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"Time Series Analysis": models, code, and papers

RobustTrend: A Huber Loss with a Combined First and Second Order Difference Regularization for Time Series Trend Filtering

Jun 27, 2019
Qingsong Wen, Jingkun Gao, Xiaomin Song, Liang Sun, Jian Tan

Extracting the underlying trend signal is a crucial step to facilitate time series analysis like forecasting and anomaly detection. Besides noise signal, time series can contain not only outliers but also abrupt trend changes in real-world scenarios. To deal with these challenges, we propose a robust trend filtering algorithm based on robust statistics and sparse learning. Specifically, we adopt the Huber loss to suppress outliers, and utilize a combination of the first order and second order difference on the trend component as regularization to capture both slow and abrupt trend changes. Furthermore, an efficient method is designed to solve the proposed robust trend filtering based on majorization minimization (MM) and alternative direction method of multipliers (ADMM). We compared our proposed robust trend filter with other nine state-of-the-art trend filtering algorithms on both synthetic and real-world datasets. The experiments demonstrate that our algorithm outperforms existing methods.

* Accepted to the 28th International Joint Conference on Artificial Intelligence (IJCAI 2019), 7 pages. v2: added related references and adjusted font size in figures 
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MultiSegVA: Using Visual Analytics to Segment Biologging Time Series on Multiple Scales

Sep 02, 2020
Philipp Meschenmoser, Juri F. Buchmüller, Daniel Seebacher, Martin Wikelski, Daniel A. Keim

Segmenting biologging time series of animals on multiple temporal scales is an essential step that requires complex techniques with careful parameterization and possibly cross-domain expertise. Yet, there is a lack of visual-interactive tools that strongly support such multi-scale segmentation. To close this gap, we present our MultiSegVA platform for interactively defining segmentation techniques and parameters on multiple temporal scales. MultiSegVA primarily contributes tailored, visual-interactive means and visual analytics paradigms for segmenting unlabeled time series on multiple scales. Further, to flexibly compose the multi-scale segmentation, the platform contributes a new visual query language that links a variety of segmentation techniques. To illustrate our approach, we present a domain-oriented set of segmentation techniques derived in collaboration with movement ecologists. We demonstrate the applicability and usefulness of MultiSegVA in two real-world use cases from movement ecology, related to behavior analysis after environment-aware segmentation, and after progressive clustering. Expert feedback from movement ecologists shows the effectiveness of tailored visual-interactive means and visual analytics paradigms at segmenting multi-scale data, enabling them to perform semantically meaningful analyses. A third use case demonstrates that MultiSegVA is generalizable to other domains.

* IEEE VAST 2020 - Proceedings of IEEE Conference on Visual Analytics Science and Technology (VAST), 2020 
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Stochastic Identification-based Active Sensing Acousto-Ultrasound SHM Using Stationary Time Series Models

Jan 26, 2022
Shabbir Ahmed, Fotis Kopsaftopoulos

In this work, a probabilistic damage detection and identification scheme using stochastic time series models in the context of acousto-ultrasound guided wave-based SHM is proposed, and its performance is assessed experimentally. In order to simplify the damage detection and identification process, model parameters are modified based on the singular value decomposition (SVD) as well as the principal component analysis (PCA)-based truncation approach. The modified model parameters are then used to estimate a statistical characteristic quantity that follows a chi-squared distribution. A probabilistic threshold is used instead of a user-defined margin to facilitate automatic damage detection. The method's effectiveness is assessed via multiple experiments using both metallic and composite coupons and under various damage scenarios using damage intersecting and damage non-intersecting paths. The results of the study confirm the high potential and effectiveness of the stochastic time series methods for guided wave-based damage detection and identification in a potentially automated way.

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Prediction of financial time series using LSTM and data denoising methods

Mar 05, 2021
Qi Tang, Tongmei Fan, Ruchen Shi, Jingyan Huang, Yidan Ma

In order to further overcome the difficulties of the existing models in dealing with the non-stationary and nonlinear characteristics of high-frequency financial time series data, especially its weak generalization ability, this paper proposes an ensemble method based on data denoising methods, including the wavelet transform (WT) and singular spectrum analysis (SSA), and long-term short-term memory neural network (LSTM) to build a data prediction model, The financial time series is decomposed and reconstructed by WT and SSA to denoise. Under the condition of denoising, the smooth sequence with effective information is reconstructed. The smoothing sequence is introduced into LSTM and the predicted value is obtained. With the Dow Jones industrial average index (DJIA) as the research object, the closing price of the DJIA every five minutes is divided into short-term (1 hour), medium-term (3 hours) and long-term (6 hours) respectively. . Based on root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and absolute percentage error standard deviation (SDAPE), the experimental results show that in the short-term, medium-term and long-term, data denoising can greatly improve the accuracy and stability of the prediction, and can effectively improve the generalization ability of LSTM prediction model. As WT and SSA can extract useful information from the original sequence and avoid overfitting, the hybrid model can better grasp the sequence pattern of the closing price of the DJIA. And the WT-LSTM model is better than the benchmark LSTM model and SSA-LSTM model.

