Collaborative Discriminant Locality Preserving Projections With its Application to Face Recognition

AbstractWe present a novel Discriminant Locality Preserving Projections (DLPP) algorithm named Collaborative Discrim-inant Locality Preserving Projection (CDLPP). In our algorithm, the discriminating power of DLPP are furtherexploited from two aspects. On the one hand, the global optimum of class scattering is guaranteed via using thebetween-class scatter matrix to replace the original denominator of DLPP. On the other hand, motivated by the sparserepresentation and collaborative representation, a L 2 -norm constraint is imposed to the projections to discover thecollaborations of dimensions in the sample space. We apply our algorithm to face recognition. Three popular facedatabases, namely AR, ORL and LFW-a, are employed for evaluating the performance of CDLPP. Extensive experi-mental results demonstrate that CDLPP signiﬁcantly improve the discriminating power of DLPP and outperform thestate-of-the-arts.Keywords: Discriminant Locality Preserving Projections, Face recognition, Dimensionality reduction, Featureextraction, Collaborative representation1. IntroductionSubspace learning is a useful technique in computer vision, pattern recognition and machine learning, particularlyfor solving the dimensionality reduction, feature selection, feature extraction and face recognition tasks. Subspacelearning aims to learn a speciﬁc subspace of the original sample space, which has some particular desired properties.This topic has been studied for decades and many impressive algorithms have been proposed. The representativesubspace learning algorithms include Principle Component Analysis (PCA) [1, 2, 3], Linear Discriminant Analysis(LDA) [4], Non-negative Matrix factorization (NMF) [5, 6], Independent Component Analysis (ICA) [7], LocalityPreserving Projections (LPP) and so on. In face recognition, subspace learning is also known as appearance-basedface recognition. For example, PCA is known as Eigenfaces, LDA is known as Fisherfaces and LPP is known asLaplacianfaces.Some recent studies show the high-dimensional samples may reside on low-dimensional manifolds [8, 9] and suchmanifold structures are essential for data clustering and classiﬁcation [10, 11]. The manifold-based subspace learningalgorithms may start from Locality Preserving Projections (LPP). LPP constructs an adjacency matrix to weightingthe distance between each two sample points for learning a projection which can preserve the local manifold structuresof data. The weight between two nearby points is much greater than the weight between two remote points. So if twopoints are close in the original space then they will be close in the learned subspace as well. However, the conventionalLPP only takes the manifold information into consideration. Many researchers make e orts to improve LPP fromdi erent perspectives. Discriminant Locality Preserving Projections (DLPP) [12, 13, 14] is deemed as one of the mostsuccessful extension of LPP. It improves the discriminating power of LPP via simultaneously maximizing the distancebetween each two nearby classes and minimizing the original LPP objective. Orthogonal Laplacianfaces (OLPP) [15]imposes an orthogonality constraint to LPP to ensure that the learned projections are mutually orthogonal. Parametric