Dimensionality reduction: An interpretation from manifold regularization perspective

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• 作者：Mingyu Fan^a ; ^{fanmingyu@amss.ac.cn" class="auth_mail} ; ^{fanmingyu@wzu.edu.cn" class="auth_mail} ; Nannan Gu^b ; ^{nngu@cueb.edu.cn" class="auth_mail} ; Hong Qiao^c ; ^{hong.qiao@mail.ia.ac.cn" class="auth_mail} ; Bo Zhang^d ; ^{b.zhang@amt.ac.cn" class="auth_mail}
• 关键词：Dimensionality reduction ; Manifold regularization ; Feature mapping ; Manifold learning ; Out-of-sample extrapolation
• 刊名：Information Sciences
• 出版年：1 September 2014
• 年：2014
• 卷：277
• 期：Complete
• 页码：694-714
• 全文大小：1330 K

文摘

In this paper, we propose to unify various dimensionality reduction algorithms by interpreting the Manifold Regularization (MR) framework in a new way. Although the MR framework was originally proposed for learning, we utilize it to give a unified treatment for many dimensionality reduction algorithms from linear to nonlinear, supervised to unsupervised, and single class to multi-class approaches. In addition, the framework can provide a general platform to design new dimensionality reduction algorithms. The framework is expressed in the form of a regularized fitting problem in a Reproducing Kernel Hilbert Space. It consists of one error part and two regularization terms: the complexity term and the smoothness term. The error part measures the difference between the estimated (low-dimensional) data distribution and the true (high-dimensional) data distribution or the difference between the estimated and targeted low-dimensional representations of data, the complexity term is a measurement of the complexity of the feature mapping for dimensionality reduction, and the smoothness term reflects the intrinsic structure of data. Based on the framework, we propose a Manifold Regularized Kernel Least Squares (MR-KLS) method which can efficiently learn an explicit feature mapping (in the semi-supervised sense). Experiments show that our approach is effective for out-of-sample extrapolation.