figured out by the clustering technique. Second, a heuristic algorithm based on mutual information (MI) is proposed to find the optimal combination of subsequence candidates. The calculation of MI is also based on the coverage matrix. Extensive experiments were conducted on 54 UCR time series datasets with at least 3 categories, and the results show that (1) the proposed algorithm achieves the highest average accuracy and outperforms most of the existing shapelet-based TSC algorithms; (2) compared with existing methods, the proposed algorithm performs better on datasets with a large number of categories.

Diffusion Language-Shapelets for Semi-supervised Time-Series Classification

Semi-supervised time-series classification could effectively alleviate the issue of lacking labeled data. However, existing approaches usually ignore model interpretability, making it difficult for humans to understand the principles behind the predictions of a model. Shapelets are a set of discriminative subsequences that show high interpretability in time series classification tasks. Shapelet learning-based methods have demonstrated promising classification performance. Unfortunately, without enough labeled data, the shapelets learned by existing methods are often poorly discriminative, and even dissimilar to any subsequence of the original time series. To address this issue, we propose the Diffusion Language-Shapelets model (DiffShape) for semi-supervised time series classification. In DiffShape, a self-supervised diffusion learning mechanism is designed, which uses real subsequences as a condition. This helps to increase the similarity between the learned shapelets and real subsequences by using a large amount of unlabeled data. Furthermore, we introduce a contrastive language-shapelets learning strategy that improves the discriminability of the learned shapelets by incorporating the natural language descriptions of the time series. Experiments have been conducted on the UCR time series archive, and the results reveal that the proposed DiffShape method achieves state-of-the-art performance and exhibits superior interpretability over baselines.

Weighted Fuzzy Clustering for Time Series With Trend-Based Information Granulation.

The highly dimensional characteristic of time series brings many challenges on direct mining time series, such as high cost in time and space. Granular computing provides a potential strategy for representing and dealing with time series at a higher level of abstraction. In this study, we propose an information granulation-based weighted fuzzy C -means (wFCM) method to realize time-series clustering, which could avoid high dimensionality processing and provide a concise and visible granular prototype for each cluster. In this method, each time series is first transformed into a series of information granules with trend following the principle of justifiable granularity. The formed granular time series can well capture the main features lying in the original time series and help realize dimensionality reduction. Then, the wFCM method is developed to complete time-series clustering in the granular space. Here, the dynamic time warping (DTW) is extended to capture the similarity for trend-based granular time series. Furthermore, the weighted DTW barycenter averaging is introduced to derive prototypes presented in a granular format, capturing the level, the fluctuation, and the changing trend, which are meaningful and understandable clustering results. The experiments conducted on real-world datasets coming from the UCR time-series database and Chinese stocks are presented to illustrate the effectiveness and practicality of the designed time-series clustering model.

SCALE-BOSS-MR: Scalable Time Series Classification Using Multiple Symbolic Representations

Time-Series-Classification (TSC) is an important machine learning task for many branches of science. Symbolic representations of time series, especially Symbolic Fourier Approximation (SFA), have been proven very effective for this task, given their abilities to reduce noise. In this paper, we improve upon SCALE-BOSS using multiple symbolic representations of time series. More specifically, the proposed SCALE-BOSS-MR incorporates into the process a variety of window sizes combined with multiple dilation parameters applied to the original and to first-order differences’ time series, with the latter modeling trend information. SCALE-BOSS-MR has been evaluated using the eight datasets with the largest training size of the UCR time series repository. The results indicate that SCALE-BOSS-MR can be instantiated to classifiers that are able to achieve state-of-the-art accuracy and can be tuned for scalability.

Ensemble Predictors: Possibilistic Combination of Conformal Predictors for Multivariate Time Series Classification.

In this article we propose a conceptual framework to study ensembles of conformal predictors (CP), that we call Ensemble Predictors (EP). Our approach is inspired by the application of imprecise probabilities in information fusion. Based on the proposed framework, we study, for the first time in the literature, the theoretical properties of CP ensembles in a general setting, by focusing on simple and commonly used possibilistic combination rules. We also illustrate the applicability of the proposed methods in the setting of multivariate time-series classification, showing that these methods provide better performance (in terms of both robustness, conservativeness, accuracy and running time) than both standard classification algorithms and other combination rules proposed in the literature, on a large set of benchmarks from the UCR time series archive.

