This chapter addresses the graph-based linear manifold learning for object
recognition. In particular, it introduces an adaptive Locality Preserving Projections
(LPP) which has two interesting properties: (i) it does not depend on any parameter,
and (ii) there is no correlation between mapped data. The main contribution consists in
a parameterless computation of the affinity matrix built on the principle of meaningful
and Adaptive neighbors. In addition to the framework of LPP, these two properties
have been integrated to the framework of two graph-based embedding techniques:
Orthogonal Locality Preserving Projections (OLPP) and Supervised LPP (SLPP). After
introducing adaptive affinity matrices and the uncorrelated mapped data constraint, we
perform recognition tasks on six public face databases. The results show improvement
over those of classic methods such as LPP, OLPP, and SLPP. The proposed method
could also be applied to other kinds of objects.
Keywords: Affinity matrix, Classification, Dimensionality reduction, En- hanced
Locality Preserving Projections, Face recognition, Graph-based linear embedding,
Label information, Laplacian eigenmaps, Laplacian matrix, latent points, Linear
discriminant analysis, Locality preserving projections, Nearest neighbor classifier,
Orthogonal locality preserving projections, Parameter-less locality preserving
projections, Pearson’s coefficient, principal component analysis, Projection
directions, Recognition rate, Supervised locality preserving projections.
