Anomaly detection methods applied to time series are mostly viewed as a black box, which solely provides a deterministic answer to the detected target. Without a convincing explanation, domain experts can hardly trust the detection results and conduct a further time series diagnosis in real-world applications. To overcome the challenge, we mathematically analyzed the sources of anomalies and novelties in multivariate time series as well as their relationships from the perspective of Gaussian-distributed non-stationary noise. Furthermore, we proposed mathematical methods to generate artificial time series and synthetic anomalies, with the goal of solving the problem that it is difficult to train and evaluate models in real-world applications due to the lack of sufficient data. In addition, we designed extbfProbabilistic extbfOutlier extbfDetection (PrOuD), which is a general solution to provide interpretable detection results to assist domain experts in time series analysis. PrOuD can convert a predictive uncertainty of a trained model about a time series value into an estimated uncertainty of the detected outlier through Monte Carlo Estimation. The experimental results obtained on both artificial time series and real-world photovoltaic inverter data demonstrated that the proposed solution could detect emerging anomalies accurately and quickly. The implemented PrOuD demo case shows the potential to makes the detection results of the existing detection methods more convincing so that domain experts can more efficiently complete their tasks, such as time series diagnosis and anomalous pattern clustering.

The subject of collective attention is central to an information age where millions of people are inundated with daily messages. It is thus of interest to understand how attention to novel items propagates and eventually fades among large populations. We have analyzed the dynamics of collective attention among 1 million users of an interactive web site, digg.com, devoted to thousands of novel news stories. The observations can be described by a dynamical model characterized by a single novelty factor. Our measurements indicate that novelty within groups decays with a stretched-exponential law, suggesting the existence of a natural time scale over which attention fades.