As we all know, a well-designed graph tends to result in good performance for graph-based semi-supervised learning. Although most graph-based semi-supervised dimensionality reduction approaches perform very well on clean data sets, they usually cannot construct a faithful graph which plays an important role in getting a good performance, when performing on the high dimensional, sparse or noisy data. So this will generally lead to a dramatic performance degradation. To deal with these issues, this paper proposes a feasible strategy called relative semi-supervised dimensionality reduction (RSSDR) by utilizing the perceptual relativity to semi-supervised dimensionality reduction. In RSSDR, firstly, relative transformation will be performed over the training samples to build the relative space. It should be indicated that relative transformation improves the distinguishing ability among data points and diminishes the impact of noise on semi-supervised dimensionality reduction. Secondly, the edge weights of neighborhood graph will be determined through minimizing the local reconstruction error in the relative space such that it can preserve the global geometric structure as well as the local one of the data. Extensive experiments on face, UCI, gene expression, artificial and noisy data sets have been provided to validate the feasibility and effectiveness of the proposed algorithm with the promising results both in classification accuracy and robustness. 
Perceptual relativity-based semi-supervised dimensionality reduction algorithm