Time Series Motifs Research Articles

Multidimensional time series motif group discovery based on matrix profile

With the continuous advancements in sensor technology and the increasing capabilities for data collection and storage, the acquisition of time series data across diverse domains has become significantly easier. Consequently, there is a growing demand for identifying potential motifs within multidimensional time series. The introduction of the Matrix Profile (MP) structure and the mSTOMP algorithm enables the detection of multidimensional motifs in large-scale time series datasets. However, the Matrix Profile (MP) does not provide information regarding the frequency of occurrence of these motifs. As a result, it is challenging to determine whether a motif appears frequently or to identify the specific time periods during which it typically occurs, thereby limiting further analysis of the discovered motifs. To address this limitation, we proposed Index Link Motif Group Discovery (ILMGD) algorithm, which uses index linking to rapidly merge and group multidimensional motifs. Based on the results of the ILMGD algorithm, we can determine the frequency and temporal positions of motifs, facilitating deeper analysis. Our proposed method requires minimal additional parameters and reduces the need for extensive manual intervention. We validate the effectiveness of our algorithm on synthetic datasets and demonstrate its applicability on three real-world datasets, highlighting how it enables a comprehensive understanding of the discovered motifs.

Temporally aligned segmentation and clustering (TASC) framework for behavior time series analysis

Behavior exhibits a complex spatiotemporal structure consisting of discrete sub-behaviors, or motifs. Continuous behavior data requires segmentation and clustering to reveal these embedded motifs. The popularity of automatic behavior quantification is growing, but existing solutions are often tailored to specific needs and are not designed for the time scale and precision required in many experimental and clinical settings. Here we propose a generalized framework with an iterative approach to refine both segmentation and clustering. Temporally aligned segmentation and clustering (TASC) uses temporal linear alignment to compute distances between and align the recurring behavior motifs in a multidimensional time series, enabling precise segmentation and clustering. We introduce an alternating-step process: evaluation of temporal neighbors against current cluster centroids using linear alignment, alternating with selecting the best non-overlapping segments and their subsequent re-clustering. The framework is evaluated on semi-synthetic and real-world experimental and clinical data, demonstrating enhanced segmentation and clustering, offering a better foundation for consequent research. The framework may be used to extend existing tools in the field of behavior research and may be applied to other domains requiring high precision of time series segmentation.

LoCoMotif: discovering time-warped motifs in time series

LoCoMotif: discovering time-warped motifs in time series

Interpretable Classifiers Based on Time-Series Motifs for Lane Change Prediction

In this paper, we address the problem of using non-interpretable Machine Learning (ML) algorithms in safety critical applications, especially automated driving functions. We focus on the lane change prediction of vehicles on a highway. In order to understand wrong decisions, which may lead to accidents, we want to interpret the reasons for a ML algorithm's decision making. To this end, we use motif discovery- a data mining method-to obtain sub-sequences representing typical driving behavior. With the help of these meaningful sub-sequences (motifs), we can study typical driving maneuvers on a highway. On top of this, we propose to replace noninterpretable ML algorithms with an interpretable alternative: a Mixture of Experts (MoE) classifier. We present an MoE classifier consisting of different <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -Nearest Neighbors ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -NN) classifiers trained only on motifs, which represent a few samples from the dataset. These <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -NN-based experts are fully interpretable, making the lane change prediction fully interpretable, too. Using our proposed MoE classifier, we are able to solve the lane change prediction problem in an interpretable manner. These MoE classifiers show a classification performance comparable to common non-interpretable ML methods from the literature.

