Marginal patch alignment for dimensionality reduction

Patch alignment (PA) framework provides us a useful way to obtain the explicit mapping for dimensionality reduction. Under the PA framework, we propose the marginal patch alignment (MPA) for dimensionality reduction. MPA performs the optimization from the part to the whole. In the phase of the patch optimization, the marginal between-class and within-class local neighborhoods of each training sample are selected to build the local marginal patches. By performing the patch optimization, on the one hand, the contributions of each sample for optimal subspace selection are distinguished. On the other hand, the marginal structure information is exploited to extract discriminative features such that the marginal distance between the two different categories is enlarged in the low transformed subspace. In the phase of the whole alignment, a trick is performed to unify all of the local patches into a globally linear system and make MPA obtain the whole optimization. The experimental results on the Yale face database, the UCI Wine dataset, the Yale-B face database, and the AR face database, show the effectiveness and efficiency of MPA.