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Anomaly detection for video surveillance gains more attention as the number of deployed cameras constantly increases while the state-of-the-art (SOTA) machine learning methods push the detection performance to its limit. Low complexity methods are relatively straightforward to train (low variance) but suffer from high bias (low performance) whereas, the complex ones can achieve high performance (low bias) with a large sample size to suppress the high variance of estimated parameters. Also, most of the SOTA methods can only detect indigenous anomalies that are spatially stationary, failing at detecting the locational anomalies that are due to nonstationary spatial statistics. To solve these issues, we propose an ensemble technique based on a context tree that generates a hierarchical ensemble of image plane partitions, which we call context tree based anomaly detection (CTBAD). With CTBAD, partitions yield anomaly detection models of varying complexities, i.e., from coarse to fine details in partitioning with each partition model (which can be any SOTA method) trained separately to allow the detection of locational anomalies, and then we combine them linearly in a weighted manner to achieve a gradual transition from simpler models to more complex ones as more data become available in a video stream. As a result, CTBAD benefits from low variance of low complexity methods when the data is sparse and exploits high complexity to achieve low bias when sufficient data is observed. Our experiments show that we significantly reduce the number of training samples to reach the same accuracy of a complex model while successfully detecting the locational anomalies.

A Hierarchical Approach for Improved Anomaly Detection in Video Surveillance