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M. Oliver and S. Vasylkevych,
Non-negative matrix factorization with factorizable feature matrix,
submitted for publication.
Abstract:
We study the following generalization of the classical non-negative
matrix factorization (NMF) problem: Given a non-negative
matrix V, i.e., a matrix with non-negative elements, find a low
rank approximation V≈CWH where all right hand
factors are non-negative, C is a given generally non-invertible
"feature map," and V and H are low rank factors to be
determined by best-approximation in a weighted Frobenius norm. We
shall refer to this setting as the FFNMF problem. In this paper, we
propose a non-multiplicatively regularized gradient descent algorithm
for the FFNMF problem, prove its consistency, and show that a
stationary or a limit point of the algorithm is a stationary point for
the cost functional except possibly at the boundary of the admissible
region, where the cost is then locally increasing when moving away
from the boundary.
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