%0 Journal Article
%A de Fréin, Ruairí
%A IEEE,
%A IET,
%D 2013
%F witeprints:3174
%I IET and IEEE
%J 24th IET Irish Signals and Systems Conference (ISSC 2013)
%P 1-8
%T Ghostbusters: A Parts-based NMF Algorithm
%U http://repository.wit.ie/3174/
%V 24
%X An exact nonnegative matrix decomposition algorithm is proposed. This is achieved by 1) Taking a nonlinear approximation of a sparse real-valued dataset at a given tolerance-to-error constraint, e; 2) Choosing an arbitrary lectic ordering on the rows or column entries; And, then 3) systematically applying a closure operator, so that all closures are selected. Assuming a nonnegative hierarchical closure structure (a Galois lattice) ensures the data has a unique ordered overcomplete dictionary representation. Parts-based constraints on these closures can then be used to specify and supervise the form of the solution. We illustrate that this approach outperforms NMF on two standard NMF datasets: it exhibits the properties described above; It is correct and exact.