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:传统上用于模拟多体物理学的Tensor网络最近因其强大的代表性能力而在机器学习领域受到极大关注。 在这项工作中,我们提议了一种由强力网络启发的基于密度的集群算法。我们将古典数据以扩展的Hilbert空间编码成强尔网络状态,并训练高压网络状态来捕捉集群的特征。在这里,我们从忠诚的角度来定义密度和相关概念,而不是使用传统的距离测量方法。我们评估了我们六套合成数据集、四套真实世界数据集和三套常用计算机视觉数据集的算法的性能。结果显示,我们的方法在一些合成数据集和真实世界数据集中提供了最先进的性能。此外,我们的算法与MNIST、USPS和Fashion-MNIST成像数据集中的最先进的算法相竞争地运行。这些结果揭示了Sronor网络在机器学习应用方面的巨大潜力。