Motiflets

A time series motif intuitively is a short time series that repeats itself approximately the same within a larger time series. Such motifs often represent concealed structures, such as heart beats in an ECG recording, the riff in a pop song, or sleep spindles in EEG sleep data. Motif discovery (MD) is the task of finding such motifs in a given input series. As there are varying definitions of what exactly a motif is, a number of different algorithms exist. As central parameters they all take the length l of the motif and the maximal distance r between the motif's occurrences. In practice, however, especially suitable values for r are very hard to determine upfront, and found motifs show a high variability even for very similar r values. Accordingly, finding an interesting motif with these methods requires extensive trial-and-error. In this paper, we present a different approach to the MD problem. We define k -Motiflets as the set of exactly k occurrences of a motif of length l , whose maximum pairwise distance is minimal. This turns the MD problem upside-down: The central parameter of our approach is not the distance threshold r , but the desired number of occurrence k of the motif, which we show is considerably more intuitive and easier to set. Based on this definition, we present exact and approximate algorithms for finding k -Motiflets and analyze their complexity. To further ease the use of our method, we describe statistical tools to automatically determine meaningful values for its input parameters. Thus, for the first time, extracting meaningful motif sets without any a-priori knowledge becomes feasible. By evaluation on several real-world data sets and comparison to four state-of-the-art MD algorithms, we show that our proposed algorithm is both quantitatively superior to its competitors, finding larger motif sets at higher similarity, and qualitatively better, leading to clearer and easier to interpret motifs without any need for manual tuning.

Practical joint human-machine exploration of industrial time series using the matrix profile

Technological advancements and widespread adaptation of new technology in industry have made industrial time series data more available than ever before. With this development grows the need for versatile methods for mining industrial time series data. This paper introduces a practical approach for joint human-machine exploration of industrial time series data using the Matrix Profile, and presents some challenges involved. The approach is demonstrated on three real-life industrial data sets to show how it enables the user to quickly extract semantic information, detect cycles, find deviating patterns, and gain a deeper understanding of the time series. A benchmark test is also presented on ECG (electrocardiogram) data, showing that the approach works well in comparison to previously suggested methods for extracting relevant time series motifs.

Multi-dimensional time-series subsequence clustering for visual feature analysis of blazar observation datasets

Exploring hidden structures in subsequences extracted from long-term time-series data is one of the primary tasks of time-series data analysis. Clustering is one of the most commonly used techniques in that context; however, various existing issues must be addressed, such as the way to extract less-overlapping subsequences and the definition of the inter-subsequence similarity. Especially in multi-dimensional data analysis, correlations among variables should also be emphasized. To boost users’ exploration of the universalities of subsequences, we incorporate multi-dimensional time-series subsequence clustering methods and visual clustering analysis interface into TimeTubesX, which is an integrated visual analytics environment for multi-dimensional time-dependent observation datasets of blazars. TimeTubesX extracts and filters subsequences with various lengths according to the characteristics of the data and clusters them automatically in consideration of correlations among observed attributes. And then, it allows users to visually examine the clustering results in terms of the cluster features, intercluster transitions, and temporal distributions of clusters. Through the application to two practical case studies, we demonstrate how the enhanced TimeTubesX enables users to see not only instances but also universalities (i.e., time-series motifs or cluster prototypes) in time-series observations of blazars.

Fast and Scalable Mining of Time Series Motifs with Probabilistic Guarantees

Mining time series motifs is a fundamental, yet expensive task in exploratory data analytics. In this paper, we therefore propose a fast method to find the top- k motifs with probabilistic guarantees. Our probabilistic approach is based on Locality Sensitive Hashing and allows to prune most of the distance computations, leading to huge speedups. We improve on a straightforward application of LSH to time series data by developing a self-tuning algorithm that adapts to the data distribution. Furthermore, we include several optimizations to the algorithm, reducing redundant computations and leveraging the structure of time series data to speed up LSH computations. We prove the correctness of the algorithm and provide bounds to the cost of the basic operations it performs. An experimental evaluation shows that our algorithm is able to tackle time series of one billion points on a single CPU-based machine, performing orders of magnitude faster than the GPU-based state of the art.

