Nonnegative Matrix Factorization Regularized by k-NN Graphs
- Nonnegative Matrix Factorization Regularized by k-NN Graphs
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- Nonnegative matrix factorization (NMF) is a widely used feature extraction method.
NMF decomposes a data matrix into a basis matrix and a feature matrix with all of
these matrices allow to have only nonnegative elements.
With only non-subtractive constraints, NMF learns a sparse basis matrix,
result in part-based representation.
The fundamental goal of feature extraction is to exploit the more compact and
discriminative representation of input data for further processing such as
classification or clustering.
NMF is unsupervised feature extraction method, which assumes that
data points are generated from Euclidean space.
Based on this observation , we use label information to directly exploit the discriminative
geometrical structure of data points to extract more discriminative and also respects
manifold structure of data.
In this paper, we propose a novel feature extraction (subspace learning) method named
NMF regularized by k-NN graphs (KNMF).
KNMF is based on two kinds of graphs:
within-class k-NN graph and between-class k-NN graph.
Within-class k-NN graph connects only the neighboring data points which belong to
the same class of the given data point,
while between-class k-NN graph connects the neighboring data points
which belong to different class of the given data point.
By minimizing the local regions of within-class neighborhood and
maximizing the local regions of between-class neighborhood,
KNMF could exploit more discriminative hidden patterns of given data set,
benefit to the following classification based on the extracted features.
Experiments on several benchmark face recognition datasets and document datasets
confirmed the useful behavior of our proposed method in the task of feature extraction.
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