Quantum Eigenfaces: Linear Feature Mapping and Nearest Neighbor Classification with Outlier Detection

We propose a quantum machine learning algorithm for data classification, inspired by the seminal computer vision approach of eigenfaces for face recognition. The algorithm enhances nearest neighbor/centroid classifiers with concepts from principal component analysis, enabling the automatic detection of outliers and finding use in anomaly detection domains beyond face recognition. Assuming classical input data, we formalize how to implement the algorithm using a quantum random access memory and state-of-the-art quantum linear algebra, discussing the complexity of performing the classification algorithm on a fault-tolerant quantum device. The asymptotic time complexity analysis shows that the quantum classification algorithm can be more efficient than its classical counterpart. We showcase an application of this algorithm for face recognition and image classification datasets with anomalies, obtaining promising results for the running time parameters. This work contributes to the growing field of quantum machine learning applications, and the algorithm's simplicity makes it easily adoptable by future quantum machine learning practitioners.