Time Series Motifs Research Articles

Matrix Profile IX: Admissible Time Series Motif Discovery With Missing Data

The discovery of time series motifs has emerged as one of the most useful primitives in time series data mining. Researchers have shown its utility for exploratory data mining, summarization, visualization, segmentation, classification, clustering, and rule discovery. Although there has been more than a decade of extensive research, there is still no technique to allow the discovery of time series motifs in the presence of missing data, despite the well-documented ubiquity of missing data in scientific, industrial, and medical datasets. In this work, we introduce a technique for motif discovery in the presence of missing data. We formally prove that our method is admissible, producing no false negatives. We also show that our method can “piggy-back” off the fastest known motif discovery method with a small constant factor time/space overhead. We will demonstrate our approach on diverse datasets with varying amounts of missing data.

Time series classification based on triadic time series motifs

It is of great significance to identify the characteristics of time series to quantify their similarity and classify different classes of time series. We define six types of triadic time-series motifs and investigate the motif occurrence profiles extracted from the time series. Based on triadic time series motif profiles, we further propose to estimate the similarity coefficients between different time series and classify these time series with high accuracy. We validate the method with time series generated from nonlinear dynamic systems (logistic map, chaotic logistic map, chaotic Henon map, chaotic Ikeda map, hyperchaotic generalized Henon map and hyperchaotic folded-tower map) and retrieved from the UCR Time Series Classification Archive. Our analysis shows that the proposed triadic time series motif analysis performs better than the classic dynamic time wrapping method in classifying time series for certain datasets investigated in this work.

Accelerating time series motif discovery in the Intel Xeon Phi KNL processor

Time series analysis is an important research topic of great interest in many fields. Recently, the Matrix Profile method, and particularly one of its implementations—the SCRIMP algorithm—has become a state-of-the-art approach in this field. This is a technique that brings the possibility of obtaining exact motifs from a time series, which can be used to infer events, predict outcomes, detect anomalies and more. However, the memory-bound nature of the SCRIMP algorithm limits the execution performance in some processor architectures. In this paper, we analyze the SCRIMP algorithm from the performance viewpoint in the context of the Intel Xeon Phi Knights Landing architecture (KNL), which integrates high-bandwidth memory (HBM) modules, and we combine several techniques aimed at exploiting the potential of this architecture. On the one hand, we exploit the multi-threading and vector capabilities of the architecture. On the other hand, we explore how to allocate data in order to take advantage of the available hybrid memory architecture that conjugates both the high-bandwidth 3D-stacked HBM and the DDR4 memory modules. The experimental evaluation shows a performance improvement up to $$190\,\times $$ with respect to the sequential execution and that the use of the HBM memory improves performance in a factor up to $$5\,\times $$ with respect to the DDR4 memory.

A motifs-based Maximum Entropy Markov Model for realtime reliability prediction in System of Systems

System of Systems (SoS) based on service composition is considered as an effective way to build large-scale complex software systems. It regards the system as a service and integrates multiple component systems into a new system. The performance of the component system may fluctuate at any time because of the complex and changeable running state and external environment of the component system, which will affect the running of the SoS. The online reliability prediction technology is used to predict the reliability of the component system of an SoS in the near future. It aims to find errors and correct them in time so as to ensure that the SoS can run continuously and smoothly. To tackle the reliability prediction problem of component system in a dynamic and uncertain environment, the paper integrates Maximum Entropy Markov Model (MEMM) with time series motifs to achieve a new prediction model (m_MEMM), which is referred to as motifs-based MEMM. Extensive experiments are conducted to demonstrate the effectiveness and accuracy of the proposed approach.

Triadic time series motifs

We introduce the concept of time series motifs for time series analysis. Time series motifs consider not only the spatial information of mutual visibility but also the temporal information of relative magnitude between the data points. We study the profiles of the six triadic time series motifs. The six motif occurrence frequencies are derived for uncorrelated time series, which are approximately linear functions of the length of the time series. The corresponding motif profile thus converges to a constant vector. These analytical results have been verified by numerical simulations. For fractional Gaussian noises, numerical simulations unveil the nonlinear dependence of motif occurrence frequencies on the Hurst exponent. Applications of the time series motif analysis uncover that the motif occurrence frequency distributions are able to capture the different dynamics in the heartbeat rates of healthy subjects, congestive heart failure (CHF) subjects, and atrial fibrillation (AF) subjects and in the price fluctuations of bullish and bearish markets. Our method shows its potential power to classify different types of time series and test the time irreversibility of time series.

