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Dynamic Time Warping (DTW) has a quadratic time and space complexity that limits its use to small time series. In this paper we introduce FastDTW, an approximation of DTW that has a linear time and space complexity. FastDTW uses a...
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Dynamic Time Warping (DTW) has a quadratic time and space complexity that limits its use to small time series. In this paper we introduce FastDTW, an approximation of DTW that has a linear time and space complexity. FastDTW uses a multilevel approach that recursively projects a solution from a coarser resolution and refines the projected solution. We prove the linear time and space complexity of FastDTW both theoretically and empirically. We also analyze the accuracy of FastDTW by comparing it to two other types of existing approximate DTW algorithms: constraints (such as Sakoe-Chiba Bands) and abstraction. Our results show a large improvement in accuracy over existing methods.
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Accurate clustering of time series is a challenging problem for data arising from areas such as financial markets, biomedical studies, and environmental sciences, especially when some, or all, of the series exhibit nonlinearity an...
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Accurate clustering of time series is a challenging problem for data arising from areas such as financial markets, biomedical studies, and environmental sciences, especially when some, or all, of the series exhibit nonlinearity and nonstationarity. When a subset of the series exhibits nonlinear characteristics, frequency domain clustering methods based on higher-order spectral properties, such as the bispectra or trispectra are useful. While these methods address nonlinearity, they rely on the assumption of series stationarity. We propose the Bispectral Smooth Localized Complex EXponential (BSLEX) approach for clustering nonlinear and nonstationary time series. BSLEX is an extension of the SLEX approach for linear, nonstationary series, and overcomes the challenges of both nonlinearity and nonstationarity through smooth partitions of the nonstationary time series into stationary subsets in a dyadic fashion. The performance of the BSLEX approach is illustrated via simulation where several nonstationary or nonlinear time series are clustered, as well as via accurate clustering of the records of 16 seismic events, eight of which are earthquakes and eight are explosions. We illustrate the utility of the approach by clustering S&P 100 financial returns.
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Analytics of mobile traffic information may take into account the time-series nature of the data itself. When employing mobile traffic data in a predictive setting to derive useful knowledge to characterize the city environment, t...
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Analytics of mobile traffic information may take into account the time-series nature of the data itself. When employing mobile traffic data in a predictive setting to derive useful knowledge to characterize the city environment, the most suitable time series processing methods must be identified. In this paper, we propose an approach to process mobile traffic data using specific time series techniques - smoothing, decomposition, filtering, time-windowing - and to establish the best approach to exploit information extracted from those time series to classify land use, according to sensitivity/specificity metrics. We apply our methodology to a large-scale mobile traffic dataset, we assess its feasibility and we discuss the suitability of different methods for land use classification. (C) 2016 Elsevier B.V. All rights reserved.
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Time series forecasting is an important research field in machine learning. Since the literature shows several techniques for the solution of this problem, combining outputs of different models is a simple and robust strategy. How...
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Time series forecasting is an important research field in machine learning. Since the literature shows several techniques for the solution of this problem, combining outputs of different models is a simple and robust strategy. However, even when using combiners, the experimenter may face the following dilemma: which technique should one use to combine the individual predictors? Inspired by classification and pattern recognition algorithms, this work presents a dynamic selection method of forecast combiners. In the dynamic selection, each test pattern is submitted to a certain combiner according to a nearest neighbor rule. The proposed method was used to forecast eight time series with chaotic behavior in short and long term. In general, the dynamic selection presented satisfactory results for all datasets. (C) 2016 Elsevier B.V. All rights reserved.
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Shapelets are discriminative subsequences of time series, usually embedded in shapelet-based decision trees. The enumeration of time series shapelets is, however, computationally costly, which in addition to the inherent difficult...
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Shapelets are discriminative subsequences of time series, usually embedded in shapelet-based decision trees. The enumeration of time series shapelets is, however, computationally costly, which in addition to the inherent difficulty of the decision tree learning algorithm to effectively handle high-dimensional data, severely limits the applicability of shapelet-based decision tree learning from large (multivariate) time series databases. This paper introduces a novel tree-based ensemble method for univariate and multivariate time series classification using shapelets, called the generalized random shapelet forest algorithm. The algorithm generates a set of shapelet-based decision trees, where both the choice of instances used for building a tree and the choice of shapelets are randomized. For univariate time series, it is demonstrated through an extensive empirical investigation that the proposed algorithm yields predictive performance comparable to the current state-of-the-art and significantly outperforms several alternative algorithms, while being at least an order of magnitude faster. Similarly for multivariate time series, it is shown that the algorithm is significantly less computationally costly and more accurate than the current state-of-the-art.
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The explosion of time series data in recent years has brought a flourish of new time series analysis methods, for forecasting, clustering, classification and other tasks. The evaluation of these new methods requires either collect...
