Topological Data Analysis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Topological data analysis is a new area of study aimed at having applications in areas such as data mining and computer vision. The human brain can easily extract global structure from representations in a strictly lower dimension, i.e. we infer a 3D environment from a 2D image from each eye. The inference of global structure also occurs when converting discrete data into continuous images. E.g. dot-matrix printers and televisions communicate images via arrays of discrete points.