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

Variational approach for learning Markov processes from time series data

Dec 11, 2017
Hao Wu, Frank Noé

Inference, prediction and control of complex dynamical systems from time series is important in many areas, including financial markets, power grid management, climate and weather modeling, or molecular dynamics. The analysis of such highly nonlinear dynamical systems is facilitated by the fact that we can often find a (generally nonlinear) transformation of the system coordinates to features in which the dynamics can be excellently approximated by a linear Markovian model. Moreover, the large number of system variables often change collectively on large time- and length-scales, facilitating a low-dimensional analysis in feature space. In this paper, we introduce a variational approach for Markov processes (VAMP) that allows us to find optimal feature mappings and optimal Markovian models of the dynamics from given time series data. The key insight is that the best linear model can be obtained from the top singular components of the Koopman operator. This leads to the definition of a family of score functions called VAMP-r which can be calculated from data, and can be employed to optimize a Markovian model. In addition, based on the relationship between the variational scores and approximation errors of Koopman operators, we propose a new VAMP-E score, which can be applied to cross-validation for hyper-parameter optimization and model selection in VAMP. VAMP is valid for both reversible and nonreversible processes and for stationary and non-stationary processes or realizations.

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Sensor selection on graphs via data-driven node sub-sampling in network time series

Apr 24, 2020
Yiye Jiang, Jérémie Bigot, Sofian Maabout

This paper is concerned by the problem of selecting an optimal sampling set of sensors over a network of time series for the purpose of signal recovery at non-observed sensors with a minimal reconstruction error. The problem is motivated by applications where time-dependent graph signals are collected over redundant networks. In this setting, one may wish to only use a subset of sensors to predict data streams over the whole collection of nodes in the underlying graph. A typical application is the possibility to reduce the power consumption in a network of sensors that may have limited battery supplies. We propose and compare various data-driven strategies to turn off a fixed number of sensors or equivalently to select a sampling set of nodes. We also relate our approach to the existing literature on sensor selection from multivariate data with a (possibly) underlying graph structure. Our methodology combines tools from multivariate time series analysis, graph signal processing, statistical learning in high-dimension and deep learning. To illustrate the performances of our approach, we report numerical experiments on the analysis of real data from bike sharing networks in different cities.

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Deeptime: a Python library for machine learning dynamical models from time series data

Oct 28, 2021
Moritz Hoffmann, Martin Scherer, Tim Hempel, Andreas Mardt, Brian de Silva, Brooke E. Husic, Stefan Klus, Hao Wu, Nathan Kutz, Steven L. Brunton, Frank Noé

Generation and analysis of time-series data is relevant to many quantitative fields ranging from economics to fluid mechanics. In the physical sciences, structures such as metastable and coherent sets, slow relaxation processes, collective variables dominant transition pathways or manifolds and channels of probability flow can be of great importance for understanding and characterizing the kinetic, thermodynamic and mechanistic properties of the system. Deeptime is a general purpose Python library offering various tools to estimate dynamical models based on time-series data including conventional linear learning methods, such as Markov state models (MSMs), Hidden Markov Models and Koopman models, as well as kernel and deep learning approaches such as VAMPnets and deep MSMs. The library is largely compatible with scikit-learn, having a range of Estimator classes for these different models, but in contrast to scikit-learn also provides deep Model classes, e.g. in the case of an MSM, which provide a multitude of analysis methods to compute interesting thermodynamic, kinetic and dynamical quantities, such as free energies, relaxation times and transition paths. The library is designed for ease of use but also easily maintainable and extensible code. In this paper we introduce the main features and structure of the deeptime software.

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A study of the Multicriteria decision analysis based on the time-series features and a TOPSIS method proposal for a tensorial approach

Oct 21, 2020
Betania S. C. Campello, Leonardo T. Duarte, João M. T. Romano

A number of Multiple Criteria Decision Analysis (MCDA) methods have been developed to rank alternatives based on several decision criteria. Usually, MCDA methods deal with the criteria value at the time the decision is made without considering their evolution over time. However, it may be relevant to consider the criteria' time series since providing essential information for decision-making (e.g., an improvement of the criteria). To deal with this issue, we propose a new approach to rank the alternatives based on the criteria time-series features (tendency, variance, etc.). In this novel approach, the data is structured in three dimensions, which require a more complex data structure, as the \textit{tensors}, instead of the classical matrix representation used in MCDA. Consequently, we propose an extension for the TOPSIS method to handle a tensor rather than a matrix. Computational results reveal that it is possible to rank the alternatives from a new perspective by considering meaningful decision-making information.