A new similarity measurement method for time series based on image fusion of recurrence plots and wavelet scalogram

The core of data series classification and clustering is how to evaluate the similarity between time series. However, for one-dimensional time series, the vast majority of similarity measurement methods currently relied on one-dimensional information. Although some classifications of time series were achieved by the images transformed from time series, they mostly relied on a single imaging mechanism (time domain or frequency domain). In order to give a new idea for time series similarity measurement, this paper proposed a similarity measurement method of time series based on the fused images. According to recurrence plots (RP) and wavelet scalogram (WS), the original time series was first transformed into images. Then, RP and WS were fused into an image. Next, the feature in the image was extracted by ResNet-18. Finally, the similarity of the time series can be obtained by the Euclidean distance between the features extracted by ResNet-18. The proposed method was verified by the time series from UCR Time Series Classification/Clustering Homepage. The results showed that the similarity measurement of time series can be effectively improved by fusing the images obtained by different imaging mechanisms in the time domain and frequency domain.

A novel distance measure based on dynamic time warping to improve time series classification

Dynamic time warping (DTW) is the most widely used method to evaluate the similarity between time series. However, the DTW distance only takes into account the difference in amplitude, but does not reflect the time distortion information between them. In this paper, we propose a novel time similarity metric, called the time distortion coefficient, based on the DTW warping path to quantify the time distortion between time series. It is able to characterize the type and degree of time distortion between two time series at each point. By summing the absolute values of the time distortion coefficients, the overall time distortion is introduced to quantify time distortion between two time series. For the Nearest Neighbor (NN) based time series classification, a fusional similarity measure combining the DTW distance and the overall time distortion measure is proposed, which is able to evaluate the similarity in both amplitude and time domains. The experimental results conducted on the UCR time series classification archive datasets demonstrate that the proposed fusional similarity measure can significantly improve the classification accuracy of the 1-NN classifier with only a small amount of additional computational cost compared to the DTW distance and other metrics.

SE-shapelets: Semi-supervised Clustering of Time Series Using Representative Shapelets

Shapelets that discriminate time series using local features (subsequences) are promising for time series clustering. Existing time series clustering methods may fail to capture representative shapelets because they discover shapelets from a large pool of uninformative subsequences, and thus result in low clustering accuracy. This paper proposes a Semi-supervised Clustering of Time Series Using Representative Shapelets (SE-Shapelets) method, which utilizes a small number of labeled and propagated pseudo-labeled time series to help discover representative shapelets, thereby improving the clustering accuracy. In SE-Shapelets, we propose two techniques to discover representative shapelets for the effective clustering of time series. (1) A salient subsequence chain (SSC) that can extract salient subsequences (as candidate shapelets) of a labeled/pseudo-labeled time series, which helps remove massive uninformative subsequences from the pool. (2) A linear discriminant selection (LDS) algorithm to identify shapelets that can capture representative local features of time series in different classes, for convenient clustering. Experiments on UCR time series datasets demonstrate that SE-shapelets discovers representative shapelets and achieves higher clustering accuracy than counterpart semi-supervised time series clustering methods.

ESDTW: Extrema-based shape dynamic time warping

As a nonlinear distance measurement, Dynamic time warping (DTW) is widely used to solve the alignment problem of time series. However, due to local distortion of signal, noise interference, and high computational cost, DTW and its variants present some limitations in terms of classification accuracy or speed. In this paper, we develop the extrema-based shape dynamic time warping (ESDTW) for the purpose of fast and accurate alignment of time series. The proposed ESDTW introduces local extrema to represent the original time series, and further uses DTW to align the descriptors of extrema shape. By considering the location information of local extrema, the proposed measure avoids unreliable time series alignment caused by local maxima and minima separately in LEDTW. The experiments on some artificially simulated pairs of aligned sequences demonstrate that ESDTW can obtain more accurate warping paths than comparison methods. Moreover, combining with the nearest neighbor classifier, ESDTW achieves higher classification accuracy than other distance measures on the 84 UCR time series datasets. We also confirm significant computational efficiency gains on long time series.

Time series clustering based on normal cloud model and complex network

When data mining research is conducted, it is difficult to obtain precise domain knowledge to set a similarity threshold. Furthermore, noise and missing values are inevitable. Missing values and noise without pre-processing are challenges for many algorithms. A time-series clustering method is proposed based on the normal cloud model and complex networks. Matrix profile similarity measurement, normal cloud model generation and filtering, cloud model expectation curve weighting, degree centrality reweighting, and community discovery in complex networks are the five stages of the proposed clustering algorithm. Local features are considered, and the effects of missing values are reduced when performing similarity measurements. The normal cloud model can be used to set thresholds adaptively. The Louvain algorithm accomplishes the clustering task in complex networks without specifying the clusters. Experiments are conducted on 94 datasets and are compared with 8 clustering methods in the UCR time-series clustering benchmark study. Experimental results indicate that the proposed method can perform well on many datasets.

