Unsupervised Anomaly Detection in Multi-Aspect Data via Tensor Decomposition and Hidden Markov Models

Abstract

Anomaly detection in unlabeled multi-aspect bio-signals with semi-periodic patterns is a challenging task. We propose a novel unsupervised anomaly scoring method called importance to effectively address this problem. Our approach combines Tucker decomposition and Gaussian Mixture Hidden Markov Models (GM-HMM) to simultaneously capture the latent patterns in the multi-aspect structure and the inherent temporal patterns of the data. The importance score’s novelty stems from 1) a new definition of error contribution from the input values, and 2) a weight definition for the temporal factor based on GM-HMM. This weighted error contribution enables more accurate anomaly detection compared to existing methods. Extensive experiments were conducted on synthetic multi-aspect time-series data to demonstrate the effectiveness of our importance score for anomaly detection compared to other approaches. Further evaluations on three real-world bio-signal datasets provide empirical evidence of the effectiveness in detecting unusual signals.