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Mathematical Problems in Engineering
Volume 2018 (2018), Article ID 2382803, 8 pages
Research Article

Robust Semi-Supervised Manifold Learning Algorithm for Classification

The School of Computer Science and Technology, Huaqiao University, Xiamen 361021, China

Correspondence should be addressed to Jing Wang

Received 17 June 2017; Accepted 4 January 2018; Published 1 February 2018

Academic Editor: Nazrul Islam

Copyright © 2018 Mingxia Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In the recent years, manifold learning methods have been widely used in data classification to tackle the curse of dimensionality problem, since they can discover the potential intrinsic low-dimensional structures of the high-dimensional data. Given partially labeled data, the semi-supervised manifold learning algorithms are proposed to predict the labels of the unlabeled points, taking into account label information. However, these semi-supervised manifold learning algorithms are not robust against noisy points, especially when the labeled data contain noise. In this paper, we propose a framework for robust semi-supervised manifold learning (RSSML) to address this problem. The noisy levels of the labeled points are firstly predicted, and then a regularization term is constructed to reduce the impact of labeled points containing noise. A new robust semi-supervised optimization model is proposed by adding the regularization term to the traditional semi-supervised optimization model. Numerical experiments are given to show the improvement and efficiency of RSSML on noisy data sets.