Genetic time series motif discovery for time series classification

Time series is a sequence of continuous data and unbounded group of observations found in many applications. Time series motif discovery is an essential and important task in time series mining. Several algorithms have been proposed to discover motifs in time series. These algorithms require user-defined parameters such as length of the motif, support or confidence. However, selection of these parameters is not an easy issue. To overcome the challenge, this paper proposes a genetic algorithm with constraints to discover good trade-off between representative and interesting motif. The discovered motifs are validated for their potential interest in time series classification problem using nearest neighbour classifier. Extensive experiments show that the proposed approach can efficiently discover motifs with different length and to be more accurate and statistically significant than state-of-the-art time series techniques. Finally, the paper demonstrates the efficiency of motif discovery in large medical data from MIT-BIH Arrhythmia database to classify the abnormal signals.

Motif identification in vital signs of chronic patients

With the development of remote medicine, more and more programs are being opened for the remote monitoring of chronic patients. The purpose of this research is to provide maximum understanding of the patient’s condition using their vital signs collected remotely. The vital signs are presented as irregular time series. Firstly, five missing value estimation methods are used to fill gaps in data. One of the best methods is to predict missing values with an artificial neural network trained on available data. Then, we use the exact method based on the matrix profile to search for motifs in one-dimensional and two-dimensional time series. The obtained motifs can be used to monitor the patient’s condition, to assess the effectiveness of therapy or to assess the physician’s actions.

HIME: discovering variable-length motifs in large-scale time series

Detecting repeated variable-length patterns, also called variable-length motifs, has received a great amount of attention in recent years. The state-of-the-art algorithm utilizes a fixed-length motif discovery algorithm as a subroutine to enumerate variable-length motifs. As a result, it may take hours or days to execute when the enumeration range is large. In this work, we introduce an approximate algorithm called hierarchical-based motif enumeration (HIME) to detect variable-length motifs with a large enumeration range in million-scale time series. We show in the experiments that the scalability of the proposed algorithm is significantly better than that of the state-of-the-art algorithm. Moreover, the motif length range detected by HIME is considerably larger than previous sequence matching-based approximate variable-length motif discovery approach. We demonstrate that HIME can efficiently detect meaningful variable-length motifs in long, real-world time series.

Limited-length Suffix-array-based Method for Variable-length Motif Discovery in Time Series

In this paper, we explore two key problems in time series motif discovery: releasing the constraints of trivial matching between subsequences with different lengths and improving the time and space efficiency. The purpose of avoiding trivial matching is to avoid too much repetition between subsequences in calculating their similarities. We describe a limited-length enhanced suffix array based framework (LiSAM) to resolve the two problems. Experimental results on Electrocardiogram signals indicate the accuracy of LiSAM on finding motifs with different lengths.

Introducing time series chains: a new primitive for time series data mining

Time series motifs were introduced in 2002 and have since become a fundamental tool for time series analytics, finding diverse uses in dozens of domains. In this work, we introduce Time Series Chains, which are related to, but distinct from, time series motifs. Informally, time series chains are a temporally ordered set of subsequence patterns, such that each pattern is similar to the pattern that preceded it, but the first and last patterns can be arbitrarily dissimilar. In the discrete space, this is similar to extracting the text chain “data, date, cate, cade, code” from text stream. The first and last words have nothing in common, yet they are connected by a chain of words with a small mutual difference. Time series chains can capture the evolution of systems, and help predict the future. As such, they potentially have implications for prognostics. In this work, we introduce two robust definitions of time series chains and scalable algorithms that allow us to discover them in massive complex datasets.

Exploring variable-length time series motifs in one hundred million length scale

The exploration of repeated patterns with different lengths, also called variable-length motifs, has received a great amount of attention in recent years. However, existing algorithms to detect variable-length motifs in large-scale time series are very time-consuming. In this paper, we introduce a time- and space-efficient approximate variable-length motif discovery algorithm, Distance-Propagation Sequitur (DP-Sequitur), for detecting variable-length motifs in large-scale time series data (e.g. over one hundred million in length). The discovered motifs can be ranked by different metrics such as frequency or similarity, and can benefit a wide variety of real-world applications. We demonstrate that our approach can discover motifs in time series with over one hundred million points in just minutes, which is significantly faster than the fastest existing algorithm to date. We demonstrate the superiority of our algorithm over the state-of-the-art using several real world time series datasets.

