Time Series Motif Discovery Research Articles

Multi-Index Ecoacoustics Analysis for Terrestrial Soundscapes: A New Semi-Automated Approach Using Time-Series Motif Discovery and Random Forest Classification

High rates of biodiversity loss caused by human-induced changes in the environment require new methods for large scale fauna monitoring and data analysis. While ecoacoustic monitoring is increasingly being used and shows promise, analysis and interpretation of the big data produced remains a challenge. Computer-generated acoustic indices potentially provide a biologically meaningful summary of sound, however, temporal autocorrelation, difficulties in statistical analysis of multi-index data and lack of consistency or transferability in different terrestrial environments have hindered the application of those indices in different contexts. To address these issues we investigate the use of time-series motif discovery and random forest classification of multi-indices through two case studies. We use a semi-automated workflow combining time-series motif discovery and random forest classification of multi-index (acoustic complexity, temporal entropy, and events per second) data to categorize sounds in unfiltered recordings according to the main source of sound present (birds, insects, geophony). Our approach showed more than 70% accuracy in label assignment in both datasets. The categories assigned were broad, but we believe this is a great improvement on traditional single index analysis of environmental recordings as we can now give ecological meaning to recordings in a semi-automated way that does not require expert knowledge and manual validation is only necessary for a small subset of the data. Furthermore, temporal autocorrelation, which is largely ignored by researchers, has been effectively eliminated through the time-series motif discovery technique applied here for the first time to ecoacoustic data. We expect that our approach will greatly assist researchers in the future as it will allow large datasets to be rapidly processed and labeled, enabling the screening of recordings for undesired sounds, such as wind, or target biophony (insects and birds) for biodiversity monitoring or bioacoustics research.

ChroMo, an Application for Unsupervised Analysis of Chromosome Movements in Meiosis.

Nuclear movements during meiotic prophase, driven by cytoskeleton forces, are a broadly conserved mechanism in opisthokonts and plants to promote pairing between homologous chromosomes. These forces are transmitted to the chromosomes by specific associations between telomeres and the nuclear envelope during meiotic prophase. Defective chromosome movements (CMs) harm pairing and recombination dynamics between homologues, thereby affecting faithful gametogenesis. For this reason, modelling the behaviour of CMs and their possible microvariations as a result of mutations or physico-chemical stress is important to understand this crucial stage of meiosis. Current developments in high-throughput imaging and image processing are yielding large CM datasets that are suitable for data mining approaches. To facilitate adoption of data mining pipelines, we present ChroMo, an interactive, unsupervised cloud application specifically designed for exploring CM datasets from live imaging. ChroMo contains a wide selection of algorithms and visualizations for time-series segmentation, motif discovery, and assessment of causality networks. Using ChroMo to analyse meiotic CMs in fission yeast, we found previously undiscovered features of CMs and causality relationships between chromosome morphology and trajectory. ChroMo will be a useful tool for understanding the behaviour of meiotic CMs in yeast and other model organisms.

Time series motifs discovery under DTW allows more robust discovery of conserved structure

In recent years, time series motif discovery has emerged as perhaps the most important primitive for many analytical tasks, including clustering, classification, rule discovery, segmentation, and summarization. In parallel, it has long been known that Dynamic Time Warping (DTW) is superior to other similarity measures such as Euclidean Distance under most settings. However, due to the computational complexity of both DTW and motif discovery, virtually no research efforts have been directed at combining these two ideas. The current best mechanisms to address their lethargy appear to be mutually incompatible. In this work, we present the first efficient, scalable and exact method to find time series motifs under DTW. Our method automatically performs the best trade-off of time-to-compute versus tightness-of-lower-bounds for a novel hierarchy of lower bounds that we introduce. As we shall show through extensive experiments, our algorithm prunes up to 99.99% of the DTW computations under realistic settings and is up to three to four orders of magnitude faster than the brute force search, and two orders of magnitude faster than the only other competitor algorithm. This allows us to discover DTW motifs in massive datasets for the first time. As we will show, in many domains, DTW-based motifs represent semantically meaningful conserved behavior that would escape our attention using all existing Euclidean distance-based methods.

ScrimpCo: scalable matrix profile on commodity heterogeneous processors

The discovery of time series motifs and discords is considered a paramount and challenging problem regarding time series analysis. In this work, we present ScrimpCo, a heterogeneous implementation of a previous algorithm called SCRIMP that excels at finding relevant subsequences in time series. We propose and evaluate several static, dynamic and adaptive partition strategies targeting commodity processors, on both homogeneous (CPU multicore) and heterogeneous (CPU + GPU) architectures. For the CPU + GPU implementation, we explore a heterogeneous parallel_reduce pattern that computes part of the computation onto an OpenCL capable GPU, whereas the CPU cores take care of the other part. Our heterogeneous scheduler, built on top of TBB, pays special attention to appropriately balance the computational load among the GPU and CPU cores. The experimental results show that our homogeneous implementation scales linearly and that our heterogeneous implementation allows us to reach near-ideal performance on commodity processors that feature an on-chip GPU.

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.

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.

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.

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.

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.

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.

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.

An efficient implementation of EMD algorithm for motif discovery in time series data

The extended motif discovery (EMD) algorithm, developed by Tanaka et al. (2005), is a well-known time series motif discovery algorithm which is based on minimum description length principle. One unique feature of the EMD algorithm is that it can determine the suitable length of the motif and hence does not require the length of the motif as a parameter supplied by user. Another interesting feature of the EMD is the lengths of each instances of a motif can be a bit different from each other and hence Tanaka et al. suggested that dynamic time warping (DTW) distance should be used to calculate the distances between the motif instances in this case. Due to the second feature, the EMD algorithm leads to a high computational complexity and is not easy to implement in practice. In this paper, we present an efficient implementation of the EMD algorithm in which we apply homothetic transformation to convert all pattern instances of different lengths into the same length so that we can easily calculate Euclidean distances between them. This modification accelerates the execution of the EMD remarkably and makes it easier to implement. Experimental results on seven real world time series datasets demonstrate the effectiveness of our EMD implementation method in time series motif discovery.

