Ghostbusters: A Parts-based NMF Algorithm

Ruairí de Fréin

    Research output: Contribution to journalArticlepeer-review


    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.
    Original languageEnglish
    Pages (from-to)1-8
    JournalIrish Signals and Systems Conference
    Publication statusPublished - 2013


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