Seismic monitoring systems sift through seismograms in real-time, searching for target events, such as underground explosions. In this monitoring system, a burst of aftershocks (minor earthquakes occur after a major earthquake over days or even years) can be a source of confounding signals. Such a burst of aftershock signals can overload the human analysts of the monitoring system. To alleviate this burden at the onset of a sequence of events (e.g., aftershocks), a human analyst can label the first few of these events and start an online classifier to filter out subsequent aftershock events. We propose an online few-shot classification model FewSig for time series data for the above use case. The framework of FewSig consists of a selective model to identify the high-confidence positive events which are used for updating the models and a general classifier to label the remaining events. Our specific technique uses a %two-level decision tree selective model based on sliding DTW distance and a general classifier model based on distance metric learning with Neighborhood Component Analysis (NCA). The algorithm demonstrates surprising robustness when tested on univariate datasets from the UEA/UCR archive. Furthermore, we show two real-world earthquake events where the FewSig reduces the human effort in monitoring applications by filtering out the aftershock events.

The depth of a seismic event is an essential feature to discriminate natural earthquakes from events induced or created by humans. However, estimating the depth of a seismic event with a sparse set of seismic stations is a daunting task, and there is no globally usable method. This paper focuses on developing a machine learning model to accurately estimate the depth of arbitrary seismic events directly from seismograms. Our proposed deep learning architecture is not-so-deep compared to commonly found models in the literature for related tasks, consisting of two loosely connected levels of neural networks, associated with the seismic stations at the higher level and the individual channels of a station at the lower level. Thus, the model has significant advantages, including a reduced number of parameters for tuning and better interpretability to geophysicists. We evaluate our solution on seismic data collected from the SCEDC (Southern California Earthquake Data Center) catalog for regional events in California. The model can learn waveform features specific to a set of stations, while it struggles to generalize to completely novel sets of event sources and stations. In a simplified setting of separating shallow events from deep ones, the model achieved an 86.5% F1-score using the Southern California stations.

Monitoring systems have hundreds or thousands of distributed sensors gathering and transmitting real-time streaming data. The early detection of events in these systems, such as an earthquake in a seismic monitoring system, is the base for essential tasks as warning generations. To detect such events is usual to compute pairwise correlation across the disparate signals generated by the sensors. Since the data sources (e.g., sensors) are spatially separated, it is essential to consider the lagged correlation between the signals. Besides, many applications require to process a specific band of frequencies depending on the event’s type, demanding a pre-processing step of filtering before computing correlations. Due to the high speed of data generation and a large number of sensors in these systems, the operations of filtering and lagged cross-correlation need to be efficient to provide real-time responses without data losses. This article proposes a technique named FilCorr that efficiently computes both operations in one single step. We achieve an order of magnitude speedup by maintaining frequency transforms over sliding windows. Our method is exact, devoid of sensitive parameters, and easily parallelizable. Besides our algorithm, we also provide a publicly available real-time system named Seisviz that employs FilCorr in its core mechanism for monitoring a seismometer network. We demonstrate that our technique is suitable for several monitoring applications as seismic signal monitoring, motion monitoring, and neural activity monitoring.

This paper introduces a new pattern mining task that considers aligning or joining a set of time series based on an arbitrary number of subsequences (i.e., patterns) with arbitrary lengths. Joining multiple time series along common patterns can be pivotal in clustering and summarizing large time series datasets. An exact algorithm to join hundreds of time series based on multi-length patterns is impractical due to the high computational costs. This paper proposes a fast algorithm named MultiPAL to join multiple time series at interactive speed to summarize large time series datasets. The algorithm exploits Matrix Profiles of the individual time series to enable a greedy search over possible joins. The algorithm is orders of magnitude faster than the exact solution and can utilize hundreds of Matrix Profiles. We evaluate our algorithm for sequential mining on data from various real-world domains, including power management and bioacoustics monitoring.

Changes in data distribution of streaming data (i.e., concept drifts), constitute a central issue in online data mining. The main reason is that these changes are responsible for outdating stream learning models, reducing their predictive performance over time. A common approach adopted by real-time adaptive systems to deal with concept drifts is to employ detectors that indicate the best time for updates. However, an unrealistic assumption of most detectors is that the labels become available immediately after data arrives. In this paper, we introduce an unsupervised and model-independent concept drift detector suitable for high-speed and high-dimensional data streams in realistic scenarios with the scarcity of labels. We propose a straightforward two-dimensional representation of the data aiming faster processing for detection. We develop a simple adaptive drift detector on this visual representation that is efficient for fast streams with thousands of features and is accurate as existing costly methods that perform various statistical tests. Our method achieves better performance measured by execution time and accuracy in classification problems for different types of drifts, including abrupt, oscillating, and incremental. Experimental evaluation demonstrates the versatility of the method in several domains, including astronomy, entomology, public health, political science, and medical science.

