  We present a novel Discriminant Locality Preserving Projections (DLPP)
algorithm named Collaborative Discriminant Locality Preserving Projection
(CDLPP). In our algorithm, the discriminating power of DLPP are further
exploited from two aspects. On the one hand, the global optimum of class
scattering is guaranteed via using the between-class scatter matrix to replace
the original denominator of DLPP. On the other hand, motivated by collaborative
representation, an $L_2$-norm constraint is imposed to the projections to
discover the collaborations of dimensions in the sample space. We apply our
algorithm to face recognition. Three popular face databases, namely AR, ORL and
LFW-A, are employed for evaluating the performance of CDLPP. Extensive
experimental results demonstrate that CDLPP significantly improves the
discriminating power of DLPP and outperforms the state-of-the-arts.
