Anomaly Detection from Multilinear Observations via Time-Series Analysis and 3DTPCA

In the era of big data, there is massive demand for new techniques to forecast and analyze multi-dimensional data. One task that has seen great interest in the community is anomaly detection of streaming data. Toward this end, the current research develops a novel approach to anomaly detection of streaming 2-dimensional observations via multilinear time-series analysis and 3-dimensional tensor principal component analysis (3DTPCA). We approach this problem utilizing dimensionality reduction and probabilistic inference in a low-dimensional space. We first propose a natural extension to 2-dimensional tensor principal component analysis (2DTPCA) to perform data dimensionality reduction on 4-dimensional tensor objects, aptly named 3DTPCA. We then represent the sub-sequences of our time-series observations as a 4-dimensional tensor utilizing a sliding window. Finally, we use 3DTPCA to compute reconstruction errors for inferring anomalous instances within the multilinear data stream. Experimental validation is presented via MovingMNIST data. Results illustrate that the proposed approach has a significant speedup in training time compared with deep learning, while performing competitively in terms of accuracy.