MULTI-OBJECTIVE GENETIC MOTIF DISCOVERY TECHNIQUE FOR TIME SERIES CLASSIFICATION

Time series is a sequence of continuous and unbounded group of data observations recorded from many applications. Time series motif discovery is an essential and important task in time series mining. Discovering motifs in time series has attracted the researcher's attention for efficient time series classification problems and several algorithms have been proposed to solve the problem. However, these algorithms depend on predefined parameters like support, confidence, and length of the motif and they are sensitive to the parameters. To overcome the challenge, this paper proposes a multi-objective genetic algorithm to discover a good trade-off between representative and interesting motif. The discovered motifs are validated for their potential interest in time series classification using nearest neighbour classifier. Extensive experiments show that the proposed approach can efficiently discover motifs with different lengths and more accurate than state-of-the-art time series techniques. The paper also demonstrates the efficiency of motif discovery in classifying the large time series medical data from MIT-BIH-arrhythmia database.

Particle swarm optimization for time series motif discovery

Efficiently finding similar segments or motifs in time series data is a fundamental task that, due to the ubiquity of these data, is present in a wide range of domains and situations. Because of this, countless solutions have been devised but, to date, none of them seems to be fully satisfactory and flexible. In this article, we propose an innovative standpoint and present a solution coming from it: an anytime multimodal optimization algorithm for time series motif discovery based on particle swarms. By considering data from a variety of domains, we show that this solution is extremely competitive when compared to the state-of-the-art, obtaining comparable motifs in considerably less time using minimal memory. In addition, we show that it is robust to different implementation choices and see that it offers an unprecedented degree of flexibility with regard to the task. All these qualities make the presented solution stand out as one of the most prominent candidates for motif discovery in long time series streams. Besides, we believe the proposed standpoint can be exploited in further time series analysis and mining tasks, widening the scope of research and potentially yielding novel effective solutions.

Discovery of time series $$k$$ k -motifs based on multidimensional index

Time series motifs are frequently occurring but previously unknown subsequences of a longer time series. Discovering time series motifs is a crucial task in time series data mining. In time series motif discovery algorithm, finding nearest neighbors of a subsequence is the basic operation. To make this basic operation efficient, we can make use of some advanced multidimensional index structure for time series data. In this paper, we propose two novel algorithms for discovering motifs in time series data: The first algorithm is based on $$\hbox {R}^{*}$$R?-tree and early abandoning technique and the second algorithm makes use of a dimensionality reduction method and state-of-the-art Skyline index. We demonstrate that the effectiveness of our proposed algorithms by experimenting on real datasets from different areas. The experimental results reveal that our two proposed algorithms outperform the most popular method, random projection, in time efficiency while bring out the same accuracy.

Rare time series motif discovery from unbounded streams

The detection of time series motifs , which are approximately repeated subsequences in time series streams, has been shown to have great utility as a subroutine in many higher-level data mining algorithms. However, this detection becomes much harder in cases where the motifs of interest are vanishingly rare or when faced with a never-ending stream of data. In this work we investigate algorithms to find such rare motifs. We demonstrate that under reasonable assumptions we must abandon any hope of an exact solution to the motif problem as it is normally defined; however, we introduce algorithms that allow us to solve the underlying problem with high probability.

Time series motif discovery: dimensions and applications

Time series motifs are repeated segments in a long time series that, if exist, carry precise information about the underlying source of the time series. Motif discovery in time series data has received significant attention in the data mining community since its inception, principally because, motif discovery is meaningful and more likely to succeed when the data is large.Algorithms for motif discovery generally deal with three aspects the definition of the motifs, domain based preprocessing, and finally, the algorithmic steps. Typical definitions of motifs signify the similarity or the support of the motifs. Domains impose preprocessing requirements to meaningful motif finding such as data alignment, interpolation, and transformation. Motif discovery algorithms vary based on exact or approximate evaluation of the definition. In addition, algorithms require different representations [Symbolic Aggregate approXimation (SAX), DFT etc.] and similarity measures [correlation, dynamic time warping (DTW) distance etc.] for time series segments. In this paper, we discuss these three facets in detail with examples taken from the literature.We briefly describe a set of applications of time series motif in various domains and elaborate on a certain application in entomology to analyze insect behavior.This article is categorized under: Algorithmic Development > Spatial and Temporal Data Mining Technologies > Structure Discovery and Clustering

Significant motifs in time series

Time series motif discovery is the task of extracting previously unknown recurrent patterns from time series data. It is an important problem within applications that range from finance to health. ...

Comprehensive and efficient discovery of time series motifs

Time series motifs are previously unknown, frequently occurring patterns in time series or approximately repeated subsequences that are very similar to each other. There are two issues in time series motifs discovery, the deficiency of the definition of K-motifs given by Lin et al. (2002) and the large computation time for extracting motifs. In this paper, we propose a relatively comprehensive definition of K-motifs to obtain more valuable motifs. To minimize the computation time as much as possible, we extend the triangular inequality pruning method to avoid unnecessary operations and calculations, and propose an optimized matrix structure to produce the candidate motifs almost immediately. Results of two experiments on three time series datasets show that our motifs discovery algorithm is feasible and efficient.