Stastical Estimation of the Intrinsic Dimensionality of a Noisy Signal Collection

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Abstract
Let W be an N-dimensional vector space and let the signal locus V be a K-dimensional topological hypersurface in W. The intrinsic dimensionality problem can be stated as follows. Given M randomly selected points (signals) vi, vi ϵ V, estimate K, which is the dimensionality of V and is called the intrinsic dimensionality of the points vi. A statistical method, which is developed from geometric considerations, is used to estimate the dimensionality. This ad hoc statistical method avoids the approximations and assumptions required by the maximum likelihood solution. The problem of estimating dimensionality in the presence of additive white noise is also considered. A pseudo, signal-to-noise ratio, which has meaning with respect to estimating the dimensionality of a noisy signal collection, is defined. A filtering method, based on this ratio, is used to estimate the dimensionality of a noisy signal collection. The accuracy of the method is demonstrated by estimating the dimensionality of a collection of pulsed signals which have four free parameters.