@article{witeprints3174,
          volume = {24},
           month = {July},
          author = {Ruair{\'i} de Fr{\'e}in},
           title = {Ghostbusters: A Parts-based NMF Algorithm},
       publisher = {IET and IEEE},
         journal = {24th IET Irish Signals and Systems Conference (ISSC 2013)},
           pages = {1--8},
            year = {2013},
             url = {http://repository.wit.ie/3174/},
        abstract = {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.}
}