A novel shape-based averaging algorithm for time series

Time series averaging is one of the essential subroutines in time series analysis. DTW Barycenter Averaging (DBA) has proven to be an effective and popular DTW-based time series averaging algorithm. However, DBA lacks the ability to average time series in the time domain, making it sensitive to initialization. In this research, we propose a novel shape-based time series averaging algorithm, called Shape DTW Weighted Averaging (ShapeDWA), to address the shortcomings of DBA. The proposed ShapeDWA algorithm combines the advantages of the DBA and the Cubic-spline DTW (CDTW) averaging methods. The concepts of time index averaging and re-sampling in the CDTW algorithm are incorporated into the DBA algorithm, giving ShapeDWA the ability to average a set of time series in both the amplitude and time domains. Moreover, ShapeDWA utilizes a weighed average instead of the barycenter average in DBA, which effectively attenuate the effects of noise, outliers, and local amplitude differences between the time series. To qualitatively evaluate and compare the proposed time series averaging algorithm, two metrics have been developed: average discrepancy distance and average time distortion. Extensive experimental results on the UCR time series database illustrate the superior performance of ShapeDWA over DBA and SSG, with an average reduction of 23.42% and 24.89% for average discrepancy distance, and 18.76% and 19.81% for average time distortion. Furthermore, the template matching-based classification experiment shows that ShapeDWA combined with these two developed metrics improves the classification rate by 17.07% and 16.42% compared to DBA and SSG, respectively.

PLAHS: A Partial Labelling Autonomous Hyper-heuristic System for Industry 4.0 with application on classification of cold stamping process

In real-life industry it is difficult to have fully-labelled datasets due to lack of time, resources or knowledge. In this sense, this paper proposes the design and development of a Partial Labelling Autonomous Hyper-heuristic System PLAHS, a solution that autonomously labels partially labelled databases and evaluates the yielded labelling solution by means of a novel Trustworthiness Metric (TM). The proposal combines a hyper-heuristic inspired approach with a Semi Supervised Learning Clustering (SSLC) methodology that optimizes the parameters of different clustering algorithms, based on a novel semi-supervised metric named Partially Supervised Optimization Metric (PSOM). The proposal has been tested with promising and excellent results on both a real use case for labelling work orders in a cold stamping press, and 13 databases from the UCI (multivariate data) and UCR (time series data) repositories.

Similarity Measurement and Classification of Temporal Data Based on Double Mean Representation

Time series data typically exhibit high dimensionality and complexity, necessitating the use of specific approximation methods to perform computations on the data. The currently employed compression methods suffer from varying degrees of feature loss, leading to potential distortions in similarity measurement results. Considering the aforementioned challenges and concerns, this paper proposes a double mean representation method, SAX-DM (Symbolic Aggregate Approximation Based on Double Mean Representation), for time series data, along with a similarity measurement approach based on SAX-DM. Addressing the trade-off between compression ratio and accuracy in the improved SAX representation, SAX-DM utilizes the segment mean and the segment trend distance to represent corresponding segments of time series data. This method reduces the dimensionality of the original sequences while preserving the original features and trend information of the time series data, resulting in a unified representation of time series segments. Experimental results demonstrate that, under the same compression ratio, SAX-DM combined with its similarity measurement method achieves higher expression accuracy, balanced compression rate, and accuracy, compared to SAX-TD and SAX-BD, in over 80% of the UCR Time Series dataset. This approach improves the efficiency and precision of similarity calculation.

Nonlinear neural-like P model for time series classification

Gated spiking neural P (GSNP) model is a novel recurrent model proposed recently, which is viewed as a variant of recurrent neural network. Time series classification (TSC) is one of the most challenging problems in data mining. In this work, based on the GSNP model, a nonlinear neural-like P (NNP) model for TSC is proposed. NNP model introduces the bidirectional mechanism and attention mechanism in deep learning, and builds nonlinear neuron modules together with GSNP to realize end-to-end learning. The neuron modules excavate the hidden features of time series to distinguish data and realize effective classification. Through evaluating on UCR Time Series Classification Archive, the classification performance of NNP model is significantly better than that of GSNP and other classification models. The NNP model can compete with advanced models on TSC task.