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Detecting anomalies accurately in time series data has been receiving considerable attention due to its enormous potential for a wide array of applications. Numerous unsupervised anomaly detection methods for time series have been developed because of the difficulty of obtaining accurate labels. However, most existing unsupervised approaches suffer from the problem of anomaly contamination, which results in models that are unable to learn the normal pattern well and further deteriorate the performance of detection methods. To this end, a novel unsupervised method, called Self-adversarial Variational Autoencoder with Spectral Residual (SaVAE-SR), is introduced for time series anomaly detection in this paper. The SaVAE-SR first produces labels for unlabeled training data using the spectral residual technique to identify the most critical anomalies. A VAE model with a modified loss that can leverage label information to remove the influence of anomalous points is then trained in a self-adversarial manner, enabling the model to self-evaluate the learning of complex data distribution and improve itself accordingly. Specifically, the encoder acts as an encoder to approximate the posterior of latent variables and as a discriminator to evaluate the generative ability of the generator and improve itself accordingly. The generator is trained to capture the underlying data distribution and attempts to produce real samples to deceive the discriminator. The encoder and generator of the model compete with each other just like the behavior of GANs but work together under the theoretical framework of VAEs. As a result, the SaVAE-SR model combines the respective strengths of the VAE and adversarial training but does not require an additional discriminator, which makes the whole model very compact. Extensive experiments on five datasets demonstrate the superiority of the proposed method over the existing state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Multiscale entropy analysis has become a prevalent complexity measurement and been successfully applied in various fields. However, it only takes into account the information of mean values (first moment) in coarse-graining procedure. Then generalized multiscale entropy (MSE n ) considering higher moments to coarse-grain a time series was proposed and MSE σ 2 has been implemented. However, the MSE σ 2 sometimes may yield an imprecise estimation of entropy or undefined entropy, and reduce statistical reliability of sample entropy estimation as scale factor increases. For this purpose, we developed the refined model, RMSE σ 2 , to improve MSE σ 2 . Simulations on both white noise and 1 ∕ f noise show that RMSE σ 2 provides higher entropy reliability and reduces the occurrence of undefined entropy, especially suitable for short time series. Besides, we discuss the effect on RMSE σ 2 analysis from outliers, data loss and other concepts in signal processing. We apply the proposed model to evaluate the complexity of heartbeat interval time series derived from healthy young and elderly subjects, patients with congestive heart failure and patients with atrial fibrillation respectively, compared to several popular complexity metrics. The results demonstrate that RMSE σ 2 measured complexity (a) decreases with aging and diseases, and (b) gives significant discrimination between different physiological/pathological states, which may facilitate clinical application. [ABSTRACT FROM AUTHOR]

Causal analysis based on non-uniform embedding schemes is an important way to detect the underlying interactions between dynamic systems. However, there are still some obstacles to estimating high-dimensional conditional mutual information and forming optimal mixed embedding vector in traditional non-uniform embedding schemes. In this study, we present a new non-uniform embedding method framed in information theory to detect causality for multivariate time series, named LM-PMIME, which integrates the low-dimensional approximation of conditional mutual information and the mixed search strategy for the construction of the mixed embedding vector. We apply the proposed method to simulations of linear stochastic, nonlinear stochastic, and chaotic systems, demonstrating its superiority over partial conditional mutual information from mixed embedding (PMIME) method. Moreover, the proposed method works well for multivariate time series with weak coupling strengths, especially for chaotic systems. In the actual application, we show its applicability to epilepsy multichannel electrocorticographic recordings. [ABSTRACT FROM AUTHOR]

Correlated time series refer to multiple time series which are recorded simultaneously to monitor the changing of multiple observations in a whole system. Correlated time series prediction plays a significant role in many real-world applications to help people make reasonable decisions. Yet it is very challenging, because different from single time series, correlated time series show both intra-sequence temporal dependencies and inter-sequence spatial dependencies. In addition, correlated time series are also affected by external factors in actual scenarios. Although RNNs have been proved to be effective on sequential data modeling, existing related works only focus on sequential patterns in a single time series, failing to comprehensively consider the inter-dependencies among multiple time series, which is essential for correlated time series prediction. In this paper, we propose a novel variant of LSTM, named CTS-LSTM, to collectively forecast correlated time series. Specifically, spatial and temporal correlations are explicitly modeled and respectively maintained in cells to capture the complex non-linear patterns in correlated time series. A general interface for handling external factors is further designed to enhance forecasting performance of the model. Experiments are conducted on two types of real-world datasets, viz., civil aviation passenger demand data and air quality data. And our CTS-LSTM achieves at least 9.0%, 16.5% and 21.3% lower RMSE, MAE and MAPE compared to the state-of-the-art baselines. [ABSTRACT FROM AUTHOR]