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.

中文翻译：

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基于Grover搜索算法的量子自组织特征映射神经网络算法

自组织特征映射神经网络是一种典型的无监督神经网络算法，常用于聚类分析和数据压缩。随着数据量的增加，算法所需的时间消耗也越来越大，这成为新的挑战。为了解决这个问题，本文提出了一种量子自组织特征映射神经网络。该算法提供了一种基于量子相位估计的样本与神经元相似度获取方法，并演示了Grover算法获取获胜神经元的方案。该算法利用量子的叠加性实现并行计算。时间复杂度分析表明，所提出的算法比经典算法要快得多。量子电路已经设计出来，同时在Qiskit框架内进行了数值模拟和心脏病数据集的实验编程。两者都验证了算法的可行性。此外，基于训练好的自组织特征映射神经网络开发了分类应用，这证明了该算法的有效性。