10,735 research outputs found
New SVD based initialization strategy for Non-negative Matrix Factorization
There are two problems need to be dealt with for Non-negative Matrix
Factorization (NMF): choose a suitable rank of the factorization and provide a
good initialization method for NMF algorithms. This paper aims to solve these
two problems using Singular Value Decomposition (SVD). At first we extract the
number of main components as the rank, actually this method is inspired from
[1, 2]. Second, we use the singular value and its vectors to initialize NMF
algorithm. In 2008, Boutsidis and Gollopoulos [3] provided the method titled
NNDSVD to enhance initialization of NMF algorithms. They extracted the positive
section and respective singular triplet information of the unit matrices
{C(j)}k j=1 which were obtained from singular vector pairs. This strategy aims
to use positive section to cope with negative elements of the singular vectors,
but in experiments we found that even replacing negative elements by their
absolute values could get better results than NNDSVD. Hence, we give another
method based SVD to fulfil initialization for NMF algorithms (SVD-NMF).
Numerical experiments on two face databases ORL and YALE [16, 17] show that our
method is better than NNDSVD
A deep matrix factorization method for learning attribute representations
Semi-Non-negative Matrix Factorization is a technique that learns a
low-dimensional representation of a dataset that lends itself to a clustering
interpretation. It is possible that the mapping between this new representation
and our original data matrix contains rather complex hierarchical information
with implicit lower-level hidden attributes, that classical one level
clustering methodologies can not interpret. In this work we propose a novel
model, Deep Semi-NMF, that is able to learn such hidden representations that
allow themselves to an interpretation of clustering according to different,
unknown attributes of a given dataset. We also present a semi-supervised
version of the algorithm, named Deep WSF, that allows the use of (partial)
prior information for each of the known attributes of a dataset, that allows
the model to be used on datasets with mixed attribute knowledge. Finally, we
show that our models are able to learn low-dimensional representations that are
better suited for clustering, but also classification, outperforming
Semi-Non-negative Matrix Factorization, but also other state-of-the-art
methodologies variants.Comment: Submitted to TPAMI (16-Mar-2015
Adaptive Graph via Multiple Kernel Learning for Nonnegative Matrix Factorization
Nonnegative Matrix Factorization (NMF) has been continuously evolving in
several areas like pattern recognition and information retrieval methods. It
factorizes a matrix into a product of 2 low-rank non-negative matrices that
will define parts-based, and linear representation of nonnegative data.
Recently, Graph regularized NMF (GrNMF) is proposed to find a compact
representation,which uncovers the hidden semantics and simultaneously respects
the intrinsic geometric structure. In GNMF, an affinity graph is constructed
from the original data space to encode the geometrical information. In this
paper, we propose a novel idea which engages a Multiple Kernel Learning
approach into refining the graph structure that reflects the factorization of
the matrix and the new data space. The GrNMF is improved by utilizing the graph
refined by the kernel learning, and then a novel kernel learning method is
introduced under the GrNMF framework. Our approach shows encouraging results of
the proposed algorithm in comparison to the state-of-the-art clustering
algorithms like NMF, GrNMF, SVD etc.Comment: This paper has been withdrawn by the author due to the terrible
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