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 ℓ 1 -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.

Quasi-Matrix and Quasi-Inverse-Matrix Projective Synchronization for Delayed and Disturbed Fractional Order Neural Network

This paper is concerned with the quasi-matrix and quasi-inverse-matrix projective synchronization between two nonidentical delayed fractional order neural networks subjected to external disturbances. First, the definitions of quasi-matrix and quasi-inverse-matrix projective synchronization are given, respectively. Then, in order to realize two types of synchronization for delayed and disturbed fractional order neural networks, two sufficient conditions are established and proved by constructing appropriate Lyapunov function in combination with some fractional order differential inequalities. And their estimated synchronization error bound is obtained, which can be reduced to the required standard as small as what we need by selecting appropriate control parameters. Because of the generality of the proposed synchronization, choosing different projective matrix and controllers, the two synchronization types can be reduced to some common synchronization types for delayed fractional order neural networks, like quasi-complete synchronization, quasi-antisynchronization, quasi-projective synchronization, quasi-inverse projective synchronization, quasi-modified projective synchronization, quasi-inverse-modified projective synchronization, and so on. Finally, as applications, two numerical examples with simulations are employed to illustrate the efficiency and feasibility of the new synchronization analysis.