3 research outputs found
Ranking Preserving Nonnegative Matrix Factorization
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
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Orderly Subspace Clustering
Semi-supervised representation-based subspace clustering is
to partition data into their underlying subspaces by finding
effective data representations with partial supervisions. Essentially, an effective and accurate representation should be
able to uncover and preserve the true data structure. Meanwhile, a reliable and easy-to-obtain supervision is desirable
for practical learning. To meet these two objectives, in this
paper we make the first attempt towards utilizing the orderly relationship, such as the data a is closer to b than to c, as
a novel supervision. We propose an orderly subspace clustering approach with a novel regularization term. OSC enforces the learned representations to simultaneously capture
the intrinsic subspace structure and reveal orderly structure
that is faithful to true data relationship. Experimental results
with several benchmarks have demonstrated that aside from
more accurate clustering against state-of-the-arts, OSC interprets orderly data structure which is beyond what current approaches can offer
Recommended from our members
Ranking preserving nonnegative matrix factorization
Nonnegative matrix factorization (NMF), a well-known 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, current NMFs pay no attention to this. 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