The Matrix Profile is a data structure that annotates a time series by recording each subsequence’s Euclidean distance to its nearest neighbor. In recent years the community has shown that using the Matrix Profile it is possible to discover many useful properties of a time series, including repeated behaviors, anomalies, evolving patterns, regimes, etc. However, the Matrix Profile is limited to representing the relationship between the subsequence’s shapes. It is known that, for some domains, useful information is conserved not in the subsequence’s shapes, but in the subsequence’s features. In recent years a new set of features for time series called catch22 has revolutionized feature-based mining of time series. Combining these two ideas seems to offer many possibilities for novel data mining applications, however, there are two difficulties in attempting this. A direct application of the Matrix Profile with the catch22 features would be prohibitively slow. Less obviously, as we will demonstrate, in almost all domains, using all twenty-two of the catch22 features produces poor results, and we must somehow select the subset appropriate for the domain. In this work we introduce novel algorithms to solve both problems and demonstrate that for most domains, the proposed $\mathrm{C}^{22}$MP is a state-of-the-art anomaly detector.

While offline exploration of time series can be useful, time series analysis is almost unique in allowing the possibility of direct and immediate intervention. For example, if we are monitoring an industrial process and our algorithm predicts imminent failure, the algorithm could direct a controller to open a release valve or alert a response team. There now exist mature tools to monitor time series for known behaviors (template matching), previously unknown highly conserved behaviors (motifs) and unexpected behaviors (anomalies). In this work we claim that there is another useful primitive, emerging behaviors, that are worth monitoring for. We call such behaviors Novelets. We explain that Novelets are neither anomalies nor motifs but can be loosely thought of as initially apparent anomalies that are later realized to be motifs. We will show Novelets have a natural interpretation in many disciplines, including science, medicine, and industry. As we will further demonstrate, Novelet discovery can have many downstream uses, including prognostics and abnormal behavior detection. We will demonstrate the utility of our proposed primitive on a diverse set of domains.

Time series similarity matrices (informally, recurrence plots), are useful tools for time series data mining. They can be used to guide data exploration, and various useful features can be derived from them and then fed into downstream analytics. However, time series similarity matrices suffer from very poor scalability, taxing both time and memory requirements. In this work, we introduce novel ideas that allow us to scale the largest time series similarity matrices that can be examined by several orders of magnitude. The first idea is a novel algorithm to compute the matrices in a way that removes dependency on the subsequence length. This algorithm is so fast that it allows us to now address datasets where the memory limitations begin to dominate. Our second novel contribution is a multiscale algorithm that computes an approximation of the matrix appropriate for the limitations of the user’s memory/screen-resolution, then performs a local, just-in-time recomputation of any region that the user wishes to zoom-in on. Given that we can largely remove time and space barriers, human visual attention then becomes the bottleneck. We further introduce algorithms that search massive matrices with quadrillions of cells and then prioritize regions for later attention by either humans or algorithms. We will demonstrate the utility of our ideas for data exploration, segmentation, and classification in diverse domains.

Predicting metrics associated with entities' transnational behavior within payment processing networks is essential for system monitoring. Multivariate time series, aggregated from the past transaction history, can provide valuable insights for such prediction. The general multivariate time series prediction problem has been well studied and applied across several domains, including manufacturing, medical, and entomology. However, new domain-related challenges associated with the data such as concept drift and multi-modality have surfaced in addition to the real-time requirements of handling the payment transaction data at scale. In this work, we study the problem of multivariate time series prediction for estimating transaction metrics associated with entities in the payment transaction database. We propose a model with five unique components to estimate the transaction metrics from multi-modality data. Four of these components capture interaction, temporal, scale, and shape perspectives, and the fifth component fuses these perspectives together. We also propose a hybrid offline/online training scheme to address concept drift in the data and fulfill the real-time requirements. Combining the estimation model with a graphical user interface, the prototype transaction metric estimation system has demonstrated its potential benefit as a tool for improving a payment processing company's system monitoring capability.

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 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.

Time series anomaly detection remains a perennially important research topic. If anything, it is a task that has become increasingly important in the burgeoning age of IoT. 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 parameter laden methods, discords require only a single parameter to be set by the user: the subsequence length. In this work we argue that the utility of discords is reduced by sensitivity to this single user choice. The obvious solution to this problem, computing discords of all lengths then selecting the best anomalies (under some measure), seems to be computationally untenable. However, in this work we introduce MERLIN, an algorithm that can efficiently and exactly find discords of all lengths in massive time series archives.