Abstract
In this paper, a multiple sub-manifold learning method–oriented classification is presented via sparse representation, which is named maximum variance sparse mapping. Based on the assumption that data with the same label locate on a sub-manifold and different class data reside in the corresponding sub-manifolds, the proposed algorithm can construct an objective function which aims to project the original data into a subspace with maximum sub-manifold distance and minimum manifold locality. Moreover, instead of setting the weights between any two points directly or obtaining those by a square optimal problem, the optimal weights in this new algorithm can be approached using L1 minimization. The proposed algorithm is efficient, which can be validated by experiments on some benchmark databases.
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Acknowledgments
This work was supported by the grants of the National Natural Science Foundation of China (61070013, 60703018, 61070012 & 90924026), 973 Program (2007CB310800), Twelfth Five Years Plan Key National Project (GFZX0101050302), 863 Program (2008AA022503, 2008AA01Z208, 2009AA01Z405), the Science and Technology Commission of Wuhan Municipality “Chenguang Jihua” (201050231058), the 111 Project (B07037), Natural Science Foundation of Hubei Province (2010CDB03302), Postdoctoral Science Foundation of China (20100470613), Shanghai Key Laboratory of Intelligent Information Processing, China (IIPL-2010-004), the Open Fund Project of State Key Laboratory of Software Engineering (Wuhan University, China, SKLSE08-11), and Science Foundation of Wuhan University of Science and Technology (2010XG7&2010XZ015).
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Liu, J., Li, B. & Zhang, WS. Feature extraction using maximum variance sparse mapping. Neural Comput & Applic 21, 1827–1833 (2012). https://doi.org/10.1007/s00521-010-0519-9
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DOI: https://doi.org/10.1007/s00521-010-0519-9