Enumeration of Harmonic Frames and Frame Based Dimension Reduction

Abstract

We investigate two aspects of frame theory, one of a theoretical

nature, the other very much on the applied side. In the former, we

enumerate all harmonic frames of prime order, and develop partial

proofs concerning the structure of the symmetry group for this subset

of frames. In the latter, we develop frame theory in the context of

kernel eigenmap methods, merging the two theories in a practical

manner and applying new algorithms to hyperspectral imagery data for

the purposes of material classification. These two problems, while

seemingly separate, are united by frame theory and serve to illustrate

both the beautiful theoretical nature of frames as well as their

practicality in dealing with real world problems.