Time Series Representation Method Research Articles

Distance- and Momentum-Based Symbolic Aggregate Approximation for Highly Imbalanced Classification.

Time-series representation is the most important task in time-series analysis. One of the most widely employed time-series representation method is symbolic aggregate approximation (SAX), which converts the results from piecewise aggregate approximation to a symbol sequence. SAX is a simple and effective method; however, it only focuses on the mean value of each segment in the time-series. Here, we propose a novel time-series representation method—distance- and momentum-based symbolic aggregate approximation (DM-SAX)—that can secure time-series distributions by calculating the perpendicular distance from the time-axis to each data point and consider the time-series trend by adding a momentum factor reflecting the direction of previous data points. Experimental results for 29 highly imbalanced classification problems on the UCR datasets revealed that DM-SAX affords the optimal area under the curve (AUC) among competing time-series representation methods (SAX, extreme-SAX, overlap-SAX, and distance-based SAX). We statistically verified that performance improvements resulted in significant differences in the rankings. In addition, DM-SAX yielded the optimal AUC for real-world wire cutting and crimping process dataset. Meaningful data points such as outliers could be identified in a time-series outlier detection framework via the proposed method.

Hexadecimal Aggregate Approximation Representation and Classification of Time Series Data

Time series data are widely found in finance, health, environmental, social, mobile and other fields. A large amount of time series data has been produced due to the general use of smartphones, various sensors, RFID and other internet devices. How a time series is represented is key to the efficient and effective storage and management of time series data, as well as being very important to time series classification. Two new time series representation methods, Hexadecimal Aggregate approXimation (HAX) and Point Aggregate approXimation (PAX), are proposed in this paper. The two methods represent each segment of a time series as a transformable interval object (TIO). Then, each TIO is mapped to a spatial point located on a two-dimensional plane. Finally, the HAX maps each point to a hexadecimal digit so that a time series is converted into a hex string. The experimental results show that HAX has higher classification accuracy than Symbolic Aggregate approXimation (SAX) but a lower one than some SAX variants (SAX-TD, SAX-BD). The HAX has the same space cost as SAX but is lower than these variants. The PAX has higher classification accuracy than HAX and is extremely close to the Euclidean distance (ED) measurement; however, the space cost of PAX is generally much lower than the space cost of ED. HAX and PAX are general representation methods that can also support geoscience time series clustering, indexing and query except for classification.

A Boundary Distance-Based Symbolic Aggregate Approximation Method for Time Series Data

A large amount of time series data is being generated every day in a wide range of sensor application domains. The symbolic aggregate approximation (SAX) is a well-known time series representation method, which has a lower bound to Euclidean distance and may discretize continuous time series. SAX has been widely used for applications in various domains, such as mobile data management, financial investment, and shape discovery. However, the SAX representation has a limitation: Symbols are mapped from the average values of segments, but SAX does not consider the boundary distance in the segments. Different segments with similar average values may be mapped to the same symbols, and the SAX distance between them is 0. In this paper, we propose a novel representation named SAX-BD (boundary distance) by integrating the SAX distance with a weighted boundary distance. The experimental results show that SAX-BD significantly outperforms the SAX representation, ESAX representation, and SAX-TD representation.

An Adversarial Examples Identification Method for Time Series in Internet-of-Things System

Adversarial examples (AEs) make Internet-of-Things (IoT) systems to face a great challenge. The tiny fluctuations in AEs mislead the learning model, let the model accept, and make wrong decisions. So, accurately identifying AEs is significant for improving the robustness in IoT systems. In this article, a method to identify AEs for time-series data is proposed. We analyze the characteristics of adversarial time-series examples and normal time-series samples and propose a time-series representation method. The tiny fluctuations in AEs are easily discovered by this representation. A metric is also designed to support this representation method to identify AEs with supervised learning and unsupervised learning methods. Our representation method and the metric is applied with supervised learning and unsupervised learning methods to identify time series in real data set and data sets in the official UCR repository. The experimental results show that our method has a great ability to identify AEs, compared to previous approaches.

