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

EigenNetworks

Jun 05, 2018
Jonathan Mei, José M. F. Moura

In many applications, the interdependencies among a set of $N$ time series $\{ x_{nk}, k>0 \}_{n=1}^{N}$ are well captured by a graph or network $G$. The network itself may change over time as well (i.e., as $G_k$). We expect the network changes to be at a much slower rate than that of the time series. This paper introduces eigennetworks, networks that are building blocks to compose the actual networks $G_k$ capturing the dependencies among the time series. These eigennetworks can be estimated by first learning the time series of graphs $G_k$ from the data, followed by a Principal Network Analysis procedure. Algorithms for learning both the original time series of graphs and the eigennetworks are presented and discussed. Experiments on simulated and real time series data demonstrate the performance of the learning and the interpretation of the eigennetworks.

  
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Geometric feature performance under downsampling for EEG classification tasks

Feb 15, 2021
Bryan Bischof, Eric Bunch

We experimentally investigate a collection of feature engineering pipelines for use with a CNN for classifying eyes-open or eyes-closed from electroencephalogram (EEG) time-series from the Bonn dataset. Using the Takens' embedding--a geometric representation of time-series--we construct simplicial complexes from EEG data. We then compare $\epsilon$-series of Betti-numbers and $\epsilon$-series of graph spectra (a novel construction)--two topological invariants of the latent geometry from these complexes--to raw time series of the EEG to fill in a gap in the literature for benchmarking. These methods, inspired by Topological Data Analysis, are used for feature engineering to capture local geometry of the time-series. Additionally, we test these feature pipelines' robustness to downsampling and data reduction. This paper seeks to establish clearer expectations for both time-series classification via geometric features, and how CNNs for time-series respond to data of degraded resolution.

* 10 pages 
  
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RobustPeriod: Time-Frequency Mining for Robust Multiple Periodicities Detection

Feb 21, 2020
Qingsong Wen, Kai He, Liang Sun, Yingying Zhang, Min Ke, Huan Xu

Periodicity detection is an important task in time series analysis as it plays a crucial role in many time series tasks such as classification, clustering, compression, anomaly detection, and forecasting. It is challenging due to the following reasons: 1, complicated non-stationary time series; 2, dynamic and complicated periodic patterns, including multiple interlaced periodic components; 3, outliers and noises. In this paper, we propose a robust periodicity detection algorithm to address these challenges. Our algorithm applies maximal overlap discrete wavelet transform to transform the time series into multiple temporal-frequency scales such that different periodicities can be isolated. We rank them by wavelet variance and then at each scale, and then propose Huber-periodogram by formulating the periodogram as the solution to M-estimator for introducing robustness. We rigorously prove the theoretical properties of Huber-periodogram and justify the use of Fisher's test on Huber-periodogram for periodicity detection. To further refine the detected periods, we compute unbiased autocorrelation function based on Wiener-Khinchin theorem from Huber-periodogram for improved robustness and efficiency. Experiments on synthetic and real-world datasets show that our algorithm outperforms other popular ones for both single and multiple periodicity detection. It is now implemented and provided as a public online service at Alibaba Group and has been used extensive in different business lines.

* 9 pages, 7 figures, and 4 tables 
  
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Prediction Algorithm for Heat Demand of Science and Technology Topics Based on Time Convolution Network

Mar 21, 2022
Cui Haiyan, Li Yawen, Xu Xin

Thanks to the rapid development of deep learning, big data analysis technology is not only widely used in the field of natural language processing, but also more mature in the field of numerical prediction. It is of great significance for the subject heat prediction and analysis of science and technology demand data. How to apply theme features to accurately predict the theme heat of science and technology demand is the core to solve this problem. In this paper, a prediction method of subject heat of science and technology demand based on time convolution network (TCN) is proposed to obtain the subject feature representation of science and technology demand. Time series prediction is carried out based on TCN network and self attention mechanism, which increases the accuracy of subject heat prediction of science and technology demand data Experiments show that the prediction accuracy of this algorithm is better than other time series prediction methods on the real science and technology demand datasets.

