Robust Image Representation via Low Rank Locality Preserving Projection

Locality preserving projection (LPP) is a dimensionality reduction algorithm preserving the neighhorhood graph structure of data. However, the conventional LPP is sensitive to outliers existing in data. This article proposes a novel low-rank LPP model called LR-LPP. In this new model, original data are decomposed into the clean intrinsic component and noise component. Then the projective matrix is learned based on the clean intrinsic component which is encoded in low-rank features. The noise component is constrained by the ℓ1-norm which is more robust to outliers. Finally, LR-LPP model is extended to LR-FLPP in which low-dimensional feature is measured by F-norm. LR-FLPP will reduce aggregated error and weaken the effect of outliers, which will make the proposed LR-FLPP even more robust for outliers. The experimental results on public image databases demonstrate the effectiveness of the proposed LR-LPP and LR-FLPP.