Quantum self-organizing feature mapping neural network algorithm based on Grover search algorithm

Self-organizing feature mapping neural network is a typical unsupervised neural network algorithm, which is often used for clustering analysis and data compression. As the amount of data increases, the time consumption required by the algorithm becomes increasingly large, which becomes a new challenge. To address this issue, a quantum self-organizing feature mapping neural network is proposed in this paper. This algorithm provides a method to obtain the similarity between samples and neurons based on quantum phase estimation and demonstrates the scheme to obtain winning neurons by Grover algorithm. By utilizing the superposition of quantum, the algorithm achieves parallel computing. The time complexity analysis indicates that the proposed algorithm is exponentially faster than the classical counterpart. The quantum circuit has been devised, while numerical simulation and experiment on a heart disease dataset have been conducted programming within the Qiskit framework. Both have verified the feasibility of the algorithm. Moreover, an application of classification has been developed based on the trained self-organizing feature mapping neural network, which demonstrates the effectiveness of the proposed algorithm.