Abstract
In this paper, we propose a novel machine-learning method for anomaly detection applicable to data with periodic characteristics where randomly varying period lengths are explicitly allowed. A multi-dimensional time series analysis is conducted by training a data-adapted classifier consisting of deep convolutional neural networks performing phase classification. The entire algorithm including data pre-processing, period detection, segmentation, and even dynamic adjustment of the neural networks is implemented for fully automatic execution. The proposed method is evaluated on three example datasets from the areas of cardiology, intrusion detection, and signal processing, presenting reasonable performance.
Highlights
Many real-world systems, both natural and anthropogenic, exhibit periodic behaviour
2.3.2 ARIMA methodology and Kalman filtering A more sophisticated class of methods arises from mathematical statistics, e.g. autoregressive integrated moving average (ARIMA) methodology, methods based on structural component time series models or more general Kalman filtering, cf. [20, 21] for detailed description of the corresponding mathematical models
We provide a short description of the mathematical basis of a convolutional neural network
Summary
Many real-world systems, both natural and anthropogenic, exhibit periodic behaviour. Monitoring such systems necessarily produces periodic time series. 2.3.2 ARIMA methodology and Kalman filtering A more sophisticated class of methods arises from mathematical statistics, e.g. autoregressive integrated moving average (ARIMA) methodology, methods based on structural component time series models or more general Kalman filtering (based on the linear case of the general state-space model or hidden Markov model), cf [20, 21] for detailed description of the corresponding mathematical models These approaches can be directly applied to problems of type B described in Section 2.2 and are based on relating a stochastic model with parameters.
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