Streaming Time Series Research Articles

A novel incremental ensemble learning for real-time explainable forecasting of electricity price

The development of a stable, safe, secure and sustainable energy future is a challenge for all countries these days. In terms of electricity price, its volatile nature makes its prediction a complex task. A precise real-time forecast of the electricity price can have significant consequences for the economy and risks faced. This work presents a new ensemble learning algorithm for making real-time predictions of electricity price in Spain. It combines long and short-term behavior patterns following an online incremental learning approach, keeping the model always up to date. The detection of novelties and unexpected behaviors in the time series streams allows the algorithm to provide more accurate predictions than the reference machine learning algorithms with which it is compared. In addition, the proposed algorithm predicts in real-time and the predictions obtained are interpretable, thus contributing to the Explainable Artificial Intelligence.

ADAPTATION OF THE ALGORITHM FOR DETECTING ANOMALIES IN TIME SERIES FOR NON-STATIONARY STREAMING DATA

Detection of anomalies in streaming time series data has become an important research topic due to the wide range of possible applications, including the detection of extreme weather conditions, malicious attacks on protected facilities, monitoring unauthorised gas and oil leaks, illegal pipeline connections, power cable faults, and water and other environmental pollution. Rapid detection of abnormal conditions and identifying these critical events is essential to protect lives and assets. Therefore, developing appropriate systems and detection methods is an urgent task. Anomaly detection in streaming data is challenging due to its large volume and high speed, presence of noise, and non-stationarity of the signal (or ‘concept drift’). The latter significantly complicates the identification of differences between new ‘typical’ behaviour and abnormal events. Solving this problem requires the algorithm for processing such data to learn and adapt to changing conditions. The paper proposes a modification of the algorithm for detecting anomalies in time series. This algorithm provides early detection of abnormal series in a massive collection of non-stationary streaming time series data. Anomalies are observations that are highly improbable given the previous time series values. The proposed approach is based on the primary detection of the predictive limit for the typical system behaviour using the theory of extreme values, followed by checking for the abnormality of the following series using the sliding window technique. The time series parameters are used as input data and compared by density distribution to detect any significant changes in the distribution of the characteristics. It allows the decision-making model to automatically adapt to the changing environment according to detected changes. Since anomalies are, by definition, exceptions to the typical behaviour of a system, most of the available stored data should reflect that typical behaviour of the system in question. It is unnecessary to have representative samples of all possible types of the standard behaviour of a given system for the algorithm to work well. The basic idea is to have a warm-up data set to obtain initial values for the decision model parameters. It makes it possible to determine if there is any significant difference between the last typical behaviour and the new typical behaviour. The proposed algorithm demonstrates its performance under conditions of noisy non-stationary data in several time series classes. Keywords: concept drift, extreme value theory, multivariate time series, outlier detection.

Memory Shapelet Learning for Early Classification of Streaming Time Series.

Early classification predicts the class of the incoming sequences before it is completely observed. How to quickly classify streaming time series without losing interpretability through early classification method is a challenging problem. A novel memory shapelet learning framework for early classification is proposed in this article. First, a memory distance matrix is introduced to store the historical characteristics of streaming time series, which can alleviate repetitive calculations caused by the growing length of time series. Second, early interpretable shapelets are extracted in the proposed method by optimizing both accuracy objective and earliness objective simultaneously. The proposed method employs end-to-end learning, which allows the model to directly learn early shapelets without the necessity of searching for numerous candidate shapelets. Third, an objective function of memory shapelet learning is proposed by overall considering accuracy and earliness, which can be optimized by gradient descent algorithm. Finally, experiments are conducted on benchmark dataset UCR, Tennessee Eastman process, and real-world aluminum electrolysis process in China. Comparable results with other state-of-the-art methods demonstrate the superior performance of the proposed method in interpretability, accuracy, earliness, and time complexity.

Analysis of irregularly sampled stream temperature time series: challenges and solutions

Water temperature is a key physical indicator of stream health, and as such, is commonly measured as part of long-term river health monitoring programs. However, analysis of long-term stream water temperature time series can be challenging, due to typically low frequencies of sampling combined with common characteristics of data collection from streams – such as observations unevenly spaced across seasons, changes to routine sampling frequencies, or improvements in the accuracy of measurements over time – known as sampling artifacts. While there are many models regularly used to estimate trends and summary statistics in long-term stream temperature datasets, there is limited understanding of the impact that commonly encountered sampling artifacts have on the accuracy and uncertainty of their estimates. This study constructed Monte-Carlo simulations to examine the influence that common sampling artifacts and the choice of analysis model can have on trend and mean estimates from long-term stream temperature time series covering tropical, temperate and cold climates. We found that, if not appropriately accounted for during analysis, sampling artifacts may obscure true trends or summary statistics, such as site means, and lead to inaccurate or misleading estimates. However, models that included components to account for seasonal variation within the model structure could estimate trends and means with high confidence, in the presence of almost all of the sampling artifacts commonly found in long-term stream temperature datasets. Structural biases in the time-of-day of sampling, such as always sampling in the morning, or where the start and end of the record are sampled at different times of day, could make estimates highly inaccurate and uncertain, and should be avoided in data collection strategies. This work aims to facilitate the analysis of historical stream temperature datasets with confidence, through identifying models that perform reliably in the presence of common sampling artifacts. The findings will enable further global insights into stream temperature, support management decisions based on accurate analysis and assist the design of future stream sampling programs using cost-effective, low-frequency sampling strategies.

