  Given an image of a white shoe drawn on a blackboard, how are the white
pixels deemed (say by human minds) to be informative for recognizing the shoe
without any labeling information on the pixels? Here we investigate such a
``white shoe'' recognition problem from the perspective of tensor network (TN)
machine learning and quantum entanglement. Utilizing a generative TN that
captures the probability distribution of the features as quantum amplitudes, we
propose an unsupervised recognition scheme of informative features with the
variations of entanglement entropy (EE) caused by designed measurements. In
this way, a given sample, where the values of its features are statistically
meaningless, is mapped to the variations of EE that statistically characterize
the gain of information. We show that the EE variations identify the features
that are critical to recognize this specific sample, and the EE itself reveals
the information distribution of the probabilities represented by the TN model.
The signs of the variations further reveal the entanglement structures among
the features. We test the validity of our scheme on a toy dataset of strip
images, the MNIST dataset of hand-drawn digits, the fashion-MNIST dataset of
the pictures of fashion articles, and the images of brain cells. Our scheme
opens the avenue to the quantum-inspired and interpreted unsupervised learning,
which can be applied to, e.g., image segmentation and object detection.
