A single-class SVM based algorithm for computing an identifiable NMF

The geometric interpretation of Nonnegative Matrix Factorisation (NMF) as the problem of determining a convex cone that “well describes” the data under analysis has been key for addressing a major shortcoming of the “mainstream” NMF algorithms, that is the non-identifiability of the factorisation. On the basis of such geometric motivations, this paper proposes a novel algorithm that makes use of single-class support vector machines to recover the targeted NMF components. Not only does this new approach alleviate the NMF illposedness issue, but also it allows for automatically estimating the number of relevant NMF components, as demonstrated through experiments described in the paper. Moreover, it is readily kernelised thus opening the way for non-linear factorisations of the data.