Raising the ClaSS of Streaming Time Series Segmentation

Raising the ClaSS of Streaming Time Series Segmentation

Energy Efficient Streaming Time Series Classification with Attentive Power Iteration

Efficiently processing time series data streams in real-time on resource-constrained devices offers significant advantages in terms of enhanced computational energy efficiency and reduced time-related risks. We introduce an innovative streaming time series classification network that utilizes attentive power iteration, enabling real-time processing on resource-constrained devices. Our model continuously updates a compact representation of the entire time series, enhancing classification accuracy while conserving energy and processing time. Notably, it excels in streaming scenarios without requiring complete time series access, enabling swift decisions. Experimental results show that our approach excels in classification accuracy and energy efficiency, with over 70% less consumption and threefold faster task completion than benchmarks. This work advances real-time responsiveness, energy conservation, and operational effectiveness for constrained devices, contributing to optimizing various applications.

Subsequence Join in Streaming Time Series under Dynamic Time Warping

Subsequence join in time series is to search for couples of similar subsequences from multiple time series. The task is useful in data mining on time series; nevertheless, it is extremely difficult because of its enormous computational cost. The task should use normalized time series during the search execution and be performed under an efficient distance measure to obtain accurate resulting couples. The task is more challenging when it works in a streaming environment in which time-series data might be collected very quickly. To address this problem, we propose an efficient method of subsequence join in streaming time series under Dynamic Time Warping (DTW), supporting z-score normalization. The proposed method utilizes a technique of subsequence extraction based on major extrema of streaming time series to search for couples of similar subsequences from coevolving time series. This method can identify couples of similar subsequences of the same length or different lengths. The experimental results show that the proposed method has high performance and can bring out interesting couples of similar subsequences. In addition, this method acts as an approximation algorithm suitable for a streaming scenario where users often expect fast responses from the task of subsequence join over time-series streams of high rates.

FPCS: Feature Preserving Compensated Sampling of Streaming Time Series Data.

Data visualization aids in making data analysis more intuitive and in-depth, with widespread applications in fields such as biology, finance, and medicine. For massive and continuously growing streaming time series data, these data are typically visualized in the form of line charts, but the data transmission puts significant pressure on the network, leading to visualization lag or even failure to render completely. This paper proposes a universal sampling algorithm FPCS, which retains feature points from continuously received streaming time series data, compensates for the frequent fluctuating feature points, and aims to achieve efficient visualization. This algorithm bridges the gap in sampling for streaming time series data. The algorithm has several advantages: (1) It optimizes the sampling results by compensating for fewer feature points, retaining the visualization features of the original data very well, ensuring high-quality sampled data; (2) The execution time is the shortest compared to similar existing algorithms; (3) It has an almost negligible space overhead; (4) The data sampling process does not depend on the overall data; (5) This algorithm can be applied to infinite streaming data and finite static data.

Optimal sampling designs for multidimensional streaming time series with application to power grid sensor data

Optimal sampling designs for multidimensional streaming time series with application to power grid sensor data

Non‐crossing quantile double‐autoregression for the analysis of streaming time series data

Many financial time series not only have varying structures at different quantile levels and exhibit the phenomenon of conditional heteroscedasticity at the same time but also arrive in the stream. Quantile double‐autoregression is very useful for time series analysis but faces challenges with model fitting of streaming data sets when estimating other quantiles in subsequent batches. This article proposes a renewable estimation method for quantile double‐autoregression analysis of streaming time series data due to its ability to break with storage barrier and computational barrier. Moreover, the proposed flexible parametric structure of the quantile function enables us to predict any interested quantile value without quantile curve crossing problem or keeping the desirable monotone property of the conditional quantile function. The proposed methods are illustrated using current data and the summary statistics of historical data. Theoretically, the proposed statistic is shown to have the same asymptotic distribution as the standard version computed on an entire data stream with the data batches pooled into one data set, without additional condition. Simulation studies and an empirical example are presented to illustrate the finite sample performance of the proposed methods.