Forecasting Through Motifs Discovered by Genetic Algorithms

ABSTRACTForecasting is very important in the present world and has vast applications in various domains like weather forecasting, stock market trading, energy forecasting, etc. One of the ways of doing forecasts is through motifs. The present paper proposes an algorithm which first discovers multi-dimensional motifs in a real-valued time series using genetic algorithm with specially designed operators. The discovered motifs are then used to predict future values of the time series. The forecast values are compared with forecast values obtained using Vector Auto-regressive (VAR) prediction model and a naïve model. The results obtained show the effectiveness of the proposed algorithm.

GrammarViz 3.0

The problems of recurrent and anomalous pattern discovery in time series, e.g., motifs and discords, respectively, have received a lot of attention from researchers in the past decade. However, since the pattern search space is usually intractable, most existing detection algorithms require that the patterns have discriminative characteristics and have its length known in advance and provided as input, which is an unreasonable requirement for many real-world problems. In addition, patterns of similar structure, but of different lengths may co-exist in a time series. Addressing these issues, we have developed algorithms for variable-length time series pattern discovery that are based on symbolic discretization and grammar inference—two techniques whose combination enables the structured reduction of the search space and discovery of the candidate patterns in linear time. In this work, we present GrammarViz 3.0—a software package that provides implementations of proposed algorithms and graphical user interface for interactive variable-length time series pattern discovery. The current version of the software provides an alternative grammar inference algorithm that improves the time series motif discovery workflow, and introduces an experimental procedure for automated discretization parameter selection that builds upon the minimum cardinality maximum cover principle and aids the time series recurrent and anomalous pattern discovery.

Exploiting a novel algorithm and GPUs to break the ten quadrillion pairwise comparisons barrier for time series motifs and joins

Time series motifs are approximately repeated subsequences found within a longer time series. They have been in the literature since 2002, but recently they have begun to receive significant attention in research and industrial communities. This is perhaps due to the growing realization that they implicitly offer solutions to a host of time series problems, including rule discovery, anomaly detection, density estimation, semantic segmentation, summarization, etc. Recent work has improved the scalability so exact motifs can be computed on datasets with up to a million data points in tenable time. However, in some domains, for example seismology or climatology, there is an immediate need to address even larger datasets. In this work, we demonstrate that a combination of a novel algorithm and a high-performance GPU allows us to significantly improve the scalability of motif discovery. We demonstrate the scalability of our ideas by finding the full set of exact motifs on a dataset with one hundred and forty-three million subsequences, which is by far the largest dataset ever mined for time series motifs/joins; it requires ten quadrillion pairwise comparisons. Furthermore, we demonstrate that our algorithm can produce actionable insights into seismology and ethology.

A novel clustering-based method for time series motif discovery under time warping measure

The problem of time series motif discovery has attracted a lot of attention and is useful in many real-world applications. However, most of the proposed methods so far use Euclidean distance to deal with this problem. There has been one proposed method, called MDTW_WedgeTree, for time series motif discovery under DTW distance. But this method aims to deal with the case in which motif is the time series in a time series database which has the highest count of its similar time series within a range r. To adapt the above-mentioned method to the case in which motifs are frequently occurring subsequences of a longer time series, we modify MDTW_WedgeTree to a new algorithm for discovering “subsequence” motifs in time series under DTW. The proposed method consists of a segmentation method to divide the time series into motif candidates and a BIRCH-based clustering which can efficiently cluster motif candidate subsequences under DTW distance. Experimental results showed that our proposed method for discovering “subsequence” motifs performs very efficiently on large time series datasets while brings out high accuracy.

Time series joins, motifs, discords and shapelets: a unifying view that exploits the matrix profile

The last decade has seen a flurry of research on all-pairs-similarity-search (or similarity joins) for text, DNA and a handful of other datatypes, and these systems have been applied to many diverse data mining problems. However, there has been surprisingly little progress made on similarity joins for time series subsequences. The lack of progress probably stems from the daunting nature of the problem. For even modest sized datasets the obvious nested-loop algorithm can take months, and the typical speed-up techniques in this domain (i.e., indexing, lower-bounding, triangular-inequality pruning and early abandoning) at best produce only one or two orders of magnitude speedup. In this work we introduce a novel scalable algorithm for time series subsequence all-pairs-similarity-search. For exceptionally large datasets, the algorithm can be trivially cast as an anytime algorithm and produce high-quality approximate solutions in reasonable time and/or be accelerated by a trivial porting to a GPU framework. The exact similarity join algorithm computes the answer to the time series motif and time series discord problem as a side-effect, and our algorithm incidentally provides the fastest known algorithm for both these extensively-studied problems. We demonstrate the utility of our ideas for many time series data mining problems, including motif discovery, novelty discovery, shapelet discovery, semantic segmentation, density estimation, and contrast set mining. Moreover, we demonstrate the utility of our ideas on domains as diverse as seismology, music processing, bioinformatics, human activity monitoring, electrical power-demand monitoring and medicine.