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Explaining Aviation Safety Incidents Using Deep Temporal Multiple Instance Learning

Feb 12, 2018
Vijay Manikandan Janakiraman

Although aviation accidents are rare, safety incidents occur more frequently and require a careful analysis to detect and mitigate risks in a timely manner. Analyzing safety incidents using operational data and producing event-based explanations is invaluable to airline companies as well as to governing organizations such as the Federal Aviation Administration (FAA) in the United States. However, this task is challenging because of the complexity involved in mining multi-dimensional heterogeneous time series data, the lack of time-step-wise annotation of events in a flight, and the lack of scalable tools to perform analysis over a large number of events. In this work, we propose a precursor mining algorithm that identifies events in the multidimensional time series that are correlated with the safety incident. Precursors are valuable to systems health and safety monitoring and in explaining and forecasting safety incidents. Current methods suffer from poor scalability to high dimensional time series data and are inefficient in capturing temporal behavior. We propose an approach by combining multiple-instance learning (MIL) and deep recurrent neural networks (DRNN) to take advantage of MIL's ability to learn using weakly supervised data and DRNN's ability to model temporal behavior. We describe the algorithm, the data, the intuition behind taking a MIL approach, and a comparative analysis of the proposed algorithm with baseline models. We also discuss the application to a real-world aviation safety problem using data from a commercial airline company and discuss the model's abilities and shortcomings, with some final remarks about possible deployment directions.

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Memristive LSTM network hardware architecture for time-series predictive modeling problem

Sep 10, 2018
Kazybek Adam, Kamilya Smagulova, Alex Pappachen James

Analysis of time-series data allows to identify long-term trends and make predictions that can help to improve our lives. With the rapid development of artificial neural networks, long short-term memory (LSTM) recurrent neural network (RNN) configuration is found to be capable in dealing with time-series forecasting problems where data points are time-dependent and possess seasonality trends. Gated structure of LSTM cell and flexibility in network topology (one-to-many, many-to-one, etc.) allows to model systems with multiple input variables and control several parameters such as the size of the look-back window to make a prediction and number of time steps to be predicted. These make LSTM attractive tool over conventional methods such as autoregression models, the simple average, moving average, naive approach, ARIMA, Holt's linear trend method, Holt's Winter seasonal method, and others. In this paper, we propose a hardware implementation of LSTM network architecture for time-series forecasting problem. All simulations were performed using TSMC 0.18um CMOS technology and HP memristor model.

* IEEE Asia Pacific Conference on Circuits and Systems, 2018 
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Time Series Imaging for Link Layer Anomaly Classification in Wireless Networks

Apr 02, 2021
Blaz Bertalanic, Marko Meza, Carolina Fortuna

The number of end devices that use the last mile wireless connectivity is dramatically increasing with the rise of smart infrastructures and require reliable functioning to support smooth and efficient business processes. To efficiently manage such massive wireless networks, more advanced and accurate network monitoring and malfunction detection solutions are required. In this paper, we perform a first time analysis of image-based representation techniques for wireless anomaly detection using recurrence plots and Gramian angular fields and propose a new deep learning architecture enabling accurate anomaly detection. We examine the relative performance of the proposed model and show that the image transformation of time series improves the performance of anomaly detection by up to 29% for binary classification and by up to 27% for multiclass classification. At the same time, the best performing model based on recurrence plot transformation leads to up to 55% increase compared to the state of the art where classical machine learning techniques are used. We also provide insights for the decisions of the classifier using an instance based approach enabled by insights into guided back-propagation. Our results demonstrate the potential of transformation of time series signals to images to improve classification performance compared to classification on raw time series data.