  
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OPP-Miner: Order-preserving sequential pattern mining

Feb 09, 2022
Youxi Wu, Qian Hu, Yan Li, Lei Guo, Xingquan Zhu, Xindong Wu

A time series is a collection of measurements in chronological order. Discovering patterns from time series is useful in many domains, such as stock analysis, disease detection, and weather forecast. To discover patterns, existing methods often convert time series data into another form, such as nominal/symbolic format, to reduce dimensionality, which inevitably deviates the data values. Moreover, existing methods mainly neglect the order relationships between time series values. To tackle these issues, inspired by order-preserving matching, this paper proposes an Order-Preserving sequential Pattern (OPP) mining method, which represents patterns based on the order relationships of the time series data. An inherent advantage of such representation is that the trend of a time series can be represented by the relative order of the values underneath the time series data. To obtain frequent trends in time series, we propose the OPP-Miner algorithm to mine patterns with the same trend (sub-sequences with the same relative order). OPP-Miner employs the filtration and verification strategies to calculate the support and uses pattern fusion strategy to generate candidate patterns. To compress the result set, we also study finding the maximal OPPs. Experiments validate that OPP-Miner is not only efficient and scalable but can also discover similar sub-sequences in time series. In addition, case studies show that our algorithms have high utility in analyzing the COVID-19 epidemic by identifying critical trends and improve the clustering performance.

  
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Remaining Useful Life Estimation Using Functional Data Analysis

Apr 12, 2019
Qiyao Wang, Shuai Zheng, Ahmed Farahat, Susumu Serita, Chetan Gupta

Remaining Useful Life (RUL) of an equipment or one of its components is defined as the time left until the equipment or component reaches its end of useful life. Accurate RUL estimation is exceptionally beneficial to Predictive Maintenance, and Prognostics and Health Management (PHM). Data driven approaches which leverage the power of algorithms for RUL estimation using sensor and operational time series data are gaining popularity. Existing algorithms, such as linear regression, Convolutional Neural Network (CNN), Hidden Markov Models (HMMs), and Long Short-Term Memory (LSTM), have their own limitations for the RUL estimation task. In this work, we propose a novel Functional Data Analysis (FDA) method called functional Multilayer Perceptron (functional MLP) for RUL estimation. Functional MLP treats time series data from multiple equipment as a sample of random continuous processes over time. FDA explicitly incorporates both the correlations within the same equipment and the random variations across different equipment's sensor time series into the model. FDA also has the benefit of allowing the relationship between RUL and sensor variables to vary over time. We implement functional MLP on the benchmark NASA C-MAPSS data and evaluate the performance using two popularly-used metrics. Results show the superiority of our algorithm over all the other state-of-the-art methods.

* Accepted by IEEE International Conference on Prognostics and Health Management 2019 
  
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Identifying nonlinear dynamical systems via generative recurrent neural networks with applications to fMRI

Feb 19, 2019
Georgia Koppe, Hazem Toutounji, Peter Kirsch, Stefanie Lis, Daniel Durstewitz

A major tenet in theoretical neuroscience is that cognitive and behavioral processes are ultimately implemented in terms of the neural system dynamics. Accordingly, a major aim for the analysis of neurophysiological measurements should lie in the identification of the computational dynamics underlying task processing. Here we advance a state space model (SSM) based on generative piecewise-linear recurrent neural networks (PLRNN) to assess dynamics from neuroimaging data. In contrast to many other nonlinear time series models which have been proposed for reconstructing latent dynamics, our model is easily interpretable in neural terms, amenable to systematic dynamical systems analysis of the resulting set of equations, and can straightforwardly be transformed into an equivalent continuous-time dynamical system. The major contributions of this paper are the introduction of a new observation model suitable for functional magnetic resonance imaging (fMRI) coupled to the latent PLRNN, an efficient stepwise training procedure that forces the latent model to capture the 'true' underlying dynamics rather than just fitting (or predicting) the observations, and of an empirical measure based on the Kullback-Leibler divergence to evaluate from empirical time series how well this goal of approximating the underlying dynamics has been achieved. We validate and illustrate the power of our approach on simulated 'ground-truth' dynamical (benchmark) systems as well as on actual experimental fMRI time series. Given that fMRI is one of the most common techniques for measuring brain activity non-invasively in human subjects, this approach may provide a novel step toward analyzing aberrant (nonlinear) dynamics for clinical assessment or neuroscientific research.

