Anomaly detection on multivariate time series (MTS) is an important research topic in data mining, which has a wide range of applications in information technology, financial management, manufacturing system, and so on. However, the state-of-the-art unsupervised deep learning models for MTS anomaly detection are vulnerable to noise and have poor performance on the training data containing anomalies. In this article, we propose a novel Self-Training based Anomaly Detection with Generative Adversarial Network (GAN) model called STAD-GAN to address the practical challenge. The STAD-GAN model consists of a generator-discriminator structure for adversarial learning and a neural network classifier for anomaly classification. The generator is learned to capture the normal data distribution, and the discriminator is learned to amplify the reconstruction error of abnormal data for better recognition. The proposed model is optimized with a self-training teacher-student framework, where a teacher model generates reliable high-quality pseudo-labels to train a student model iteratively with a refined dataset so that the performance of the anomaly classifier can be gradually improved. Extensive experiments based on six open MTS datasets show that STAD-GAN is robust to noise and achieves significant performance improvement compared to the state-of-the-art.

Multivariate time series (MTS) clustering is an important technique for discovering co-evolving patterns and interpreting group characteristics in many areas including economics, bioinformatics, data science, etc. Although time series clustering has been widely studied in the past decades, no enough attention has been paid to capture time-varying correlation patterns in MTS. In this article, we propose a novel clustering approach for MTS data based on time-varying features. We introduce a time-varying Gaussian Markov Random Fields (T-GMRF) model to describe the correlation structure between MTS variables, and formulate the time-varying feature extraction problem as a convex optimization problem, which can be solved by a T-GMRF learning algorithm based on random block coordinate descent. We further apply a principal component analysis (PCA) based method on GMRF sequences to obtain low-dimensional feature vectors, and adopt a multi-density based clustering approach to form the cluster assignments. We conduct extensive experiments to compare the proposed T-GMRF method with 11 clustering algorithms based on 33 open MTS datasets, which show that T-GMRF significantly outperforms the state-of-the-arts with performance improvement up to 16%-64.5% on a variety of clustering performance metrics. The source codes of T-GMRF are publicly available at GitHub.