An essential task on streaming time series data is to compute pairwise correlation across disparate signal sources to identify significant events. In many monitoring applications, such as geospatial monitoring, motion monitoring and critical infrastructure monitoring, correlation is observed at various frequency bands and temporal lags. In this paper, we consider computing filtered and lagged correlation on streaming time series data, which is challenging because the computation must be “in-sync” with the incoming stream for any detected events to be useful. We propose a technique to compute filtered and lagged correlation on streaming data efficiently by merging two individual operations: filtering and cross-correlations. We achieve an order of magnitude speed-up by maintaining frequency transforms over sliding windows. Our method is exact, devoid of sensitive parameters, and easily parallelizable. We demonstrate our technique in a seismic signal monitoring application.

The choice of the most promising algorithm to model and predict a particular phenomenon is one of the most prominent activities of the temporal data forecasting. Forecasting (or prediction), similarly to other data mining tasks, uses empirical evidence to select the most suitable model for a problem at hand since no modeling method can be considered as the best. However, according to our systematic literature review of the last decade, few scientific publications rigorously expose the benefits and limitations of the most popular algorithms for time series prediction. At the same time, there is a limited performance record of these models when applied to complex and highly nonlinear data. In this paper, we present one of the most extensive, impartial and comprehensible experimental evaluations ever done in the time series prediction field. From 95 datasets, we evaluate eleven predictors, seven parametric and four non-parametric, employing two multi-step-ahead projection strategies and four performance evaluation measures. We report many lessons learned and recommendations concerning the advantages, drawbacks, and the best conditions for the use of each model. The results show that SARIMA is the only statistical method able to outperform, but without a statistical difference, the following machine learning algorithms: ANN, SVM, and kNN-TSPI. However, such forecasting accuracy comes at the expense of a larger number of parameters. The evaluated datasets, as well detailed results achieved by different indexes as MSE, Theil’s U coefficient, POCID, and a recently-proposed multi-criteria performance measure are available online in our repository. Such repository is another contribution of this paper since other researchers can replicate our results and evaluate their methods more rigorously. The findings of this study will impact further research on this topic since they provide a broad insight into models selection, parameters setting, evaluation measures, and experimental setup.

Data stream classification algorithms for nonstationary environments frequently assume the availability of class labels, instantly or with some lag after the classification. However, certain applications, mainly those related to sensors and robotics, involve high costs to obtain new labels during the classification phase. Such a scenario in which the actual labels of processed data are never available is called extreme verification latency. Extreme verification latency requires new classification methods capable of adapting to possible changes over time without external supervision. This paper presents a fast, simple, intuitive and accurate algorithm to classify nonstationary data streams in an extreme verification latency scenario, namely Stream Classification Algorithm Guided by Clustering – SCARGC. Our method consists of a clustering followed by a classification step applied repeatedly in a closed loop fashion. We show in several classification tasks evaluated in synthetic and real data that our method is faster and more accurate than the state-of-the-art.

There is a huge increase of interest for time series methods and techniques. Virtually every piece of information collected from human, natural, and biological processes is susceptible to changes over time, and the study of how these changes occur is a central issue in fully understanding such processes. Among all time series mining tasks, classification is likely to be the most prominent one. In time series classification there is a significant body of empirical research that indicates that k-nearest neighbor rule in the time domain is very effective. However, certain time series features are not easily identified in this domain and a change in representation may reveal some significant and unknown features. In this work, we propose the use of recurrence plots as representation domain for time series classification. Our approach measures the similarity between recurrence plots using Campana-Keogh (CK-1) distance, a Kolmogorov complexity-based distance that uses video compression algorithms to estimate image similarity. We show that recurrence plots allied to CK-1 distance lead to significant improvements in accuracy rates compared to Euclidean distance and Dynamic Time Warping in several data sets. Although recurrence plots cannot provide the best accuracy rates for all data sets, we demonstrate that we can predict ahead of time that our method will outperform the time representation with Euclidean and Dynamic Time Warping distances.