Edge4TSC: Binary Distribution Tree-Enabled Time Series Classification in Edge Environment.

In the past decade, time series data have been generated from various fields at a rapid speed, which offers a huge opportunity for mining valuable knowledge. As a typical task of time series mining, Time Series Classification (TSC) has attracted lots of attention from both researchers and domain experts due to its broad applications ranging from human activity recognition to smart city governance. Specifically, there is an increasing requirement for performing classification tasks on diverse types of time series data in a timely manner without costly hand-crafting feature engineering. Therefore, in this paper, we propose a framework named Edge4TSC that allows time series to be processed in the edge environment, so that the classification results can be instantly returned to the end-users. Meanwhile, to get rid of the costly hand-crafting feature engineering process, deep learning techniques are applied for automatic feature extraction, which shows competitive or even superior performance compared to state-of-the-art TSC solutions. However, because time series presents complex patterns, even deep learning models are not capable of achieving satisfactory classification accuracy, which motivated us to explore new time series representation methods to help classifiers further improve the classification accuracy. In the proposed framework Edge4TSC, by building the binary distribution tree, a new time series representation method was designed for addressing the classification accuracy concern in TSC tasks. By conducting comprehensive experiments on six challenging time series datasets in the edge environment, the potential of the proposed framework for its generalization ability and classification accuracy improvement is firmly validated with a number of helpful insights.

A pattern representation of stock time series based on DTW

Time series analysis based on pattern discovery has received a lot of interests in the fields of economic physics and machine learning due to its simplicity and ability to reveal complex nonlinear behavior in stock market. Dynamic Time Warping (DTW) is a useful tool to extract morphological characteristics of time series for its capacity to cope with time shifts and warpings. In this paper, we propose a new time series representation method for stock time series based on dynamic time warping (DTW) called PR-DTW. A combinatorial optimization model with strict constraints is built to get the pattern representation of stock time series. To simplify the calculation, we construct another unconstrained global optimization problem whose optimal solution includes the optimal solution of the original combinatorial optimization problem based on a theorem proved in this paper. Particle Swarm Optimization algorithm is used to solve the global optimization problem, then the results can be converted into the optimal solution of the combinatorial optimization problem through a few simple formulas given in the theorem. The results of three classifiers (1NN, Decision Tree, Multi-layer Perceptron) implemented on 15 sectors in Chinese A-share market unanimously demonstrate that PR-DTW has the capability of extracting time series short-term patterns which is widely regarded as difficulty. And we conclude that PR-DTW has the capability of prevention of End Effect, anti-noise and segmentation. Moreover, by extracting the top ten patterns predicting stock’s rise and fall in short term (10 days) according to the ranking of stock’s rising probability in the next three days, we find out the short-term patterns obtained by PR-DTW have prospective directive to the stock trend analysis in short term.

Dynamic Adaptive Piecewise Linear Representation Approach Based on Streaming Time Series

With the burgeoning of IoE (Internet of Everything), massive numbers of IoT devices in extensive fields are continuously producing huge number of streaming time series. The high dimensionality and dynamic uncertainty of this kind of data lead to the main challenge on traditional time series data mining research. Accordingly, time series representation methods have been regarded as a necessary pre-processing tool to provide data support for the follow-up time series data mining research. In this paper, we propose a novel dynamic time series representation approach called dynamic adaptive piecewise linear representation (DAPLR) for streaming time series, which can automatically provide a series of piecewise linear representation results to meet the diverse needs of different users.

