A quantum feature selection algorithm for multi-classification problem

ReliefF is a feature selection algorithm for the multi classification problem, and its complexity of the algorithm grows rapidly as the number of samples and features increases. in order to reduce the complexity, a quantum-based feature selection algorithm for the multi-classification problem, also called QReliefF algorithm, is proposed. Firstly, all features of each sample are encoded into the quantum slate by CMP and rotation operation for similarity calculation. After that, the similarity is encoded into a quantum slate using the amplitude estimation, the nearest k neighbor samples in each class are found by Grover method, and are used to update the weight vector. Finally, the features are selected according to the final weight vector and threshold. Compared with the classical ReliefF algorithm, our algorithm changes from O(M N) to O(M) in terms of the complexity of similarity calculation and the complexity of finding the nearest neighbor is changed from O(M) to O(root M). Our algorithm consumes O(M log N) qubits in terms of resource consumption, while the ReliefF algorithm consumes O(M N) bits. Obviously, our algorithm is better than the ReliefF algorithm in efficiency and resource consumption.