Multiscale Geometry and Harmonic Analysis of Data Bases

We describe a method for geometrization of databases such as, questionnaires, or lists of sensor outputs. Interlacing multiscale diffusion geometries of rows and columns of a data matrix, results in a pair of language ontologies which are mutually supportive (certain words are used in certain contexts). This mutual geometry serves a structure of Harmonic Analysis and signal processing on the database. We will illustrate, on databases of audio (music), psychological questionnaires, science documents, images and many others. Joint work with Mata Gavish, Yale University.