Anomaly Detection on Graph Time Series

In this paper, we use variational recurrent neural network to investigate the anomaly detection problem on graph time series. The temporal correlation is modeled by the combination of recurrent neural network (RNN) and variational inference (VI), while the spatial information is captured by the graph convolutional network. In order to incorporate external factors, we use feature extractor to augment the transition of latent variables, which can learn the influence of external factors. With the target function as accumulative ELBO, it is easy to extend this model to on-line method. The experimental study on traffic flow data shows the detection capability of the proposed method

Machine learning approaches to complex time series

It has been noted that there are numerous similarities between the behaviour of chaotic and stochastic systems. The theoretical links between chaotic and stochastic systems are investigated based on the evolution of the density of dynamics and an equivalency relationship based on the invariant measure of an ergodic system. It is shown that for simple chaotic systems an equivalent stochastic model can be analytically derived when the initial position in state space is only known to a limited precision. Based on this a new methodology for the modelling of complex nonlinear time series displaying chaotic behaviour with stochastic models is proposed. This consists of using a stochastic model to learn the evolution of the density of the dynamics of the chaotic system by estimating initial and transitional density functions directly from a time series. A number of models utilising this methodology are proposed, based on Markov chains and hidden Markov models. These are implemented and their performance and characteristics compared using computer simulation with several standard techniques

Neural Learning of Chaotic Dynamics: The Error Propagation Algorithm

An algorithm is introduced that trains a neural network to identify chaotic dynamics from a single measured timeseries. The algorithm has four special features: 1. The state of the system is extracted from the time-series using delays, followed by weighted Principal Component Analysis (PCA) data reduction. 2. The prediction model consists of both a linear model and a Multi-Layer-Perceptron (MLP). 3. The effective prediction horizon during training is user-adjustable, due to ‘error propagation’: prediction errors are partially propagated to the next time step. 4. A criterion is monitored during training to select the model that has a chaotic attractor most similar to the real system’s attractor. The algorithm is applied to laser data from the Santa Fe time-series competition (set A). The resulting model is not only useful for short-term predictions but it also generates time-series with similar chaotic characteristics as the measured data