Clustering-based forecasting method for individual consumers electricity load using time series representations

Abstract This paper presents a new method for forecasting a load of individual electricity consumers using smart grid data and clustering. The data from all consumers are used for clustering to create more suitable training sets to forecasting methods. Before clustering, time series are efficiently preprocessed by normalisation and the computation of various model-based time series representation methods. Final centroid-based forecasts are scaled by saved normalisation parameters to create the forecast for every consumer. Our method is compared with the approach that creates forecasts for every consumer separately. Evaluation and experiments were conducted on three smart meter datasets from residences of Ireland and Australia, and factories of Slovakia. The achieved results proved that our clustering-based method improves forecasting accuracy mainly for residential consumers.We can also proclaim that it can be found such time series representation and clustering setting that will our forecasting method perform more accurately than fully disaggregated approach. Our method is also more scalable since it is necessary to train the model only on clusters and not for every consumer separately

Asymptotic Dynamic Time Warping calculation with utilizing value repetition

Dynamic Time Warping (DTW) is a popular method for measuring the similarity of time series. It is widely used in various domains. A major drawback of DTW is that it has a high computational complexity. To address this problem, pruning techniques to calculate the exact DTW distance, as well as DTW approximation methods, have become important approaches. In this paper, we introduce Blocked Dynamic Time Warping (BDTW), a new similarity measure which works on run-length encoded time series representation. BDTW utilizes any repetitive values (zero and nonzero) in time series to reduce DTW computation time. BDTW closely approximates DTW distance, and it is significantly faster than traditional DTW for time series with high levels of value repetition. Moreover, BDTW can be combined with time series representation methods which provide constant segments, to serve as a close approximation method even for the time series without value repetition. Constrained BDTW, BDTW upper bound and BDTW lower bound are discussed as variations of BDTW. BDTW upper bound and BDTW lower bound are presented as a new DTW upper bound and lower bound which can be efficiently applied on time series with high levels of value repetition for pruning unhopeful alignments and matches in the exact DTW calculation. We show the effectiveness of BDTW and its variations on different applications using the following datasets: Almanac of Minutely Power, Refit Smart Homes, as well as the 85 datasets from the University of California, Riverside time series classification archive (UCR archive).

An adaptive time series representation method for anode current signals in aluminium electrolysis

In aluminum electrolysis, anode current signals can not only provide an insight into the localized anodic dynamic behavior, but also can be used as a new way to study the process in the harsh industrial environment. This kind of the data is stored in the form of time series, which is a sequence of real numeric values. Because the data is huge and growing fast, the number of elements in anode current signals must be reduced to make further analysis much easier and faster, which is a typical time series representation problem. In this paper, an adaptive time series representation method for anode current signals is proposed for this purpose. The essence of this method is that the time series representation problem is transformed into the optimization problem. In addition, a new cognitively inspired optimization method named state transition algorithm (STA) is introduced to solve the optimization problem. The experimental results indicate that the proposed method outperforms common methods used for time series representation in aluminum electrolysis.

Process monitoring using maximum sequence divergence

Process Monitoring involves tracking a system's behaviors, evaluating the current state of the system, and discovering interesting events that require immediate actions. In this paper, we consider monitoring temporal system state sequences to help detect the changes of dynamic systems, check the divergence of the system development, and evaluate the significance of the deviation. We begin with discussions of data reduction, symbolic data representation, and the anomaly detection in temporal discrete sequences. Time-series representation methods are also discussed and used in this paper to discretize raw data into sequences of system states. Markov Chains and stationary state distributions are continuously generated from temporal sequences to represent snapshots of the system dynamics in different time frames. We use generalized Jensen-Shannon Divergence as the measure to monitor changes of the stationary symbol probability distributions and evaluate the significance of system deviations. We prove that the proposed approach is able to detect deviations of the systems we monitor and assess the deviation significance in probabilistic manner.

