Time Series Search Research Articles

Querying Similar Multi-Dimensional Time Series with a Spatial Database

Similar time series search is one of the most important time series mining tasks in our daily life. As recent advances in sensor technologies accumulate abundant multi-dimensional time series data associated with multivariate quantities, it becomes a privilege to adapt similar time series searches for large-scale and multi-dimensional time series data. However, traditional similar time series search methods are mainly designed for one-dimensional time series, while advanced methods applicable for multi-dimensional time series data are largely immature and, more importantly, are not friendly to users from the domain of geography. As an alternative, we propose a novel method to search similar multi-dimensional time series with spatial databases. Compared with traditional methods that often conduct the similarity search based on features of the raw time series data sequence, the proposed method stores multi-dimensional time series as spatial objects in a spatial database, and then searches similar time series based on their spatial features. To demonstrate the validity of the proposed method, we analyzed the correlation between temporal features of the raw time series and spatial features of their corresponding spatial objects theoretically and empirically. Results indicate that the proposed method can not only support similar multi-dimensional time series searches but also markedly improve its efficiency under many specific scenarios. We believe that such a new paradigm will shed further light on the similarity search in large-scale multi-dimensional time series data, and will lower the barrier for users familiar with spatial databases to conduct complex time series mining tasks.

SAXRegEx: Multivariate time series pattern search with symbolic representation, regular expression, and query expansion

We present SAXRegEx, a method for pattern search in multivariate time series in the presence of various distortions, such as duration variation, warping, and time delay between signals. For example, in the automotive industry, calibration engineers spontaneously search for event-induced patterns in new measurements under time pressure. Current methods do not sufficiently address duration (horizontal along the time axis) scaling and inter-track time delay. One reason is that it can be overwhelmingly complex to consider scaling and warping jointly and analyze temporal dynamics and attribute interrelation simultaneously. SAXRegEx meets this challenge with a novel symbolic representation adapted to handle time series with multiple tracks. We employ methods from text retrieval, i.e., regular expression matching, to perform a pattern retrieval and develop a novel query expansion algorithm to deal flexibly with pattern distortions. Experiments show the effectiveness of our approach, especially in the presence of such distortions, and its efficiency surpassing the benchmarking methods. We have developed a user interface with the emphasis on multivariate query definition with inter-track time shifts and algorithm parameter setting. While we design the method primarily for automotive data, it is well transferable to other domains.

Efficient Range and kNN Twin Subsequence Search in Time Series

Analyzing time series data is crucial for many applications. In particular, subsequence search refers to finding subsequences within an input time series T that are similar to a query sequence Q. Existing subsequence search approaches typically employ Euclidean distance or Dynamic Time Warping as similarity measures and address range queries. In this paper, we focus on Chebyshev distance, which is the largest difference between each individual pair of points across the entire length of two compared subsequences. We call such similar pairstwins. We first show how existing time series indices can be extended to perform twin subsequence search. Then, we introduce TS-Index, a novel index tailored to the computation of twin subsequence search queries. Moreover, given that specifying a distance threshold is often not straightforward, we show how TS-Index can also be used to evaluate kNN queries. Our extensive experimental evaluation compares these approaches using real time series datasets. The results demonstrate that TS-Index can retrieve twin subsequences faster than all other methods under various conditions.

PSEUDo: Interactive Pattern Search in Multivariate Time Series with Locality-Sensitive Hashing and Relevance Feedback.

We present PSEUDo, a visual pattern retrieval tool for multivariate time series. It aims to overcome the uneconomic (re-)training problem accompanying deep learning-based methods. Very high-dimensional time series emerge on an unprecedented scale due to increasing sensor usage and data storage. Visual pattern search is one of the most frequent tasks on time series. Automatic pattern retrieval methods often suffer from inefficient training data, a lack of ground truth labels, and a discrepancy between the similarity perceived by the algorithm and required by the user or the task. Our proposal is based on the query-aware locality-sensitive hashing technique to create a representation of multivariate time series windows. It features sub-linear training and inference time with respect to data dimensions. This performance gain allows an instantaneous relevance-feedback-driven adaption to converge to users' similarity notion. We demonstrate PSEUDo's performance in terms of accuracy, speed, steerability, and usability through quantitative benchmarks with representative time series retrieval methods and a case study. We find that PSEUDo detects patterns in high-dimensional time series efficiently, improves the result with relevance feedback through feature selection, and allows an understandable as well as user-friendly retrieval process.

