Proceedings of the International Joint Conference on Artificial Intelligence
Abstract
Nonnegative matrix factorization (NMF), a wellknown
technique to find parts-based representations
of nonnegative data, has been widely studied.
In reality, ordinal relations often exist among data,
such as data i is more related to j than to q. Such
relative order is naturally available, and more importantly,
it truly reflects the latent data structure.
Preserving the ordinal relations enables us to find
structured representations of data that are faithful
to the relative order, so that the learned representations
become more discriminative. However, this
cannot be achieved by current NMFs. In this paper,
we make the first attempt towards incorporating the
ordinal relations and propose a novel ranking preserving
nonnegative matrix factorization (RPNMF)
approach, which enforces the learned representations
to be ranked according to the relations.
We derive iterative updating rules to solve RPNMF’s
objective function with convergence guaranteed.
Experimental results with several datasets for
clustering and classification have demonstrated that
RPNMF achieves greater performance against the
state-of-the-arts, not only in terms of accuracy, but
also interpretation of orderly data structure