Topological data analysis (TDA) is a new area of study aimed at having applications in areas such as data mining and computer vision. The main problems are: how one infers high-dimensional structure from low-dimensional representations; and how one assembles discrete points into global structure.The human brain can easily extract global structure from representations in a strictly lower dimension, e.g. we infer a 3D environment from a 2D image from each eye.
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