Multiscale Geometry and Harmonic Analysis of Data Bases
author:
Ronald Coifman,
Department of Computer Science, Yale University
Description
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.
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| Slides | |
| 0:00 | Multiscale Analysis of Digital Data Bases (Matrices) |
| 2:20 | Goal (1) |
| 2:35 | Consider the problem |
| 3:34 | Describing (1) |
| 4:22 | Describing (2) |
| 11:29 | Describing (4) |
| 13:44 | Describing (2) |
| 13:46 | Describing (3) |
| 16:25 | Describing (5) |
| 17:37 | A similar organization in the vocabulary of a body of Science (1) |
| 19:50 | A similar organization in the vocabulary of a body of Science (2) |
| 20:01 | A similar organization in the vocabulary of a body of Science (3) |
| 22:17 | A similar organization in the vocabulary of a body of Science (4) |
| 22:47 | A similar organization in the vocabulary of a body of Science (5) |
| 23:20 | A similar organization in the vocabulary of a body of Science (6) |
| 23:28 | A similar organization in the vocabulary of a body of Science (7) |
| 28:53 | A similar organization in the vocabulary of a body of Science (8) |
| 30:01 | Multiscale Geometric Analysis on Digital data clouds (1) |
| 30:27 | Multiscale Geometric Analysis on Digital data clouds (2) |
| 32:00 | Multiscale Geometric Analysis on Digital data clouds (3) |
| 34:44 | Diffusion Geometry (1) |
| 37:05 | Diffusion Geometryc (2) |
| 37:45 | Another similar construction for empirical data (3) |
| 38:53 | Another similar construction for empirical data (8) |
| 40:33 | Another similar construction for empirical data (9) |
| 40:44 | Another similar construction for empirical data (11) |
| 42:00 | Another similar construction for empirical data (12) |
| 42:48 | Another similar construction for empirical data (13) |
| 43:11 | Another similar construction for empirical data (14) |
| 43:59 | Another similar construction for empirical data (15) |
| 44:45 | Another similar construction for empirical data (16) |
| 46:34 | Another similar construction for empirical data (17) |
| 47:34 | A similar organization in the vocabulary of a body of Science (5) |
| 50:50 | Describing (6) |
| 51:34 | A similar organization in the vocabulary of a body of Science (6) |
| 55:44 | - Questions |
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