Whitney reduction networks for process discovery

Abstract

The author presents an application of Whitney's embedding theorem to the data reduction problem, and introduces a new reduction technique motivated, in part, by a constructive proof of the theorem. In this setting, we introduce the notion of a "good projection". We show it is useful to optimize empirical projections with respect to their inverses, i.e., these should be well-conditioned. One possibility is computation of the singular vectors of the secants of the data. This may be improved upon by using an adaptive algorithm. A method for constructing the nonlinear inverse of the projection and a discussion of its properties are also presented. Finally, well-known methods of data reduction are compared with our approach within the context of Whitney's Theorem.