TOPOMA: Time-Series Orthogonal Projection Operator with Moving Average for Interpretable and Training-Free Anomaly Detection

We present TOPOMA, a time-series orthogonal projection operator with moving average that can identify anomalous points for multivariate time-series, without requiring any labels nor training. Despite intensive research the problem has received, it remains challenging due to 1) scarcity of labels, 2) occurrence of non-stationarity in online streaming, and 3) trust issues posed by the black-box nature of deep learning models. We tackle these issues by avoiding training a complex model on historical data as in previous work, rather we track a moving average estimate of variable subspaces that can compute the deviation of each time step via orthogonal projection onto the subspace. Further, we propose to replace the popular yet less principled global thresholding function of anomaly scores used in previous work with an adaptive one that can bound the occurrence of anomalous events to a given small probability. Our algorithm is shown to compare favourably with deep learning methods while being transparent to interpret.