  We present an improved Locality Preserving Projections (LPP) method, named
Gloablity-Locality Preserving Projections (GLPP), to preserve both the global
and local geometric structures of data. In our approach, an additional
constraint of the geometry of classes is imposed to the objective function of
conventional LPP for respecting some more global manifold structures. Moreover,
we formulate a two-dimensional extension of GLPP (2D-GLPP) as an example to
show how to extend GLPP with some other statistical techniques. We apply our
works to face recognition on four popular face databases, namely ORL, Yale,
FERET and LFW-A databases, and extensive experimental results demonstrate that
the considered global manifold information can significantly improve the
performance of LPP and the proposed face recognition methods outperform the
state-of-the-arts.
