caa a22 4500 445871377 CHVBK 20180317145512.0 cr unu---uuuuu 170323e20110501xx s 000 0 eng 10.1007/s10618-010-0182-x doi (NATIONALLICENCE)springer-10.1007/s10618-010-0182-x Manifold elastic net: a unified framework for sparse dimension reduction [Elektronische Daten] [Tianyi Zhou, Dacheng Tao, Xindong Wu] It is difficult to find the optimal sparse solution of a manifold learning based dimensionality reduction algorithm. The lasso or the elastic net penalized manifold learning based dimensionality reduction is not directly a lasso penalized least square problem and thus the least angle regression (LARS) (Efron etal., Ann Stat 32(2):407-499, 2004), one of the most popular algorithms in sparse learning, cannot be applied. Therefore, most current approaches take indirect ways or have strict settings, which can be inconvenient for applications. In this paper, we proposed the manifold elastic net or MEN for short. MEN incorporates the merits of both the manifold learning based dimensionality reduction and the sparse learning based dimensionality reduction. By using a series of equivalent transformations, we show MEN is equivalent to the lasso penalized least square problem and thus LARS is adopted to obtain the optimal sparse solution of MEN. In particular, MEN has the following advantages for subsequent classification: (1) the local geometry of samples is well preserved for low dimensional data representation, (2) both the margin maximization and the classification error minimization are considered for sparse projection calculation, (3) the projection matrix of MEN improves the parsimony in computation, (4) the elastic net penalty reduces the over-fitting problem, and (5) the projection matrix of MEN can be interpreted psychologically and physiologically. Experimental evidence on face recognition over various popular datasets suggests that MEN is superior to top level dimensionality reduction algorithms. The Author(s), 2010 Manifold learning nationallicence Elastic net nationallicence Dimensionality reduction nationallicence Zhou Tianyi School of Computer Engineering, Nanyang Technological University, 639798, Singapore, Singapore aut Tao Dacheng School of Computer Engineering, Nanyang Technological University, 639798, Singapore, Singapore aut Wu Xindong Department of Computer Science, University of Vermont, 33 Colchester Avenue, 05405, Burlington, VT, USA aut Data Mining and Knowledge Discovery Springer US; http://www.springer-ny.com 22/3(2011-05-01), 340-371 1384-5810 22:3<340 2011 22 10618 https://doi.org/10.1007/s10618-010-0182-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10618-010-0182-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Zhou Tianyi School of Computer Engineering, Nanyang Technological University, 639798, Singapore, Singapore aut NATIONALLICENCE 700 1- Tao Dacheng School of Computer Engineering, Nanyang Technological University, 639798, Singapore, Singapore aut NATIONALLICENCE 700 1- Wu Xindong Department of Computer Science, University of Vermont, 33 Colchester Avenue, 05405, Burlington, VT, USA aut NATIONALLICENCE 773 0- Data Mining and Knowledge Discovery Springer US; http://www.springer-ny.com 22/3(2011-05-01), 340-371 1384-5810 22:3<340 2011 22 10618 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer