Article ID Journal Published Year Pages File Type
6858114 Information Sciences 2014 21 Pages PDF
Abstract
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.
Related Topics
Physical Sciences and Engineering Computer Science Artificial Intelligence
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