A Novel Deep Learning Approach for Anomaly Detection of Time Series Data

Anomalies in time series, also called “discord,” are the abnormal subsequences. The occurrence of anomalies in time series may indicate that some faults or disease will occur soon. Therefore, development of novel computational approaches for anomaly detection (discord search) in time series is of great significance for state monitoring and early warning of real-time system. Previous studies show that many algorithms were successfully developed and were used for anomaly classification, e.g., health monitoring, traffic detection, and intrusion detection. However, the anomaly detection of time series was not well studied. In this paper, we proposed a long short-term memory- (LSTM-) based anomaly detection method (LSTMAD) for discord search from univariate time series data. LSTMAD learns the structural features from normal (nonanomalous) training data and then performs anomaly detection via a statistical strategy based on the prediction error for observed data. In our experimental evaluation using public ECG datasets and real-world datasets, LSTMAD detects anomalies more accurately than other existing approaches in comparison.

EPLA-DSTree: Extending Piecewise Linear Approximation on a Dynamic Segmentation Tree Index in Sensor-Cloud Systems

In sensor-cloud applications, a huge amount of time series are generated. Efficient similarity search approaches are necessary for processing these sensor time series data. Concerning of time series search, whole matching similarity search and subsequence similarity search are two main research focuses. In this paper, we study the whole matching similarity search problem. We propose EPLA-DSTree, which extends piecewise linear approximation on a dynamic segmentation tree index for whole matching on time series. Compared with DSTree, EPLA-DSTree improves data locality of nodes by a better time series representation. EPLA-DSTree has a tighter lower bound for nodes which leads to a better query performance. Experiments show that it has a less index building time and a better query performance. To meet the requirements of sensor-cloud applications, we present an parallel EPLA-DSTree on MapReduce, which is a popular cloud programming model.

Optimal solutions for online conversion problems with interrelated prices

We consider various online conversion problems with interrelated prices. The first variant is the online time series search problem with unknown bounds on the relative price change factors. We design the optimal online algorithm IPN to solve this problem. We then consider the time series search with known bounds. Using the already established UND algorithm of Zhang et al. (J Comb Optim 23(2):159–166, 2012), we develop a new optimal online algorithm oUND which improves the experimental performance of the already existing optimal online algorithm for selected parameter constellations. We conduct a comparative experimental testing of UND and oUND and establish the parameter combinations for which one algorithm is better than the other. We then combine these two algorithms into a new one called cUND. This algorithm incorporates the strengths of UND and oUND and is also optimal online. Finally, we consider another variant, the general k-max search problem with interrelated prices, and also develop an optimal online algorithm.

On the Competitive Analysis for the Multi-Objective Time Series Search Problem

On the Competitive Analysis for the Multi-Objective Time Series Search Problem

Local Recurrence Rates with Automatic Time Windows for Discord Search in Multivariate Time Series

Discord search in time series data plays an important role in analyzing data collected from the manufacturing site. By identifying anomalous subsequences of time series data collected from manufacturing machines, the issue of malfunction can be detected based on the evaluation of operating conditions. Recently, the method called Local Recurrence Rate based Discord Search (LRRDS) was proposed to convert time series data to Recurrence Plot (RP) for further discord investigation. Although LRRDS shows promising performance, it will need to pre-determine the window size for local search and might miss the discord if the small time series data is used for scanning. In this research, an improved computational framework for discord search under LRRDS is proposed. First, the time series data is transformed as a single image by utilizing the recurrence plot (RP)-based method and the Kullblack-Leibler Divergence is used to provide more accurate distance measures to its RP formulation. Second, the subsequence search is performed through automatic time window local search. The time window is adjusted to the characteristic of the element exists in the time window. Then, each corresponding subsequence could be compared with the other non-overlapping neighbor subsequences. Subsequences with the largest value of dissimilarity are considered the discord by the algorithm. The results show that the proposed approach can detect discords and works well under smaller data sizes without pre-determining the size of the windows.

SSTS: A syntactic tool for pattern search on time series

Nowadays, data scientists are capable of manipulating and extracting complex information from time series data, given the current diversity of tools at their disposal. However, the plethora of tools that target data exploration and pattern search may require an extensive amount of time to develop methods that correspond to the data scientist's reasoning, in order to solve their queries. The development of new methods, tightly related with the reasoning and visual analysis of time series data, is of great relevance to improving complexity and productivity of pattern and query search tasks. In this work, we propose a novel tool, capable of exploring time series data for pattern and query search tasks in a set of 3 symbolic steps: Pre-Processing, Symbolic Connotation and Search. The framework is called SSTS (Symbolic Search in Time Series) and uses regular expression queries to search the desired patterns in a symbolic representation of the signal. By adopting a set of symbolic methods, this approach has the purpose of increasing the expressiveness in solving standard pattern and query tasks, enabling the creation of queries more closely related to the reasoning and visual analysis of the signal. We demonstrate the tool's effectiveness by presenting 9 examples with several types of queries on time series. The SSTS queries were compared with standard code developed in Python, in terms of cognitive effort, vocabulary required, code length, volume, interpretation and difficulty metrics based on the Halstead complexity measures. The results demonstrate that this methodology is a valid approach and delivers a new abstraction layer on data analysis of time series.

