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

Optimal Transport Based Change Point Detection and Time Series Segment Clustering

Nov 04, 2019
Kevin C. Cheng, Shuchin Aeron, Michael C. Hughes, Erika Hussey, Eric L. Miller

Two common problems in time series analysis are the decomposition of the data stream into disjoint segments, each of which is in some sense 'homogeneous' - a problem that is also referred to as Change Point Detection (CPD) - and the grouping of similar nonadjacent segments, or Time Series Segment Clustering (TSSC). Building upon recent theoretical advances characterizing the limiting distribution free behavior of the Wasserstein two-sample test, we propose a novel algorithm for unsupervised, distribution-free CPD, which is amenable to both offline and online settings. We also introduce a method to mitigate false positives in CPD, and address TSSC by using the Wasserstein distance between the detected segments to build an affinity matrix to which we apply spectral clustering. Results on both synthetic and real data sets show the benefits of the approach.

  
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Piece-wise Matching Layer in Representation Learning for ECG Classification

Sep 26, 2020
Behzad Ghazanfari, Fatemeh Afghah, Sixian Zhang

This paper proposes piece-wise matching layer as a novel layer in representation learning methods for electrocardiogram (ECG) classification. Despite the remarkable performance of representation learning methods in the analysis of time series, there are still several challenges associated with these methods ranging from the complex structures of methods, the lack of generality of solutions, the need for expert knowledge, and large-scale training datasets. We introduce the piece-wise matching layer that works based on two levels to address some of the aforementioned challenges. At the first level, a set of morphological, statistical, and frequency features and comparative forms of them are computed based on each periodic part and its neighbors. At the second level, these features are modified by predefined transformation functions based on a receptive field scenario. Several scenarios of offline processing, incremental processing, fixed sliding receptive field, and event-based triggering receptive field can be implemented based on the choice of length and mechanism of indicating the receptive field. We propose dynamic time wrapping as a mechanism that indicates a receptive field based on event triggering tactics. To evaluate the performance of this method in time series analysis, we applied the proposed layer in two publicly available datasets of PhysioNet competitions in 2015 and 2017 where the input data is ECG signal. We compared the performance of our method against a variety of known tuned methods from expert knowledge, machine learning, deep learning methods, and the combination of them. The proposed approach improves the state of the art in two known completions 2015 and 2017 around 4% and 7% correspondingly while it does not rely on in advance knowledge of the classes or the possible places of arrhythmia.

  
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Quantile-based fuzzy C-means clustering of multivariate time series: Robust techniques

Sep 22, 2021
Ángel López-Oriona, Pierpaolo D'Urso, José Antonio Vilar, Borja Lafuente-Rego

Three robust methods for clustering multivariate time series from the point of view of generating processes are proposed. The procedures are robust versions of a fuzzy C-means model based on: (i) estimates of the quantile cross-spectral density and (ii) the classical principal component analysis. Robustness to the presence of outliers is achieved by using the so-called metric, noise and trimmed approaches. The metric approach incorporates in the objective function a distance measure aimed at neutralizing the effect of the outliers, the noise approach builds an artificial cluster expected to contain the outlying series and the trimmed approach eliminates the most atypical series in the dataset. All the proposed techniques inherit the nice properties of the quantile cross-spectral density, as being able to uncover general types of dependence. Results from a broad simulation study including multivariate linear, nonlinear and GARCH processes indicate that the algorithms are substantially effective in coping with the presence of outlying series (i.e., series exhibiting a dependence structure different from that of the majority), clearly poutperforming alternative procedures. The usefulness of the suggested methods is highlighted by means of two specific applications regarding financial and environmental series.

* arXiv admin note: text overlap with arXiv:2109.03728 
  
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A Visual Analytics Framework for Reviewing Multivariate Time-Series Data with Dimensionality Reduction

Aug 17, 2020
Takanori Fujiwara, Shilpika, Naohisa Sakamoto, Jorji Nonaka, Keiji Yamamoto, Kwan-Liu Ma

Data-driven problem solving in many real-world applications involves analysis of time-dependent multivariate data, for which dimensionality reduction (DR) methods are often used to uncover the intrinsic structure and features of the data. However, DR is usually applied to a subset of data that is either single-time-point multivariate or univariate time-series, resulting in the need to manually examine and correlate the DR results out of different data subsets. When the number of dimensions is large either in terms of the number of time points or attributes, this manual task becomes too tedious and infeasible. In this paper, we present MulTiDR, a new DR framework that enables processing of time-dependent multivariate data as a whole to provide a comprehensive overview of the data. With the framework, we employ DR in two steps. When treating the instances, time points, and attributes of the data as a 3D array, the first DR step reduces the three axes of the array to two, and the second DR step visualizes the data in a lower-dimensional space. In addition, by coupling with a contrastive learning method and interactive visualizations, our framework enhances analysts' ability to interpret DR results. We demonstrate the effectiveness of our framework with four case studies using real-world datasets.

