The ability to detect anomalies in time series is considered highly valuable in numerous application domains. The sequential nature of time series objects is responsible for an additional feature complexity, ultimately requiring specialized approaches in order to solve the task. Essential characteristics of time series, situated outside the time domain, are often difficult to capture with state-of-the-art anomaly detection methods when no transformations have been applied to the time series. Inspired by the success of deep learning methods in computer vision, several studies have proposed transforming time series into image-like representations, used as inputs for deep learning models, and have led to very promising results in classification tasks. In this paper, we first review the signal to image encoding approaches found in the literature. Second, we propose modifications to some of their original formulations to make them more robust to the variability in large datasets. Third, we compare them on the basis of a common unsupervised task to demonstrate how the choice of the encoding can impact the results when used in the same deep learning architecture. We thus provide a comparison between six encoding algorithms with and without the proposed modifications. The selected encoding methods are Gramian Angular Field, Markov Transition Field, recurrence plot, grey scale encoding, spectrogram, and scalogram. We also compare the results achieved with the raw signal used as input for another deep learning model. We demonstrate that some encodings have a competitive advantage and might be worth considering within a deep learning framework. The comparison is performed on a dataset collected and released by Airbus SAS, containing highly complex vibration measurements from real helicopter flight tests. The different encodings provide competitive results for anomaly detection.
Spatial hotspot discovery aims at discovering regions with statistically significant concentration of activities. It has shown great value in many important societal applications such as transportation engineering, public health, and public safety. This paper formulates the problem of Linear Hotspot Detection on All Simple Paths (LHDA) which identifies hotspots from the complete set of simple paths enumerated from a given spatial network. LHDA overcomes the limitations of existing methods which miss hotspots that naturally occur along linear simple paths on a road network. To address the computational challenges, we propose a novel algorithm named bidirectional fragment-multi-graph traversal (ASP_FMGT) and two path reduction approaches ASP_NR and ASP_HD. Experimental analyses show that ASP_FMGT has substantially improved performance over state-of-the-art approach (ASP_Base) while keeping the solution complete and correct. Moreover, a case study on real-world datasets showed that ASP_FMGT outperforms existing approaches.
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