Quantum Algorithm for Density Peak Anomaly Detection Based on KNN

The density peak anomaly detection algorithm based on KNN, one of the most frequently utilized classical algorithms, is widely applied in communication fields, such as network fault detection, network traffic detection, user behavior detection, and network intrusion detection. In this algorithm, the local density value and KNN distance of all data points must be calculated, which faces enormous computational cost and computational delay challenges when the data set is processed as the network scale increases. To address this trouble, we introduce quantum computing into the algorithm and propose a quantum version of the density peak anomaly detection algorithm based on KNN. The proposed quantum algorithm first utilizes the inner product estimate algorithm and the quantum minimum search algorithm to accelerate the determination of the K nearest neighbor set of each data point and the calculation of KNN distance. Then, it performs amplitude estimation to concurrently obtain the local density of all data points. Our quantum algorithm is shown to be exponentially faster than its classical counterpart in the dimensionality of the data points and polynomially faster than the classical algorithm in the number of data points.