  The model described in this paper belongs to the family of non-negative
matrix factorization methods designed for data representation and dimension
reduction. In addition to preserving the data positivity property, it aims also
to preserve the structure of data during matrix factorization. The idea is to
add, to the NMF cost function, a penalty term to impose a scale relationship
between the pairwise similarity matrices of the original and transformed data
points. The solution of the new model involves deriving a new parametrized
update scheme for the coefficient matrix, which makes it possible to improve
the quality of reduced data when used for clustering and classification. The
proposed clustering algorithm is compared to some existing NMF-based algorithms
and to some manifold learning-based algorithms when applied to some real-life
datasets. The obtained results show the effectiveness of the proposed
algorithm.
