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Extra resources for Advances in Face Image Analysis:: Theory and applications
Firstly, the proposed framework overcomes the SSS problem without discarding the discriminant information that was contained in the null space of the locality preserving scatter matrices associated with LDE. Secondly, the proposed ELDE is equivalent to transforming original data into a new space by distance diffusion mapping (similar to Kernel-based non-linear mapping), and then, LDE is applied in such a new space. As a result of diffusion mapping, the margin between samples belonging to different classes is enlarged, which is helpful in improving classification accuracy.
Moreover, the optimized criterion integrates uncorrelation and orthogonality constraints. In , the authors assessed the performance of the quotient and difference criteria used in LDA. They also proposed a unified criterion that combines Quotient-LDA and Dif-ference-LDA criteria. It associates to every sample a margin that is set to the difference between the average distance to heterogeneous neighbors and the average distance to the homogeneous neighbors. The linear transform is then derived by maximizing the sum of the margins in the embedded space.
It aims to preserve the sparse reconstructive relationship of the data obtained by solving a L1 objective function. Label information is used as additional constraints for graph embedding in the SPP-CGE algorithm. In SPP-CGE, both the intrinsic structure and the label information of the data are used. In addition, to deal with new incoming samples, out-of-sample extension of SPP-CGE is also proposed. Promising experimental results on several popular face databases illustrate the effectiveness of the proposed method.
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