  
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Hierarchical Clustering using Auto-encoded Compact Representation for Time-series Analysis

Jan 11, 2021
Soma Bandyopadhyay, Anish Datta, Arpan Pal

Getting a robust time-series clustering with best choice of distance measure and appropriate representation is always a challenge. We propose a novel mechanism to identify the clusters combining learned compact representation of time-series, Auto Encoded Compact Sequence (AECS) and hierarchical clustering approach. Proposed algorithm aims to address the large computing time issue of hierarchical clustering as learned latent representation AECS has a length much less than the original length of time-series and at the same time want to enhance its performance.Our algorithm exploits Recurrent Neural Network (RNN) based under complete Sequence to Sequence(seq2seq) autoencoder and agglomerative hierarchical clustering with a choice of best distance measure to recommend the best clustering. Our scheme selects the best distance measure and corresponding clustering for both univariate and multivariate time-series. We have experimented with real-world time-series from UCR and UCI archive taken from diverse application domains like health, smart-city, manufacturing etc. Experimental results show that proposed method not only produce close to benchmark results but also in some cases outperform the benchmark.

* 6 figures, 8 pages , 6 tables, accepted and presented conference IJCAI-PRICAI LDRC Learning Data Representation for Clustering (LDRC) workshop 2020 https://ldrcworkshop.github.io/LDRC2020/ 
  
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Causal Inference for Time series Analysis: Problems, Methods and Evaluation

Feb 11, 2021
Raha Moraffah, Paras Sheth, Mansooreh Karami, Anchit Bhattacharya, Qianru Wang, Anique Tahir, Adrienne Raglin, Huan Liu

Time series data is a collection of chronological observations which is generated by several domains such as medical and financial fields. Over the years, different tasks such as classification, forecasting, and clustering have been proposed to analyze this type of data. Time series data has been also used to study the effect of interventions over time. Moreover, in many fields of science, learning the causal structure of dynamic systems and time series data is considered an interesting task which plays an important role in scientific discoveries. Estimating the effect of an intervention and identifying the causal relations from the data can be performed via causal inference. Existing surveys on time series discuss traditional tasks such as classification and forecasting or explain the details of the approaches proposed to solve a specific task. In this paper, we focus on two causal inference tasks, i.e., treatment effect estimation and causal discovery for time series data, and provide a comprehensive review of the approaches in each task. Furthermore, we curate a list of commonly used evaluation metrics and datasets for each task and provide in-depth insight. These metrics and datasets can serve as benchmarks for research in the field.

  
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Integrating Domain Knowledge in Data-driven Earth Observation with Process Convolutions

Apr 16, 2021
Daniel Heestermans Svendsen, Maria Piles, Jordi Muñoz-Marí, David Luengo, Luca Martino, Gustau Camps-Valls

The modelling of Earth observation data is a challenging problem, typically approached by either purely mechanistic or purely data-driven methods. Mechanistic models encode the domain knowledge and physical rules governing the system. Such models, however, need the correct specification of all interactions between variables in the problem and the appropriate parameterization is a challenge in itself. On the other hand, machine learning approaches are flexible data-driven tools, able to approximate arbitrarily complex functions, but lack interpretability and struggle when data is scarce or in extrapolation regimes. In this paper, we argue that hybrid learning schemes that combine both approaches can address all these issues efficiently. We introduce Gaussian process (GP) convolution models for hybrid modelling in Earth observation (EO) problems. We specifically propose the use of a class of GP convolution models called latent force models (LFMs) for EO time series modelling, analysis and understanding. LFMs are hybrid models that incorporate physical knowledge encoded in differential equations into a multioutput GP model. LFMs can transfer information across time-series, cope with missing observations, infer explicit latent functions forcing the system, and learn parameterizations which are very helpful for system analysis and interpretability. We consider time series of soil moisture from active (ASCAT) and passive (SMOS, AMSR2) microwave satellites. We show how assuming a first order differential equation as governing equation, the model automatically estimates the e-folding time or decay rate related to soil moisture persistence and discovers latent forces related to precipitation. The proposed hybrid methodology reconciles the two main approaches in remote sensing parameter estimation by blending statistical learning and mechanistic modeling.

  
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