Quantum algorithm for unsupervised anomaly detection

Anomaly detection, an important branch of machine learning, plays a critical role in fraud health care, intrusion military surveillance, etc. As one the most commonly used unsupervised anomaly detection algorithms, Local Outlier Factor algorithm (LOF algorithm) has been extensively studied. This contains three steps, i.e., determining k-distance neighborhood for each data point x, computing local reachability density and calculating outlier factor x to judge whether is abnormal. The LOF computationally expensive when processing big sets. Here we present quantum consisting parts corresponding classical algorithm. Specifically, determined by amplitude estimation minimum search; calculated parallel based on multiply-adder; obtained using estimation. It shown that our achieves exponential speedup dimension points polynomial number compared its counterpart. work demonstrates advantage detection.