Survey on time series motif discovery

Last decades witness a huge growth in medical applications, genetic analysis, and in performance of manufacturing technologies and automatised production systems. A challenging task is to identify and diagnose the behavior of such systems, which aim to produce a product with desired quality. In order to control the state of the systems, various information is gathered from different types of sensors (optical, acoustic, chemical, electric, and thermal). Time series data are a set of real‐valued variables obtained chronologically. Data mining and machine learning help derive meaningful knowledge from time series. Such tasks include clustering, classification, anomaly detection and motif discovery. Motif discovery attempts to find meaningful, new, and unknown knowledge from data. Detection of motifs in a time series is beneficial for, e.g., discovery of rules or specific events in a signal. Motifs provide useful information for the user in order to model or analyze the data. Motif discovery is applied to various areas as telecommunication, medicine, web, motion‐capture, and sensor networks. This contribution provides a review of the existing publications in time series motif discovery along with advantages and disadvantages of existing approaches. Moreover, the research issues and missing points in this field are highlighted. The main objective of this focus article is to serve as a glossary for researchers in this field. WIREs Data Mining Knowl Discov 2017, 7:e1199. doi: 10.1002/widm.1199This article is categorized under: Algorithmic Development > Spatial and Temporal Data Mining Fundamental Concepts of Data and Knowledge > Motivation and Emergence of Data Mining Technologies > Computational Intelligence Technologies > Machine Learning

A survey on time series motif discovery

Time series motifs are repeated subsequences in a long time series. Discovering time series motifs is an important task in time series data mining and this problem has received significant attention from researchers in data mining communities. In this paper, we intend to provide a comprehensive survey of the techniques applied for time series motif discovery. The survey also briefly describes a set of applications of time series motif in various domains as well as in high-level time series data mining tasks. We hope that this article can provide a broad and deep understanding of the time series motif discovery field.

Latent Time-Series Motifs

Motifs are the most repetitive/frequent patterns of a time-series. The discovery of motifs is crucial for practitioners in order to understand and interpret the phenomena occurring in sequential data. Currently, motifs are searched among series sub-sequences, aiming at selecting the most frequently occurring ones. Search-based methods, which try out series sub-sequence as motif candidates, are currently believed to be the best methods in finding the most frequent patterns. However, this paper proposes an entirely new perspective in finding motifs. We demonstrate that searching is non-optimal since the domain of motifs is restricted, and instead we propose a principled optimization approach able to find optimal motifs. We treat the occurrence frequency as a function and time-series motifs as its parameters, therefore we learn the optimal motifs that maximize the frequency function. In contrast to searching, our method is able to discover the most repetitive patterns (hence optimal), even in cases where they do not explicitly occur as sub-sequences. Experiments on several real-life time-series datasets show that the motifs found by our method are highly more frequent than the ones found through searching, for exactly the same distance threshold.

Ranking and significance of variable-length similarity-based time series motifs

The detection of very similar patterns in a time series, commonly called motifs, has received continuous and increasing attention from diverse scientific communities. In particular, recent approaches for discovering similar motifs of different lengths have been proposed. In this work, we show that such variable-length similarity-based motifs cannot be directly compared, and hence ranked, by their normalized dissimilarities. Specifically, we find that length-normalized motif dissimilarities still have intrinsic dependencies on the motif length, and that lowest dissimilarities are particularly affected by this dependency. Moreover, we find that such dependencies are generally non-linear and change with the considered data set and dissimilarity measure. Based on these findings, we propose a solution to rank (previously obtained) motifs of different lengths and measure their significance. This solution relies on a compact but accurate model of the dissimilarity space, using a beta distribution with three parameters that depend on the motif length in a non-linear way. We believe the incomparability of variable-length dissimilarities could have an impact beyond the field of time series, and that similar modeling strategies as the one used here could be of help in a more broad context and in diverse application scenarios.