High-dimensional semi-supervised learning via a fusion-refinement procedure

• Proposed a new effective approach for semi-supervised dimension reduction.
• Developed a fast algorithm for implementation of the FR method.
• Investigated the FR+LDS method for high-dimensional semi-supervised classification.
• Demonstrated the effectiveness of FR+LDS over several commonly used methods in SSL.

This paper develops a sufficient dimension reduction (SDR) approach for the high-dimensional semi-supervised learning (SSL) problem. In the proposed technique, we first modify the fusion-refinement (FR) procedure, which was proposed in [1], to extract the essential features for a lower-dimensional representation. We then apply an SSL algorithm (e.g., the low density separation (LDS)) in the lower-dimensional feature space to tackle the SSL problem. Numerical experiments are conducted on some widely-used data sets. We carry out a comparison between the proposed procedure and some recently proposed semi-supervised learning approaches (including greedy gradient Max-Cut (GGMC), semi-supervised extreme learning machines (SS-ELM)) and dimension reduction procedures (such as the semi-supervised local Fisher discriminant analysis (SELF), the trace ratio based flexible semi-supervised discriminant analysis (TR-FSDA), and trace ratio relevance feedback (TRRF)). In extensive numerical simulations, the new technique outperforms its competitors in many cases, demonstrating its effectiveness.