* 10 pages, 3 figures, 18 subfigures 
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On the suitability of generalized regression neural networks for GNSS position time series prediction for geodetic applications in geodesy and geophysics

May 22, 2020
M. Kiani

In this paper, the generalized regression neural network is used to predict the GNSS position time series. Using the IGS 24-hour final solution data for Bad Hamburg permanent GNSS station in Germany, it is shown that the larger the training of the network, the higher the accuracy is, regardless of the time span of the time series. In order to analyze the performance of the neural network in various conditions, 14 permanent stations are used in different countries, namely, Spain, France, Romania, Poland, Russian Federation, United Kingdom, Czech Republic, Sweden, Ukraine, Italy, Finland, Slovak Republic, Cyprus, and Greece. The performance analysis is divided into two parts, continuous data-without gaps-and discontinuous ones-having intervals of gaps with no data available. Three measure of error are presented, namely, symmetric mean absolute percentage error, standard deviation, and mean of absolute errors. It is shown that for discontinuous data the position can be predicted with an accuracy of up to 6 centimeters, while the continuous data positions present a higher prediction accuracy, as high as 3 centimeters. In order to compare the results of this machine learning algorithm with the traditional statistical approaches, the Theta method is used, which is well-established for high-accuracy time series prediction. The comparison shows that the generalized regression neural network machine learning algorithm presents better accuracy than the Theta method, possibly up to 250 times. In addition, it is approximately 4.6 times faster.

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An attention model to analyse the risk of agitation and urinary tract infections in people with dementia

Jan 18, 2021
Honglin Li, Roonak Rezvani, Magdalena Anita Kolanko, David J. Sharp, Maitreyee Wairagkar, Ravi Vaidyanathan, Ramin Nilforooshan, Payam Barnaghi

Behavioural symptoms and urinary tract infections (UTI) are among the most common problems faced by people with dementia. One of the key challenges in the management of these conditions is early detection and timely intervention in order to reduce distress and avoid unplanned hospital admissions. Using in-home sensing technologies and machine learning models for sensor data integration and analysis provides opportunities to detect and predict clinically significant events and changes in health status. We have developed an integrated platform to collect in-home sensor data and performed an observational study to apply machine learning models for agitation and UTI risk analysis. We collected a large dataset from 88 participants with a mean age of 82 and a standard deviation of 6.5 (47 females and 41 males) to evaluate a new deep learning model that utilises attention and rational mechanism. The proposed solution can process a large volume of data over a period of time and extract significant patterns in a time-series data (i.e. attention) and use the extracted features and patterns to train risk analysis models (i.e. rational). The proposed model can explain the predictions by indicating which time-steps and features are used in a long series of time-series data. The model provides a recall of 91\% and precision of 83\% in detecting the risk of agitation and UTIs. This model can be used for early detection of conditions such as UTIs and managing of neuropsychiatric symptoms such as agitation in association with initial treatment and early intervention approaches. In our study we have developed a set of clinical pathways for early interventions using the alerts generated by the proposed model and a clinical monitoring team has been set up to use the platform and respond to the alerts according to the created intervention plans.

* 11 pages 
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Discovering patterns of online popularity from time series

Apr 10, 2019
Mert Ozer, Anna Sapienza, Andrés Abeliuk, Goran Muric, Emilio Ferrara

How is popularity gained online? Is being successful strictly related to rapidly becoming viral in an online platform or is it possible to acquire popularity in a steady and disciplined fashion? What are other temporal characteristics that can unveil the popularity of online content? To answer these questions, we leverage a multi-faceted temporal analysis of the evolution of popular online contents. Here, we present dipm-SC: a multi-dimensional shape-based time-series clustering algorithm with a heuristic to find the optimal number of clusters. First, we validate the accuracy of our algorithm on synthetic datasets generated from benchmark time series models. Second, we show that dipm-SC can uncover meaningful clusters of popularity behaviors in a real-world Twitter dataset. By clustering the multidimensional time-series of the popularity of contents coupled with other domain-specific dimensions, we uncover two main patterns of popularity: bursty and steady temporal behaviors. Moreover, we find that the way popularity is gained over time has no significant impact on the final cumulative popularity.

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