Determining a tangent space and filtering data onto a manifold
US7124065B2 · kind B2 · utility
Assignee
Inventor
Key dates
| Filing date | Sep 15, 2003 |
| Grant date | Oct 17, 2006 |
| Priority date | — |
| Expiry date | Feb 12, 2025 |
Classification
- Technology area (CPC G)Physics
- CPC primaryG10L25/48
- WIPO fieldComputer technology
- WIPO sectorElectrical engineering
Abstract
A technique for determining the number of constraints on a set of input data, or equivalently the topological dimension, especially when such data are produced by a nonlinear system, such as a pathological vocal system or econometric data and the like. The technique characterizes the tangent space about a predetermined base point by identifying a maximal set of non-redundant nonlinear fits to the data. It needs only a modest number of data points and does not assume prior knowledge of the functional form of the true constraints, other than smoothness. Each fit is equivalent to a set of contours (including curves, surfaces, and other manifolds), with the data themselves all lying along the zero-value contour of the fit. For each fit, the gradient of the fit at the base point in the uphill direction across the contours identifies the constraint direction. Considering all fits simultaneously, the number of constraint directions that are linearly independent provides the number of constraints in the neighborhood of the base point. The remaining unconstrained directions define the tangent space, and its dimensionality, which is precisely the number of linearly independent unconstrained …
Source: USPTO / EPO open patent data. Objective bibliographic and citation counts.