Representation and Analysis of Signals. Part XXIV. Statistical Estimation of Intrinsic Dimensionality and Parameter Identification

摘要

A statistical method for estimating the intrinsic dimensionality of a signal collection was derived through the principle of invariance. Since multiple hypothesis testing yields a likelihood rule, the probability of correct decision is maximized if the assumptions made are true. However, since some of the assumptions are false, one cannot make the statement that the statistical method has probability of error less than the previous methods. By finding the intrinsic dimensionality before and after the use of a group of appropriate transforms, a specific set of parameters can be identified. While only a few parameters have been identified by this method, their general form insures a wide instance of occurrence. Finally, a signal-to-noise ratio is defined for a collection of signals; and a filtering process, by subgrouping, is based on an estimate of this ratio. (Author)