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The burgeoning age of IoT has reinforced the need for robust time series anomaly detection. While there are hundreds of anomaly detection methods in the literature, one definition, time series discords, has emerged as a competitive and popular choice for practitioners. Time series discords are subsequences of a time series that are maximally far away from their nearest neighbors. Perhaps the most attractive feature of discords is their simplicity. Unlike many of the parameter-laden methods proposed, discords require only a single parameter to be set by the user: the subsequence length. We believe that the utility of discords is reduced by sensitivity to even this single user choice. The obvious solution to this problem, computing discords of all lengths then selecting the best anomalies (under some measure), appears at first glance to be computationally untenable. However, in this work we discuss MERLIN, a recently introduced algorithm that can efficiently and exactly find discords of all lengths in massive time series archives. By exploiting computational redundancies, MERLIN is two orders of magnitude faster than comparable algorithms. Moreover, we show that by exploiting a little-known indexing technique called Orchard’s algorithm, we can create a new algorithm called MERLIN++, which is an order of magnitude faster than MERLIN, yet produces identical results. We demonstrate the utility of our ideas on a large and diverse set of experiments and show that MERLIN++ can discover subtle anomalies that defy existing algorithms or even careful human inspection. We further compare to five state-of-the-art rival methods, on the largest benchmark dataset for this task, and show that MERLIN++ is superior in terms of accuracy and speed. 

Seismic data are generally scrutinized for repeating earthquakes (REs) to evaluate slip rates, changes in the mechanical properties of a fault zone, and accelerating nucleation processes in foreshock and aftershock sequences. They are also used to study velocity changes in the medium, earthquake physics and prediction, and for constraining creep rate models at depth. For a robust detection of repeaters, multiple constraints and different parameter configurations related to waveform similarity have been proposed to measure cross‐correlation values at a local seismic network and evaluate the location of overlapping sources. In this work, we developed a Python code to identify REs (FINDRES), inspired by previous literature, which combines both seismic waveform similarity and differential S‐P travel time measured at each seismic station. A cross‐spectral method is applied to evaluate precise differential arrival travel times between earthquake pairs, allowing a subsample precision and increasing the capacity to resolve an overlapping common source radius. FINDRES is versatile and works with and without P‐ and S‐wave phase pickings, and has been validated using synthetic and real data, and provides reliable results. It would contribute to the implementation of open‐source Python packages in seismology, supporting the activities of researchers and the reproducibility of scientific results. 

Time series data remains a perennially important datatype considered in data mining. In the last decade there has been an increasing realization that time series data can be best understood by reasoning about time series subsequences on the basis of their similarity to other subsequences: the two most familiar such time series concepts being motifs and discords. Time series motifs refer to two particularly close subsequences, whereas time series discords indicate subsequences that are far from their nearest neighbors. However, we argue that it can sometimes be useful to simultaneously reason about a subsequence’s closeness to certain data and its distance to other data. In this work we introduce a novel primitive called the Contrast Profile that allows us to efficiently compute such a definition in a principled way. As we will show, the Contrast Profile has many downstream uses, including anomaly detection, data exploration, and preprocessing unstructured data for classification. We demonstrate the utility of the Contrast Profile by showing how it allows end-to-end classification in datasets with tens of billions of datapoints, and how it can be used to explore datasets and reveal subtle patterns that might otherwise escape our attention. Moreover, we demonstrate the generality of the Contrast Profile by presenting detailed case studies in domains as diverse as seismology, animal behavior, and cardiology. 

Since its introduction two decades ago, there has been increasing interest in the problem of early classification of time series . This problem generalizes classic time series classification to ask if we can classify a time series subsequence with sufficient accuracy and confidence after seeing only some prefix of a target pattern. The idea is that the earlier classification would allow us to take immediate action, in a domain in which some practical interventions are possible. For example, that intervention might be sounding an alarm or applying the brakes in an automobile. In this work, we make a surprising claim. In spite of the fact that there are dozens of papers on early classification of time series, it is not clear that any of them could ever work in a real-world setting. The problem is not with the algorithms per se but with the vague and underspecified problem description. Essentially all algorithms make implicit and unwarranted assumptions about the problem that will ensure that they will be plagued by false positives and false negatives even if their results suggested that they could obtain near-perfect results. We will explain our findings with novel insights and experiments and offer recommendations to the community 

Time series anomaly detection has been a perennially important topic in data science, with papers dating back to the 1950s. However, in recent years there has been an explosion of interest in this topic, much of it driven by the success of deep learning in other domains and for other time series tasks. Most of these papers test on one or more of a handful of popular benchmark datasets, created by Yahoo, Numenta, NASA, etc. In this work we make a surprising claim. The majority of the individual exemplars in these datasets suffer from one or more of four flaws. Because of these four flaws, we believe that many published comparisons of anomaly detection algorithms may be unreliable, and more importantly, much of the apparent progress in recent years may be illusionary. In addition to demonstrating these claims, with this paper we introduce the UCR Time Series Anomaly Archive. We believe that this resource will perform a similar role as the UCR Time Series Classification Archive, by providing the community with a benchmark that allows meaningful comparisons between approaches and a meaningful gauge of overall progress