Please use this identifier to cite or link to this item: https://doi.org/10.1109/TIP.2013.2297020
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dc.titleA general exponential framework for dimensionality reduction
dc.contributor.authorWang, S.-J.
dc.contributor.authorYan, S.
dc.contributor.authorYang, J.
dc.contributor.authorZhou, C.-G.
dc.contributor.authorFu, X.
dc.date.accessioned2014-10-07T04:22:40Z
dc.date.available2014-10-07T04:22:40Z
dc.date.issued2014-02
dc.identifier.citationWang, S.-J., Yan, S., Yang, J., Zhou, C.-G., Fu, X. (2014-02). A general exponential framework for dimensionality reduction. IEEE Transactions on Image Processing 23 (2) : 920-930. ScholarBank@NUS Repository. https://doi.org/10.1109/TIP.2013.2297020
dc.identifier.issn10577149
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/81870
dc.description.abstractAs a general framework, Laplacian embedding, based on a pairwise similarity matrix, infers low dimensional representations from high dimensional data. However, it generally suffers from three issues: 1) algorithmic performance is sensitive to the size of neighbors; 2) the algorithm encounters the well known small sample size (SSS) problem; and 3) the algorithm de-emphasizes small distance pairs. To address these issues, here we propose exponential embedding using matrix exponential and provide a general framework for dimensionality reduction. In the framework, the matrix exponential can be roughly interpreted by the random walk over the feature similarity matrix, and thus is more robust. The positive definite property of matrix exponential deals with the SSS problem. The behavior of the decay function of exponential embedding is more significant in emphasizing small distance pairs. Under this framework, we apply matrix exponential to extend many popular Laplacian embedding algorithms, e.g., locality preserving projections, unsupervised discriminant projections, and marginal fisher analysis. Experiments conducted on the synthesized data, UCI, and the Georgia Tech face database show that the proposed new framework can well address the issues mentioned above. © 1992-2012 IEEE.
dc.description.urihttp://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1109/TIP.2013.2297020
dc.sourceScopus
dc.subjectdimensionality reduction
dc.subjectFace recognition
dc.subjectLaplacian embedding
dc.subjectmanifold learning
dc.subjectmatrix exponential
dc.typeArticle
dc.contributor.departmentELECTRICAL & COMPUTER ENGINEERING
dc.description.doi10.1109/TIP.2013.2297020
dc.description.sourcetitleIEEE Transactions on Image Processing
dc.description.volume23
dc.description.issue2
dc.description.page920-930
dc.description.codenIIPRE
dc.identifier.isiut000329581800034
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