Multi‐output regression for imbalanced data stream

AbstractIn this article, we describe an imbalanced regression method for making predictions over imbalanced data streams. We present MORSTS (Multiple Output Regression for Streaming Time Series), an online ensemble regressors devoted to non‐stationary and imbalanced data streams. MORSTS relies on several multiple output regressor submodels, adopts a cost sensitive weighting technique for dealing with imbalanced datasets, and handles overfitting by means of the K‐fold cross validation. For assessment purposes, experiments have been conducted on known real datasets and compared with known base regression techniques.

Performance evaluation of artificial neural network model in hybrids with various preprocessors for river streamflow forecasting

Abstract Accurate forecasting of hydrological processes and sustainable management of water resources is inevitable, especially for flood control and water resource shortage crisis in low-water areas with an arid and semi-arid climate, which is a limitation for residents and various structures. The present study uses different data preprocessing techniques to deal with complex data and extract hidden features from the stream time series. In the next step, the decomposed time series were used, as input data, to the artificial neural network (ANN) model for streamflow modeling and forecasting. The preprocessors employed included discrete wavelet transform (DWT), empirical mode decomposition (EMD), complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), successive variational mode decomposition (SVMD), and multi-filter of the smoothing (MFS). These preprocessors were used in hybrid with the ANN model to forecast the daily streamflow. In general, the results showed that the optimal performance of hybrid models has two basic steps. The first step is choosing a suitable approach to utilizing the input data to the model. The second step is to use the appropriate preprocessor. Overall, the results show that the MFS-ANN model in short-term forecasting and the SVMD-ANN model in long-term forecasting performed better than other hybrid models.

Identifying novelties and anomalies for incremental learning in streaming time series forecasting

Time series data can be defined as a chronological sequence of observations on a variable of interest. A streaming time series is a time series that arrives continuously at high speed and has a data distribution that may change over time. Streaming time series data usually comes from electronic devices such as sensors and many of the applications dealing with streaming data in Industry 4.0 require real-time responses. Performing real-time forecasting offers the possibility to consider new types of patterns in the incoming streaming data, which is not possible when working with batch models. This paper presents a new approach to detect novelties and anomalies in real-time using a nearest-neighbors based forecasting algorithm. The algorithm works with an offline base model that is updated as stream data arrives following an incremental learning approach. It detects unknown patterns called novelties and anomalies. Novelties are included in the model in an online way and anomalies trigger an alarm as they present unexpected behaviors that need to be specifically analyzed. The algorithm has been tested with Spanish electricity demand data. Results show that the prediction errors obtained when the model is updated considering novelties and anomalies are lower than the errors obtained when the model is not updated. Thus, the model adjusts in real-time to the new patterns of data providing accurate errors and real-time predictions.

A novel distributed forecasting method based on information fusion and incremental learning for streaming time series

Real-time algorithms have to adapt and adjust to new incoming patterns to provide timely and accurate responses. This paper presents a new distributed forecasting algorithm for streaming time series called StreamWNN. StreamWNN starts with an offline stage in which a forecasting model based on tuples of information fusion is created with historical data. In particular, this model consists of the fusion of patterns composed of past values of the time series with the future values of their k-nearest neighbors. Afterwards, streaming data starts to arrive. The model is incrementally updated in the online stage using a buffer with streaming data that more accurately matches the current model patterns. The model can be updated daily, monthly, quarterly or based on error thresholds. The methodology has been applied to Spanish electricity demand time series providing more accurate results when the model is updated incrementally. The best error results are obtained with the daily update of the model, resulting in an error between 2% and 3.5% depending on the prediction horizon. The model provides better error results than other algorithms.

Параллельный алгоритм восстановления сенсорных данных в режиме реального времени для многоядерного процессора

Currently, in many subject areas, the processing of sensor data in real time assumes imputation of values missed due to a technical failure or a human factor. This article proposes a parallel algorithm for imputation the missing values of a streaming time series in real time for a many-core processor. The algorithm employs a set of reference time series that have a semantic relationship with the original time series. The algorithm exploits the following heuristics: if there are repeated (similar) subsequences in the reference time series, then in the time series containing the missing value, repeated subsequences occur in the same time intervals. For each reference time series, a query is defined as a subsequence of a given length ending at the moment when the value in the original time series was missed. The similarity of the subsequences with the query is determined based on the DTW (Dynamic Time Warping) measure that is of quadratic computational complexity relative to the subsequence length. The algorithm employs the lower bounding technique to discard subsequences that are obviously dissimilar to the query, without calculating DTW. The lower bounds have less complexity than DTW and are calculated in parallel. The imputed value is calculated as the arithmetic mean of the last elements of the found intervals. In computational experiments, the proposed algorithm demonstrates high imputation accuracy in comparison with analogs and performance acceptable for real-time applications.