Optimal solutions for the online time series search and one-way trading problem with interrelated prices and a profit function

Abstract We consider the online problems of time series search and one-way trading with interrelated prices. We derive two algorithms PUND and PDIV which extend the solutions found in literature with profit functions, derive the competitive ratio and prove optimality. For the new as well as for the established online algorithms, we give a numerical example. For the time series search problem with interrelated prices, we present another algorithm UND∗. This algorithm has constant time complexity and an explicit formula for the competitive ratio and selected period to sell. The current solution in literature has linear time complexity and no such explicit formulas.

Optimal online algorithms for the multi-objective time series search problem

Tiedemann et al. (2015) [8] formulated multi-objective online problems and several measures of the competitive analysis, and showed best possible online algorithms for the multi-objective time series search problem with respect to those measures of the competitive analysis. In this paper, we present modified definitions of the competitive analysis for multi-objective online problems and propose a simple online algorithm Balanced Price Policy (bppk) for the multi-objective (k-objective) time series search problem. Under the modified framework, we show that the algorithm bppk is best possible with respect to any measure of the competitive analysis and we also derive best possible values of the competitive ratio for the multi-objective time series search problem with respect to several natural measures of the competitive analysis.

Unsupervised Distance Learning for Plant Species Identification

Phenology is among the most trustworthy indicators of climate change effects on plants and animals. The recent application of repeated digital photographs to monitor vegetation phenology has provided accurate measures of plant life cycle changes over time. A fundamental requirement for phenology studies refers to the correct recognition of phenological patterns from plants by taking into account time series associated with their crowns. This paper presents a new similarity measure for identifying plants based on the use of an unsupervised distance learning scheme, instead of using traditional approaches based on pairwise similarities. We experimentally show that its use yields considerable improvements in time-series search tasks. In addition, we also demonstrate how the late fusion of different time series can improve the results on plant species identification.In some cases, significant gains were observed (up to +8.21% and +19.39% for mean average precision and precision at 10 scores, respectively) when compared with the use of time series in isolation.

Optimal replenishment under price uncertainty

We aim to find optimal replenishment decisions without having the entire price information available at the outset. Although it exists, the underlying price distribution is neither known nor given as part of the input. Under the competitive ratio optimality criterion, we design and analyze online algorithms for two related problems. Besides the reservation price based decision how much to buy we additionally consider the optimal scheduling of orders. We suggest an online algorithm that decides how much to buy at the optimal point in time and experimentally explore its decision making. Results show that the problem of finding a replenishment strategy with best possible worst-case performance guarantees can be considered as an extension of the online time series search problem.

Similarity search for numerous patterns over multiple time series streams under dynamic time warping which supports data normalization

A huge challenge in nowadays' data mining is similarity search in streaming time series under Dynamic Time Warping (DTW). In the similarity search, data normalization is a must to obtain accurate results. However, data normalization on the fly and the DTW calculation cost a great deal of computational time and memory space. In the paper, we present two methods, SUCR-DTW and ESUCR-DTW, which conduct similarity search for numerous prespecified patterns over multiple time-series streams under DTW supporting data normalization. These two methods utilize a combination of techniques to mitigate the aforementioned costs. The efficient methods inherit the cascading lower bounds introduced in UCR-DTW, a state-of-the-art method of similarity search in the static time series, to admissibly prune off unpromising subsequences. To be adaptive in the streaming setting, SUCR-DTW performs incremental updates on the envelopes of new-coming time-series subsequences and incremental data normalization on time-series data. However, like UCR-DTW, SUCR-DTW retrieves only similar subsequences that have the same length as the patterns. ESUCR-DTW, an extension of SUCR-DTW, can find similar subsequences whose lengths are different from those of the patterns. Furthermore, our proposed methods exploit multi-threading to have a fast response to high-speed time-series streams. The experimental results show that SUCR-DTW obtains the same precision as UCR-DTW and has lower wall clock time. Besides, the experimental results of SUCR-DTW and ESUCR-DTW reveal that the extended method has higher accuracy in spite of longer wall clock time. Also, the paper evaluates the influence of incremental z-score normalization and incremental min---max normalization on the obtained results.

