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Given an image of a white shoe drawn on a blackboard, how are the whitepixels deemed (say by human minds) to be informative for recognizing the shoewithout 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 thatcaptures the probability distribution of the features as quantum amplitudes, wepropose an unsupervised recognition scheme of informative features with thevariations of entanglement entropy (EE) caused by designed measurements. Inthis way, a given sample, where the values of its features are statisticallymeaningless, is mapped to the variations of EE that statistically characterizethe gain of information. We show that the EE variations identify the featuresthat are critical to recognize this specific sample, and the EE itself revealsthe information distribution of the probabilities represented by the TN model.The signs of the variations further reveal the entanglement structures amongthe features. We test the validity of our scheme on a toy dataset of stripimages, the MNIST dataset of hand-drawn digits, the fashion-MNIST dataset ofthe pictures of fashion articles, and the images of brain cells. Our schemeopens the avenue to the quantum-inspired and interpreted unsupervised learning,which can be applied to, e.g., image segmentation and object detection.

Unsupervised Recognition of Informative Features via Tensor Network Machine Learning and Quantum Entanglement Variations