* To appear in IEEE Transactions on Visualization and Computer Graphics and IEEE VIS 2020 (VAST) 
  
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Comparative Analysis of Machine Learning Approaches to Analyze and Predict the Covid-19 Outbreak

Feb 11, 2021
Muhammad Naeem, Jian Yu, Muhammad Aamir, Sajjad Ahmad Khan, Olayinka Adeleye, Zardad Khan

Background. Forecasting the time of forthcoming pandemic reduces the impact of diseases by taking precautionary steps such as public health messaging and raising the consciousness of doctors. With the continuous and rapid increase in the cumulative incidence of COVID-19, statistical and outbreak prediction models including various machine learning (ML) models are being used by the research community to track and predict the trend of the epidemic, and also in developing appropriate strategies to combat and manage its spread. Methods. In this paper, we present a comparative analysis of various ML approaches including Support Vector Machine, Random Forest, K-Nearest Neighbor and Artificial Neural Network in predicting the COVID-19 outbreak in the epidemiological domain. We first apply the autoregressive distributed lag (ARDL) method to identify and model the short and long-run relationships of the time-series COVID-19 datasets. That is, we determine the lags between a response variable and its respective explanatory time series variables as independent variables. Then, the resulting significant variables concerning their lags are used in the regression model selected by the ARDL for predicting and forecasting the trend of the epidemic. Results. Statistical measures i.e., Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE) are used for model accuracy. The values of MAPE for the best selected models for confirmed, recovered and deaths cases are 0.407, 0.094 and 0.124 respectively, which falls under the category of highly accurate forecasts. In addition, we computed fifteen days ahead forecast for the daily deaths, recover, and confirm patients and the cases fluctuated across time in all aspects. Besides, the results reveal the advantages of ML algorithms for supporting decision making of evolving short term policies.

* 22 pages, 10 figures 
  
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Learning the Conditional Independence Structure of Stationary Time Series: A Multitask Learning Approach

Jan 11, 2015
Alexander Jung

We propose a method for inferring the conditional independence graph (CIG) of a high-dimensional Gaussian vector time series (discrete-time process) from a finite-length observation. By contrast to existing approaches, we do not rely on a parametric process model (such as, e.g., an autoregressive model) for the observed random process. Instead, we only require certain smoothness properties (in the Fourier domain) of the process. The proposed inference scheme works even for sample sizes much smaller than the number of scalar process components if the true underlying CIG is sufficiently sparse. A theoretical performance analysis provides conditions which guarantee that the probability of the proposed inference method to deliver a wrong CIG is below a prescribed value. These conditions imply lower bounds on the sample size such that the new method is consistent asymptotically. Some numerical experiments validate our theoretical performance analysis and demonstrate superior performance of our scheme compared to an existing (parametric) approach in case of model mismatch.

* to be submitted to IEEE Trans. Sig. Proc 
  
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WATCH: Wasserstein Change Point Detection for High-Dimensional Time Series Data

Jan 18, 2022
Kamil Faber, Roberto Corizzo, Bartlomiej Sniezynski, Michael Baron, Nathalie Japkowicz

Detecting relevant changes in dynamic time series data in a timely manner is crucially important for many data analysis tasks in real-world settings. Change point detection methods have the ability to discover changes in an unsupervised fashion, which represents a desirable property in the analysis of unbounded and unlabeled data streams. However, one limitation of most of the existing approaches is represented by their limited ability to handle multivariate and high-dimensional data, which is frequently observed in modern applications such as traffic flow prediction, human activity recognition, and smart grids monitoring. In this paper, we attempt to fill this gap by proposing WATCH, a novel Wasserstein distance-based change point detection approach that models an initial distribution and monitors its behavior while processing new data points, providing accurate and robust detection of change points in dynamic high-dimensional data. An extensive experimental evaluation involving a large number of benchmark datasets shows that WATCH is capable of accurately identifying change points and outperforming state-of-the-art methods.

* 2021 IEEE International Conference on Big Data (Big Data) 
  
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Dynamic Gaussian Mixture based Deep Generative Model For Robust Forecasting on Sparse Multivariate Time Series

Mar 03, 2021
Yinjun Wu, Jingchao Ni, Wei Cheng, Bo Zong, Dongjin Song, Zhengzhang Chen, Yanchi Liu, Xuchao Zhang, Haifeng Chen, Susan Davidson

Forecasting on sparse multivariate time series (MTS) aims to model the predictors of future values of time series given their incomplete past, which is important for many emerging applications. However, most existing methods process MTS's individually, and do not leverage the dynamic distributions underlying the MTS's, leading to sub-optimal results when the sparsity is high. To address this challenge, we propose a novel generative model, which tracks the transition of latent clusters, instead of isolated feature representations, to achieve robust modeling. It is characterized by a newly designed dynamic Gaussian mixture distribution, which captures the dynamics of clustering structures, and is used for emitting timeseries. The generative model is parameterized by neural networks. A structured inference network is also designed for enabling inductive analysis. A gating mechanism is further introduced to dynamically tune the Gaussian mixture distributions. Extensive experimental results on a variety of real-life datasets demonstrate the effectiveness of our method.

* This paper is accepted by AAAI 2021 
  
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Deep Switching Auto-Regressive Factorization:Application to Time Series Forecasting

Sep 10, 2020
Amirreza Farnoosh, Bahar Azari, Sarah Ostadabbas

We introduce deep switching auto-regressive factorization (DSARF), a deep generative model for spatio-temporal data with the capability to unravel recurring patterns in the data and perform robust short- and long-term predictions. Similar to other factor analysis methods, DSARF approximates high dimensional data by a product between time dependent weights and spatially dependent factors. These weights and factors are in turn represented in terms of lower dimensional latent variables that are inferred using stochastic variational inference. DSARF is different from the state-of-the-art techniques in that it parameterizes the weights in terms of a deep switching vector auto-regressive likelihood governed with a Markovian prior, which is able to capture the non-linear inter-dependencies among weights to characterize multimodal temporal dynamics. This results in a flexible hierarchical deep generative factor analysis model that can be extended to (i) provide a collection of potentially interpretable states abstracted from the process dynamics, and (ii) perform short- and long-term vector time series prediction in a complex multi-relational setting. Our extensive experiments, which include simulated data and real data from a wide range of applications such as climate change, weather forecasting, traffic, infectious disease spread and nonlinear physical systems attest the superior performance of DSARF in terms of long- and short-term prediction error, when compared with the state-of-the-art methods.

  
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