A Framework for Similarity Search in Streaming Time Series based on Spark Streaming

A Framework for Similarity Search in Streaming Time Series based on Spark Streaming

Combining Filtering and Cross-Correlation Efficiently for Streaming Time Series

Monitoring systems have hundreds or thousands of distributed sensors gathering and transmitting real-time streaming data. The early detection of events in these systems, such as an earthquake in a seismic monitoring system, is the base for essential tasks as warning generations. To detect such events is usual to compute pairwise correlation across the disparate signals generated by the sensors. Since the data sources (e.g., sensors) are spatially separated, it is essential to consider the lagged correlation between the signals. Besides, many applications require to process a specific band of frequencies depending on the event’s type, demanding a pre-processing step of filtering before computing correlations. Due to the high speed of data generation and a large number of sensors in these systems, the operations of filtering and lagged cross-correlation need to be efficient to provide real-time responses without data losses. This article proposes a technique named FilCorr that efficiently computes both operations in one single step. We achieve an order of magnitude speedup by maintaining frequency transforms over sliding windows. Our method is exact, devoid of sensitive parameters, and easily parallelizable. Besides our algorithm, we also provide a publicly available real-time system named Seisviz that employs FilCorr in its core mechanism for monitoring a seismometer network. We demonstrate that our technique is suitable for several monitoring applications as seismic signal monitoring, motion monitoring, and neural activity monitoring.

An active adaptation strategy for streaming time series classification based on elastic similarity measures

In streaming time series classification problems, the goal is to predict the label associated to the most recently received observations over the stream according to a set of categorized reference patterns. In on-line scenarios, data arise from non-stationary processes, which results in a succession of different patterns or events. This work presents an active adaptation strategy that allows time series classifiers to accommodate to the dynamics of streamed time series data. Specifically, our approach consists of a classifier that detects changes between events over streaming time series. For this purpose, the classifier uses features of the dynamic time warping measure computed between the streamed data and a set of reference patterns. When classifying a streaming series, the proposed pattern end detector analyzes such features to predict changes and adapt off-line time series classifiers to newly arriving events. To evaluate the performance of the proposed scheme, we employ the pattern end detection model along with dynamic time warping-based nearest neighbor classifiers over a benchmark of ten time series classification problems. The obtained results present exciting insights into the detection accuracy and latency performance of the proposed strategy.

On the Evaluation, Management and Improvement of Data Quality in Streaming Time Series

The Internet of things (IoT) technologies plays a key role in the Fourth Industrial Revolution (Industry 4.0). It means the digitisation of the industry and its services to improve the productiveness. To achieve the necessary information throughout the different processes, useful data streams are obtained to provide the Artificial Intelligence and Big data algorithms. However, strategic decision-making based on these algorithms may not be successful if they have been developed based on inadequate low-quality data. This research work proposes a set of metrics to measure Data Quality (DQ) in streaming time series and implements and validates a set of techniques and tools that allow monitoring and improving the quality of the information. These techniques allow the early detection of problems that arise in relation to the quality of the data collected; and, in addition, they provide some mechanisms to solve these problems. Later, also as part of the work, a use case related to industrial field is presented, where these techniques and tools have been deployed into the data management, monitoring and data analysis platform. This integration provides additional functionality to the platform, a Decision Support System (DSS) named <i>DQ-REMAIN</i> (<i>Data Quality REport MAnagement and ImprovemeNt</i>), to decision-making regarding the quality of data obtained from streaming time series.

Hierarchical Multiresolution Representation of Streaming Time Series

• Generic time series representation model supporting streaming time series data mining at multiple time resolutions. • New representation based on the proposed model, considering fluctuations and continuity of modeled processes. • The application of the proposed model leads to higher and more stable processing speed at lower RAM consumption. • The proposed representation improves subsequent time series clustering. Real-time monitoring, analysis and operations in large industrial systems require an accurate but compact data model created on the basis of a large number of data sources continuously generating massive amounts of data modeled as streaming time series. This paper proposes a generic time series representation approach for reducing data model size and supporting streaming time series data mining at multiple time resolutions. The proposed Hierarchical Multiresolution Time Series Representation model utilizes a buffer-based approach that combines one-pass stream processing with hierarchical aggregation to achieve high processing speed without excessive hardware requirements. In addition, this paper presents a new representation based on the proposed model, Hierarchical Multiresolution Linear-function-based Piecewise Statistical Approximation. The proposed representation considers fluctuations and continuity of modeled processes in order to preserve fundamental characteristics of time series at reduced dimensionality. The usefulness of the proposed solution was proven in a case study. The case study results for generated data set confirm that the proposed model leads to higher and more stable processing speed at lower RAM consumption comparing to related model, especially when dealing with greater number of time resolutions. The case study results for real UK smart meter data confirm that the proposed representation leads to a reduced amount of information loss and an improvement in subsequent time series clustering comparing to related time series representation. Therefore, this paper's main contribution is multiresolution streaming time series data mining support convenient for application in large industrial systems.