Tensor networks, which have been traditionally used to simulate many-body physics, have recently gained significant attention in the field of machine learning due to their powerful representation capabilities. In this work, we propose a density-based clustering algorithm inspired by tensor networks. We encode classical data into tensor network states on an extended Hilbert space and train the tensor network states to capture the features of the clusters. Here, we define density and related concepts in terms of fidelity, rather than using a classical distance measure. We evaluate the performance of our algorithm on six synthetic data sets, four real world data sets, and three commonly used computer vision data sets. The results demonstrate that our method provides state-of-the-art performance on several synthetic data sets and real world data sets, even when the number of clusters is unknown. Additionally, our algorithm performs competitively with state-of-the-art algorithms on the MNIST, USPS, and Fashion-MNIST image data sets. These findings reveal the great potential of tensor networks for machine learning applications.

翻译：张量网络传统上用于模拟多体物理系统，近年来因其强大的表示能力而受到机器学习领域的广泛关注。本文提出了一种受张量网络启发的基于密度的聚类算法。我们将经典数据编码到扩展希尔伯特空间中的张量网络态上，并训练该张量网络态以捕获聚类特征。在此过程中，我们基于保真度而非经典距离度量来定义密度及相关概念。我们在六个合成数据集、四个真实世界数据集以及三个常用的计算机视觉数据集上评估了该算法的性能。结果表明，即使在聚类数未知的情况下，我们的方法在多个合成数据集和真实世界数据集上仍能达到最先进的性能。此外，在MNIST、USPS和Fashion-MNIST图像数据集上，该算法的性能与最先进算法相比具有竞争力。这些发现揭示了张量网络在机器学习应用中的巨大潜力。