  We apply the vectorized Non-negative Matrix Factorization (NMF) method to
post-processing of direct imaging data for exoplanetary systems such as
circumstellar disks. NMF is an iterative approach, which first creates a
non-orthogonal and non-negative basis of components using given reference
images, then models a target with the components. The constructed model is then
rescaled with a factor to compensate for the contribution from a disk. We
compare NMF with existing methods (classical reference differential imaging
method, and the Karhunen-Lo\`eve image projection algorithm) using synthetic
circumstellar disks, and demonstrate the superiority of NMF: with no need for
prior selection of references, NMF can detect fainter circumstellar disks,
better preserve low order disk morphology, and does not require forward
modeling. As an application to a well-known disk example, we process the
archival Hubble Space Telescope (HST) STIS coronagraphic observations of
HD~181327 with different methods and compare them. NMF is able to extract some
circumstellar material inside the primary ring for the first time. In the
appendix, we mathematically investigate the stability of NMF components during
iteration, and the linearity of NMF modeling.

Instrumentation and Methods for Astrophysics;Earth and Planetary Astrophysics;Machine Learning