The Karhunen-Loeve transform of discrete MVL functions

Abstract

The Karhunen-Loeve (KL) transform of a discrete multiple-valued logic function is studied with respect to algebraic graph theory. The spectrum of a Cayley graph defined over the symmetry group is observed to be equivalent to the KL spectrum of a discrete function when the Cayley graph is generated using that function. It is also observed that the autocorrelation of the discrete function using the symmetry group operator is equivalent to the adjacency matrix of the Cayley graph. In addition to the theoretical interests, the KL spectrum of a discrete multiple-valued logic function can have applications in compact function representation and the determination of function estimates with a reduced support set. Example computations are shown in addition to the presentation of the mathematical properties.