Patent ID: 7711529

Claim:
A computer method for generating an indication representing behavior of a real-world system based on an estimate of the topological dimension of a manifold, the method comprising: accepting data points representing a response of the real-world system, each data point having the same number of coordinates, the data points lying on the manifold or within a given error of the manifold; identifying fits to the points which are in a neighborhood of a base point, in which the gradient of each fit at 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; altering the estimated number of constraints using prior information about the real-world system; estimating the topological dimension of the manifold to be the number of coordinates of each of the data points minus the altered estimated number of constraints; generating the indication representing behavior of the real-world system based on the estimated topological dimension; and presenting the generated indication representing behavior of the real-word system to a user from a computer.