Journal of Pattern Recognition Research

This is about frames of reference for analyzing data and how the frames can be parameterized by measurements of the data. The topic is discussed in terms of a classification method that chooses among alternative frames of reference. The method, called “Best Model Classification”, can be used whenever there is a family of data measurements. We will describe how measurements induce a fiber bundle that projects from a total space of data objects onto a base space of measurement values. Local inverses of this projection, or “sections” of the fiber bundle play the role of frames of reference or ideal objects that are attached to the data, as the nearest neighbor in the fiber. In this formalism the invariant properties of personality are parameterized by the variant ones, which are measured, and classification is seen as inverse to measurement . This is expressed by an equation “e^=e*fI*mu” whose accuracy and error rates are given. Also, we introduce a tree diagram describing a nested sequence of classifications – where a frame of reference is used to provide measurements which, in turn, define a more refined frame of reference, etc. Rather than proving theorems, the article has a two goals: to provide engineers with a recipe for solving classification problems; and to bring the concept of moving frames from differential geometry into a broader discussion of classification. In this way geometric ideas help clarify the relation between frames of reference and states of knowledge, in general.