Graph Regularized Autoencoder and its Application in Unsupervised Anomaly Detection

Dimensionality reduction is a crucial first step for many unsupervised learning tasks including anomaly detection. Autoencoder is a popular mechanism to accomplish the goal of dimensionality reduction. In order to make dimensionality reduction effective for high-dimensional data embedding nonlinear low-dimensional manifold, it is understood that some sort of geodesic distance metric should be used to discriminate the data samples. Inspired by the success of neighborhood aware shortest path based geodesic approximatiors such as ISOMAP, in this work, we propose to use a minimum spanning tree (MST), a graph-based algorithm, to approximate the local neighborhood structure and generate structure-preserving distances among data points. We use this MST-based distance metric to replace the Euclidean distance metric in the embedding function of autoencoders and develop a new graph regularized autoencoder, which outperforms, over 20 benchmark anomaly detection datasets, the plain autoencoder using no regularizer as well as the autoencoders using the Euclidean-based regularizer. We furthermore incorporate the MST regularizer into two generative adversarial networks and find that using the MST regularizer improves the performance of anomaly detection substantially for both generative adversarial networks.