  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.