Statelets: Capturing recurrent transient variations in dynamic functional network connectivity

Dynamic functional network connectivity (dFNC) analysis is a widely used approach for capturing brain activation patterns, connectivity states, and network organization. However, a typical sliding window plus clustering (SWC) approach for analyzing dFNC models the system through a fixed sequence of connectivity states. SWC assumes connectivity patterns span throughout the brain, but they are relatively spatially constrained and temporally short‐lived in practice. Thus, SWC is neither designed to capture transient dynamic changes nor heterogeneity across subjects/time. We propose a state‐space time series summarization framework called “statelets” to address these shortcomings. It models functional connectivity dynamics at fine‐grained timescales, adapting time series motifs to changes in connectivity strength, and constructs a concise yet informative representation of the original data that conveys easily comprehensible information about the phenotypes. We leverage the earth mover distance in a nonstandard way to handle scale differences and utilize kernel density estimation to build a probability density profile for local motifs. We apply the framework to study dFNC of patients with schizophrenia (SZ) and healthy control (HC). Results demonstrate SZ subjects exhibit reduced modularity in their brain network organization relative to HC. Statelets in the HC group show an increased recurrence across the dFNC time‐course compared to the SZ. Analyzing the consistency of the connections across time reveals significant differences within visual, sensorimotor, and default mode regions where HC subjects show higher consistency than SZ. The introduced approach also enables handling dynamic information in cross‐modal and multimodal applications to study healthy and disordered brains.

Performance Improvement of Very Short-term Prediction Intervals for Regional Wind Power Based on Composite Conditional Nonlinear Quantile Regression

Accurate regional wind power prediction plays an important role in the security and reliability of power systems. For the performance improvement of very short-term prediction intervals (PIs), a novel probabilistic prediction method based on composite conditional nonlinear quantile regression (CCNQR) is proposed. First, the hierarchical clustering method based on weighted multivariate time series motifs (WMTSM) is studied to consider the static difference, dynamic difference, and meteorological difference of wind power time series. Then, the correlations are used as sample weights for the conditional linear programming (CLP) of CCNQR. To optimize the performance of PIs, a composite evaluation including the accuracy of PI coverage probability (PICP), the average width (AW), and the offsets of points outside PIs (OPOPI) is used to quantify the appropriate upper and lower bounds. Moreover, the adaptive boundary quantiles (ABQs) are quantified for the optimal performance of PIs. Finally, based on the real wind farm data, the superiority of the proposed method is verified by adequate comparisons with the conventional methods.

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.

SMM: Leveraging Metadata for Contextually Salient Multi-Variate Motif Discovery

A common challenge in multimedia data understanding is the unsupervised discovery of recurring patterns, or motifs, in time series data. The discovery of motifs in uni-variate time series is a well studied problem and, while being a relatively new area of research, there are also several proposals for multi-variate motif discovery. Unfortunately, motif search among multiple variates is an expensive process, as the potential number of sub-spaces in which a pattern can occur increases exponentially with the number of variates. Consequently, many multi-variate motif search algorithms make simplifying assumptions, such as searching for motifs across all variates individually, assuming that the motifs are of the same length, or that they occur on a fixed subset of variates. In this paper, we are interested in addressing a relatively broad form of multi-variate motif detection, which seeks frequently occurring patterns (of possibly differing lengths) in sub-spaces of a multi-variate time series. In particular, we aim to leverage contextual information to help select contextually salient patterns and identify the most frequent patterns among all. Based on these goals, we first introduce the contextually salient multi-variate motif (CS-motif) discovery problem and then propose a salient multi-variate motif (SMM) algorithm that, unlike existing methods, is able to seek a broad range of patterns in multi-variate time series.

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.

A Brief Survey on Techniques Used in Discovering Time Series Motifs

Time series data are set of observations collected on equal time intervals in applications of different domains like medicine, motion-capture, seismology, sensor networks, telecommunication, etc. Time series motifs are time sub-sequences data, occurring repeatedly in an application and are unknown in advance. Motifs are useful in retrieving information from time series databases using data mining techniques. Discovering time series motifs in time series data is an important task before applying a data mining technique. In literature, several algorithms have been proposed to increase the efficiency and accuracy for time series motifs discovery. This paper presents a brief survey on techniques used in discovering time series motifs.

