An Approach to the Determination of the Intrinsic Dimensionality of a Signal Collection

摘要

The intrinsic dimensionality of a collection of signals is defined in terms of the minimum number of free parameters required in a hypothetical signal generator capable of producing a close approximation to each signal in the collection. A suggested computer program outline for estimating this dimensionality from the signal coordinates on an arbitrary orthogonal basis is developed. The program is based on some results from a related multidimensional scaling problem, and utlizes an inverse relationship between the variance in interpoint distances within a hypersphere, and the dimensionality of the hypersphere. The method is independent of the choice of orthogonal basis, and no prior knowledge of the analytical form of the signals is assumed. Data points themselves are used, with no attempt to infer a continuous approximating function. (Author)