We propose a novel method for the autonomous determination of endmembers that employs recent results from the theory of lattice based auto-associative memories. In contrast to several other existing methods, the endmembers determined by the proposed method are physically linked to the data set spectra. Numerical examples are provided to illustrate lattice theoretical concepts and a hyperspectral image subcube, from the Cuprite site in Nevada, is used to find all endmember candidates in a single pass.