Patent Document ID: 20040107079
Application ID: 10662991
Patent Flag: 0

Claim One:
1. A method for estimating the topological dimension of a set of data points representing a nonlinear system response, each data point having the same number of coordinates, the method comprising the steps of: identifying a maximal set of non-redundant, nonlinear single-constraint fits to data points which are in the neighborhood of a predetermined base point, in which the gradient of each fit in the neighborhood of the base point identifies a constrained direction; estimating the number of constraints in the neighborhood of the base point to be the same as the number of such constrained directions that are linearly independent; estimating the topological dimension of the set of data points to be the original number of coordinates of the data minus the estimated number of constraints; wherein the step of identifying a set of fits further comprises the step of: using a matrix decomposition technique to find singular values and singular vectors, or eigenvalues and eigenvectors, of a design matrix formed from basis functions constructed from the data values; and wherein each fit is a linear combination of a set of basis functions for which the zero-contours of the fit, that is, the curves at which the fit has the value zero, pass near the data points and a set of individual coefficients multiplying the individual basis functions, wherein the coefficients of the basis functions are the components of singular vectors obtained from a decomposition of the design matrix.