Abstract
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.
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Acknowledgments
This work was partially supported by the National Nature Science Foundation of China (Grant nos. 61305036, 61322306, 61333013, and 61273192), the China Postdoctoral Science Foundation funded project (Grant 2014M560657 and 2015T80898), Scientific Funds approved in 2013 for Higher Level Talents by Guangdong Provincial universities and Project supported by GDHVPS 2014.
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Jie Xu, Shengli Xie and Wenkang Zhu, their immediate family, and any research foundation with which they are affiliated did not receive any financial payments or other benefits from any commercial entity related to the subject of this article.
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Xu, J., Xie, S. & Zhu, W. Marginal patch alignment for dimensionality reduction. Soft Comput 21, 2347–2356 (2017). https://doi.org/10.1007/s00500-015-1944-6
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DOI: https://doi.org/10.1007/s00500-015-1944-6