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DuPLO: A DUal view Point deep Learning architecture for time series classificatiOn

Sep 20, 2018
Roberto Interdonato, Dino Ienco, Raffaele Gaetano, Kenji Ose

Nowadays, modern Earth Observation systems continuously generate huge amounts of data. A notable example is represented by the Sentinel-2 mission, which provides images at high spatial resolution (up to 10m) with high temporal revisit period (every 5 days), which can be organized in Satellite Image Time Series (SITS). While the use of SITS has been proved to be beneficial in the context of Land Use/Land Cover (LULC) map generation, unfortunately, machine learning approaches commonly leveraged in remote sensing field fail to take advantage of spatio-temporal dependencies present in such data. Recently, new generation deep learning methods allowed to significantly advance research in this field. These approaches have generally focused on a single type of neural network, i.e., Convolutional Neural Networks (CNNs) or Recurrent Neural Networks (RNNs), which model different but complementary information: spatial autocorrelation (CNNs) and temporal dependencies (RNNs). In this work, we propose the first deep learning architecture for the analysis of SITS data, namely \method{} (DUal view Point deep Learning architecture for time series classificatiOn), that combines Convolutional and Recurrent neural networks to exploit their complementarity. Our hypothesis is that, since CNNs and RNNs capture different aspects of the data, a combination of both models would produce a more diverse and complete representation of the information for the underlying land cover classification task. Experiments carried out on two study sites characterized by different land cover characteristics (i.e., the \textit{Gard} site in France and the \textit{Reunion Island} in the Indian Ocean), demonstrate the significance of our proposal.

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The development of an information criterion for Change-Point Analysis

May 21, 2015
Paul A. Wiggins, Colin H. LaMont

Change-point analysis is a flexible and computationally tractable tool for the analysis of times series data from systems that transition between discrete states and whose observables are corrupted by noise. The change-point algorithm is used to identify the time indices (change points) at which the system transitions between these discrete states. We present a unified information-based approach to testing for the existence of change points. This new approach reconciles two previously disparate approaches to Change-Point Analysis (frequentist and information-based) for testing transitions between states. The resulting method is statistically principled, parameter and prior free and widely applicable to a wide range of change-point problems.

* 10 pages + supplement. 5 Figures 
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Linear Multiple Low-Rank Kernel Based Stationary Gaussian Processes Regression for Time Series

Apr 21, 2019
Feng Yin, Lishuo Pan, Xinwei He, Tianshi Chen, Sergios Theodoridis, Zhi-Quan, Luo

Gaussian processes (GP) for machine learning have been studied systematically over the past two decades and they are by now widely used in a number of diverse applications. However, GP kernel design and the associated hyper-parameter optimization are still hard and to a large extend open problems. In this paper, we consider the task of GP regression for time series modeling and analysis. The underlying stationary kernel can be approximated arbitrarily close by a new proposed grid spectral mixture (GSM) kernel, which turns out to be a linear combination of low-rank sub-kernels. In the case where a large number of the sub-kernels are used, either the Nystr\"{o}m or the random Fourier feature approximations can be adopted to deal efficiently with the computational demands. The unknown GP hyper-parameters consist of the non-negative weights of all sub-kernels as well as the noise variance; their estimation is performed via the maximum-likelihood (ML) estimation framework. Two efficient numerical optimization methods for solving the unknown hyper-parameters are derived, including a sequential majorization-minimization (MM) method and a non-linearly constrained alternating direction of multiplier method (ADMM). The MM matches perfectly with the proven low-rank property of the proposed GSM sub-kernels and turns out to be a part of efficiency, stable, and efficient solver, while the ADMM has the potential to generate better local minimum in terms of the test MSE. Experimental results, based on various classic time series data sets, corroborate that the proposed GSM kernel-based GP regression model outperforms several salient competitors of similar kind in terms of prediction mean-squared-error and numerical stability.

* 15 pages, 5 figures, submitted 
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Bayesian Online Change Point Detection for Baseline Shifts

Jan 07, 2022
Ginga Yoshizawa

In time series data analysis, detecting change points on a real-time basis (online) is of great interest in many areas, such as finance, environmental monitoring, and medicine. One promising means to achieve this is the Bayesian online change point detection (BOCPD) algorithm, which has been successfully adopted in particular cases in which the time series of interest has a fixed baseline. However, we have found that the algorithm struggles when the baseline irreversibly shifts from its initial state. This is because with the original BOCPD algorithm, the sensitivity with which a change point can be detected is degraded if the data points are fluctuating at locations relatively far from the original baseline. In this paper, we not only extend the original BOCPD algorithm to be applicable to a time series whose baseline is constantly shifting toward unknown values but also visualize why the proposed extension works. To demonstrate the efficacy of the proposed algorithm compared to the original one, we examine these algorithms on two real-world data sets and six synthetic data sets.

* Statistics, Optimization & Information Computing, 9(1), 1-16 (2020) 
* Published in Statistics, Optimization & Information Computing 
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Sequential visibility-graph motifs

May 02, 2016
Jacopo Iacovacci, Lucas Lacasa

Visibility algorithms transform time series into graphs and encode dynamical information in their topology, paving the way for graph-theoretical time series analysis as well as building a bridge between nonlinear dynamics and network science. In this work we introduce and study the concept of sequential visibility graph motifs, smaller substructures of n consecutive nodes that appear with characteristic frequencies. We develop a theory to compute in an exact way the motif profiles associated to general classes of deterministic and stochastic dynamics. We find that this simple property is indeed a highly informative and computationally efficient feature capable to distinguish among different dynamics and robust against noise contamination. We finally confirm that it can be used in practice to perform unsupervised learning, by extracting motif profiles from experimental heart-rate series and being able, accordingly, to disentangle meditative from other relaxation states. Applications of this general theory include the automatic classification and description of physical, biological, and financial time series.

* Physical Review E 93, 042309 (2016) 
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