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The explosion of time series data in recent years has brought a flourish of new time series analysis methods, for forecasting, clustering, classification and other tasks. The evaluation of these new methods requires either collecting or simulating a diverse set of time series benchmarking data to enable reliable comparisons against alternative approaches. We propose GeneRAting TIme Series with diverse and controllable characteristics, named GRATIS, with the use of mixture autoregressive (MAR) models. We simulate sets of time series using MAR models and investigate the diversity and coverage of the generated time series in a time series feature space. By tuning the parameters of the MAR models, GRATIS is also able to efficiently generate new time series with controllable features. In general, as a costless surrogate to the traditional data collection approach, GRATIS can be used as an evaluation tool for tasks such as time series forecasting and classification. We illustrate the usefulness of our time series generation process through a time series forecasting application.
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Time-series data are widespread in real-world industrial scenarios. To recover and infer missing information in real-world applications, the problem of time-series prediction has been widely studied as a classical research topic i...
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Time-series data are widespread in real-world industrial scenarios. To recover and infer missing information in real-world applications, the problem of time-series prediction has been widely studied as a classical research topic in data mining. Deep learning archi-tectures have been viewed as next-generation time-series prediction models. However, recent studies have shown that deep learning models are vulnerable to adversarial attacks. In this study, we prospectively examine the problem of time-series prediction adversarial attacks and propose an attack strategy for generating an adversarial time series by adding malicious perturbations to the original time series to deteriorate the performance of time -series prediction models. Specifically, a perturbation-based adversarial example generation algorithm is proposed using the gradient information of the prediction model. In practice, unlike the imperceptibility to humans in the field of image processing, time-series data are more sensitive to abnormal perturbations and there are more stringent requirements regarding the amount of perturbations. To address this challenge, we craft an adversarial time series based on the importance measurement to slightly perturb the original data. Based on comprehensive experiments conducted on real-world time-series datasets, we verify that the proposed adversarial attack methods not only effectively fool the target time-series prediction model LSTNet, they also attack state-of-the-art CNN-, RNN-, and MHANET-based models. Meanwhile, the results show that the proposed methods achieve a good transferability. That is, the adversarial examples generated for a specific prediction model can significantly affect the performance of the other methods. Moreover, through a comparison with existing adversarial attack approaches, we can see that much smaller per-turbations are sufficient for the proposed importance-measurement based adversarial attack method. The methods described in this paper are significant in understanding the impact of adversarial attacks on a time-series prediction and promoting the robustness of such prediction technologies.(c) 2021 Elsevier Inc. All rights reserved.
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This work examines the impact of data transformation (for variance stabilization) and outlier adjustment (“linearization”) on the quality of univariate time series forecasts, considering each one separately, as well as in combin...
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This work examines the impact of data transformation (for variance stabilization) and outlier adjustment (“linearization”) on the quality of univariate time series forecasts, considering each one separately, as well as in combination. Twenty of the most important time series of the Greek economy were used for this purpose. Empirical findings show a significant improvement in forecasts’ confidence intervals, but no substantial improvement in point forecasts. Furthermore, the combined transformation-linearization procedure improves substantially the non-normality problem encountered in many macroeconomic time series.
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In this paper, a nonlinear time series model is developed for the case when the underlying time series data are reported by LR fuzzy numbers. To this end, we present a three-stage nonparametric kernel-based estimation procedure fo...
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In this paper, a nonlinear time series model is developed for the case when the underlying time series data are reported by LR fuzzy numbers. To this end, we present a three-stage nonparametric kernel-based estimation procedure for the center as well as the left and right spreads of the unknown nonlinear fuzzy smooth function. In each stage, the nonparametric Nadaraya-Watson estimator is used to evaluate the center and the spreads of the fuzzy smooth function. A hybrid algorithm is proposed to estimate the unknown optimal bandwidths and autoregressive order simultaneously. Various goodness-of-fit measures are utilized for performance assessment of the fuzzy nonlinear kernel-based time series model and for comparative analysis. The practical applicability and superiority of the novel approach in comparison with further fuzzy time series models are demonstrated via a simulation study and some real-life applications.
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A large amount of time series is produced because of the frequent use of IoT devices and sensors. Time series compression is widely adopted to reduce storage overhead and transport costs. At present, most state-of-the-art approach...
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A large amount of time series is produced because of the frequent use of IoT devices and sensors. Time series compression is widely adopted to reduce storage overhead and transport costs. At present, most state-of-the-art approaches focus on univariate time series. Therefore, the task of compressing multivariate time series (MTS) is still an important but challenging problem. Traditional MTS compression methods treat each variable individually, ignoring the correlations across variables. This paper proposes a novel MTS prediction method, which can be applied to compress MTS to achieve a higher compression ratio. The method can extract the spatial and temporal correlation across multiple variables, achieving a more accurate prediction and improving the lossy compression performance of MTS based on the prediction-quantization-entropy framework. We use a convolutional neural network (CNN) to extract the temporal features of all variables within the window length. Then the features generated by CNN are transformed, and the image classification algorithm extracts the spatial features of the transformed data. Predictions are made according to spatiotemporal characteristics. To enhance the robustness of our model, we integrate the AR autoregressive linear model in parallel with the proposed network. Experimental results demonstrate that our work can improve the prediction accuracy of MTS and the MTS compression performance in most cases.(c) 2023 Elsevier Inc. All rights reserved.
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