Predefined pattern detection in large time series

Predefined pattern detection from time series is an interesting and challenging task. In order to reduce its computational cost and increase effectiveness, a number of time series representation methods and similarity measures have been proposed. Most of the existing methods focus on full sequence matching, that is, sequences with clearly defined beginnings and endings, where all data points contribute to the match. These methods, however, do not account for temporal and magnitude deformations in the data and result to be ineffective on several real-world scenarios where noise and external phenomena introduce diversity in the class of patterns to be matched. In this paper, we present a novel pattern detection method, which is based on the notions of templates, landmarks, constraints and trust regions. We employ the Minimum Description Length (MDL) principle for time series preprocessing step, which helps to preserve all the prominent features and prevents the template from overfitting. Templates are provided by common users or domain experts, and represent interesting patterns we want to detect from time series. Instead of utilising templates to match all the potential subsequences in the time series, we translate the time series and templates into landmark sequences, and detect patterns from landmark sequence of the time series. Through defining constraints within the template landmark sequence, we effectively extract all the landmark subsequences from the time series landmark sequence, and obtain a number of landmark segments (time series subsequences or instances). We model each landmark segment through scaling the template in both temporal and magnitude dimensions. To suppress the influence of noise, we introduce the concept of trust region, which not only helps to achieve an improved instance model, but also helps to catch the accurate boundaries of instances of the given template. Based on the similarities derived from instance models, we introduce the probability density function to calculate a similarity threshold. The threshold can be used to judge if a landmark segment is a true instance of the given template or not. To evaluate the effectiveness and efficiency of the proposed method, we apply it to two real-world datasets. The results show that our method is capable of detecting patterns of temporal and magnitude deformations with competitive performance.

Piecewise aggregate approximation based on the major shape features of time series

Piecewise aggregate approximation (PAA) is one of the most widely used time series representation methods in which subsequences of the time series are replaced with their mean values. Extensions of the PAA technique are often used in time series data mining. In this paper, we propose a new piecewise aggregate approximation method based on the major shape features of the time series and a novel distance measure. The major shape features, including the average (mean), slope, curvature and rate of change of the curvature, are used to describe the characteristics of each subsequence of the time series. The distance function used to measure the similarity between two time series satisfies a lower bound on the Euclidean distance, which guarantees that false dismissal is avoided when the distance measure is used in time series indexing and similarity searching. Through several experiments, we demonstrate that the proposed approach not only provides a good fit to the time series and improves the tightness of the lower bound but also achieves improved time series classification accuracy with a low dimensionality.

Investigation of Time Series Representations and Similarity Measures for Structural Damage Pattern Recognition

This paper investigates the time series representation methods and similarity measures for sensor data feature extraction and structural damage pattern recognition. Both model-based time series representation and dimensionality reduction methods are studied to compare the effectiveness of feature extraction for damage pattern recognition. The evaluation of feature extraction methods is performed by examining the separation of feature vectors among different damage patterns and the pattern recognition success rate. In addition, the impact of similarity measures on the pattern recognition success rate and the metrics for damage localization are also investigated. The test data used in this study are from the System Identification to Monitor Civil Engineering Structures (SIMCES) Z24 Bridge damage detection tests, a rigorous instrumentation campaign that recorded the dynamic performance of a concrete box-girder bridge under progressively increasing damage scenarios. A number of progressive damage test case datasets and damage test data with different damage modalities are used. The simulation results show that both time series representation methods and similarity measures have significant impact on the pattern recognition success rate.

시계열 분류를 위한 PIPs 탐지와 Persist 이산화 기법들을 결합한 시계열 표현

Various time series representation methods have been suggested in order to process time series data efficiently and effectively. SAX is the representative time series representation method combining segmentation and discretization techniques, which has been successfully applied to the time series classification task. But SAX requires a large number of segments in order to represent the meaningful dynamic patterns of time series accurately, since it loss the dynamic property of time series in the course of smoothing the movement of time series. Therefore, this paper suggests a new time series representation method that combines PIPs detection and Persist discretization techniques. The suggested method represents the dynamic movement of high-diemensional time series in a lower dimensional space by detecting PIPs indicating the important inflection points of time series. And it determines the optimal discretizaton ranges by applying self-transition and marginal probabilities distributions to KL divergence measure. It minimizes the information loss in process of the dimensionality reduction. The suggested method enhances the performance of time series classification task by minimizing the information loss in the course of dimensionality reduction.