The Swiss army knife of time series data mining: ten useful things you can do with the matrix profile and ten lines of code

The recently introduced data structure, the Matrix Profile, annotates a time series by recording the location of and distance to the nearest neighbor of every subsequence. This information trivially provides answers to queries for both time series motifs and time series discords, perhaps two of the most frequently used primitives in time series data mining. One attractive feature of the Matrix Profile is that it completely divorces the high-level details of the analytics performed, from the computational “heavy lifting.” The Matrix Profile can be computed using the appropriate computational paradigm for the task at hand: CPU, GPU, FPGA, distributed computing, anytime computation, incremental computation, and so forth. However, all the details of such computation can be hidden from the analyst who only needs to think about her analytical need. In this work, we expand on this philosophy and ask the following question: If we assume that we get the Matrix Profile for free, what interesting analytics can we do, writing at most ten lines of code? As we will show, the answer is surprisingly large and diverse. Our aim here is not to establish or compete with state-of-the-art results, but merely to show that we can both reproduce the results of many existing algorithms and find novel regularities in time series data collections with very little effort.

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.

Does the Arctic Stratospheric Polar Vortex Exhibit Signs of Preconditioning Prior to Sudden Stratospheric Warmings?

Abstract Characteristics of the Arctic stratospheric polar vortex are examined using reanalysis data with dynamic time warping (DTW) and a clustering technique to determine whether the polar vortex exhibits canonical signs of preconditioning prior to sudden stratospheric warmings (SSWs). The DTW and clustering technique is used to locate time series motifs in vortex area, vortex edge-averaged PV gradients, and vortex edge-averaged wind speeds. Composites of the motifs reveal that prior to roughly 75% of SSWs, in the middle to upper stratosphere, PV gradients and wind speeds in the vortex edge region increase, and vortex area decreases. These signs agree with prior studies that discuss potential signals of preconditioning of the vortex. However, similar motifs are also found in a majority of years without SSWs. While such non-SSW motifs are strongly associated with minor warming signals apparent only in the middle and upper stratosphere, only roughly half of these can be associated with later “significant disturbances” (SDs) that do not quite meet the threshold for major SSWs. The median lead time for sharpening vortex edge PV gradients represented in the motifs prior to SSWs and SDs is ~25 days, while the median lead time for the vortex area and edge wind speeds is ~10 days. Overall, canonical signs of preconditioning do appear to exist prior to SSWs, but their existence in years without SSWs implies that preconditioning of the vortex may be an insufficient condition for the occurrence of SSWs.

Financial time series prediction: an approach using motif information and neural networks

Financial time series prediction is an important and complex problem as well. This paper presents an approach to predict financial time series using time series motifs and artificial neural network (ANN) in tandem. A time series motif is a frequently appearing approximate pattern in a given time series. In the proposed approach, first, extreme points-clustering (EP-C) algorithm detects significant motifs. Later, ANN uses motif information to yield accurate predictions. Three ANNs namely multi-layer perceptron (MLP), general regression neural network (GRNN), and group method for data handling (GMDH) are employed. The proposed Motif+GMDH hybrid outperformed both Motif+MLP hybrid and Motif+ GRNN hybrid on three financial time series including exchange rates of both EUR/USD and INR/USD, and crude oil price (USD). Further, we compared the results of the motif-based hybrids with that of the three ANNs without motif information. We found that Motif+MLP hybrid outperformed plain MLP in all datasets statistically at 1% level of significance.

Financial time series prediction: an approach using motif information and neural networks

Financial time series prediction is an important and complex problem as well. This paper presents an approach to predict financial time series using time series motifs and artificial neural network (ANN) in tandem. A time series motif is a frequently appearing approximate pattern in a given time series. In the proposed approach, first, extreme points-clustering (EP-C) algorithm detects significant motifs. Later, ANN uses motif information to yield accurate predictions. Three ANNs namely multi-layer perceptron (MLP), general regression neural network (GRNN), and group method for data handling (GMDH) are employed. The proposed Motif+GMDH hybrid outperformed both Motif+MLP hybrid and Motif+ GRNN hybrid on three financial time series including exchange rates of both EUR/USD and INR/USD, and crude oil price (USD). Further, we compared the results of the motif-based hybrids with that of the three ANNs without motif information. We found that Motif+MLP hybrid outperformed plain MLP in all datasets statistically at 1% level of significance.