Adaptive Piecewise Approximation Based on Weighted Average Approach for Symbolic Time Series Representation

The process of time series representation has become a significant research problem. It is a challenging task to effectively manage and analyze large volumes of data with high dimensionality. Many high-level representations of time series have been proposed for mining tasks. The selection of effective and scalable method for the appropriate representation of data is another challenge. Piecewise Aggregate Approximation (PAA) method is applied in an effective similarity search of time series to minimize dimensionality by the mean values of equal-sized frames. PAA focus on mean value takes into consideration exclusively the central tendency and not the dispersion present in each segment, which may contribute to some important patterns being missed in some time series data sets and may not yield good tightness of the lower bound. We propose a method based on PAA called Time-weighted Average for Symbolic Aggregate Approximation (TWA_SAX) and compare its performance with the current methods. TWA_SAX enables raw data to be specifically compared to the minimized representation and ensures reduced limits to Euclidean distance. TWA_SAX is utilized to generate faster, more precise algorithms for similarity searches and improves the preciseness of the representation of time series data through enabling better tightness of the lower limit.

A novel parallel scheme for fast similarity search in large time series

The similarity search is one of the fundamental components in time series data mining, e.g. clustering, classification, association rules mining. Many methods have been proposed to measure the similarity between time series, including Euclidean distance, Manhattan distance, and dynamic time warping (DTW). In contrast, DTW has been suggested to allow more robust similarity measure and be able to find the optimal alignment in time series. However, due to its quadratic time and space complexity, DTW is not suitable for large time series datasets. Many improving algorithms have been proposed for DTW search in large databases, such as approximate search or exact indexed search. Unlike the previous modified algorithm, this paper presents a novel parallel scheme for fast similarity search based on DTW, which is called MRDTW (MapRedcue-based DTW). The experimental results show that our approach not only retained the original accuracy as DTW, but also greatly improved the efficiency of similarity measure in large time series.

Research on Short-Term Traffic Flow Prediction Method Based on Similarity Search of Time Series

Short-time traffic flow prediction is necessary for advanced traffic management system (ATMS) and advanced traveler information system (ATIS). In order to improve the effect of short-term traffic flow prediction, this paper presents a short-term traffic flow multistep prediction method based on similarity search of time series. Firstly, the landmark model is used to represent time series of traffic flow data. Then the input data of prediction model are determined through searching similar time series. Finally, the echo state networks model is used for traffic flow multistep prediction. The performance of the proposed method is measured with expressway traffic flow data collected from loop detectors in Shanghai, China. The experimental results demonstrate that the proposed method can achieve better multistep prediction performance than conventional methods.

Diversity based relevance feedback for time series search

We propose a diversity based relevance feedback approach for time series data to improve the accuracy of search results. We first develop the concept of relevance feedback for time series based on dual-tree complex wavelet (CWT) and SAX based approaches. We aim to enhance the search quality by incorporating diversity in the results presented to the user for feedback. We then propose a method which utilizes the representation type as part of the feedback, as opposed to a human choosing based on a preprocessing or training phase. The proposed methods utilize a weighting to handle the relevance feedback of important properties for both single and multiple representation cases. Our experiments on a large variety of time series data sets show that the proposed diversity based relevance feedback improves the retrieval performance. Results confirm that representation feedback incorporates item diversity implicitly and achieves good performance even when using simple nearest neighbor as the retrieval method. To the best of our knowledge, this is the first study on diversification of time series search to improve retrieval accuracy and representation feedback.

Discovering Anomalous Aviation Safety Events Using Scalable Data Mining Algorithms

The worldwide civilian aviation system is one of the most complex dynamical systems created. Most modern commercial aircraft have onboard flight data recorders that record several hundred discrete and continuous parameters at approximately 1 Hz for the entire duration of the flight. These data contain information about the flight control systems, actuators, engines, landing gear, avionics, and pilot commands. In this paper, recent advances in the development of a novel knowledge discovery process consisting of a suite of data mining techniques for identifying precursors to aviation safety incidents are discussed. The data mining techniques include scalable multiple-kernel learning for large-scale distributed anomaly detection. A novel multivariate time-series search algorithm is used to search for signatures of discovered anomalies on massive datasets. The process can identify operationally significant events due to environmental, mechanical, and human factors issues in the high-dimensional flight operations quality assurance data. All discovered anomalies are validated by a team of independent domain experts. This novel automated knowledge discovery process is aimed at complementing the state-of-the-art human-generated exceedance-based analysis that fails to discover previously unknown aviation safety incidents. In this paper, the discovery pipeline, the methods used, and some of the significant anomalies detected on real-world commercial aviation data are discussed.