Comment on ‘‘Singular-value decomposition and embedding dimension’’

Abstract

In this Comment we consider the conclusion drawn by Mees, Rapp, and Jennings [Phys. Rev. A 36, 340 (1987)] concerning the usefulness of the singular-system analysis of a trajectory matrix (obtained by applying Takens’s construction to time-series data). We point out that this is primarily due to their misinterpretation of our work, and to an assumption they apparently made concerning the conditions under which a map preserves the dimension of a set. We attempt to clarify the issues.