Abstract: Nonlinear dimensionality reduction and semi-supervised learning are both hot issues in machine learning area．Based on semi-supervised method,the article solved nonlinear dimensionality reduction problem to make up for the shortfall of ordinary methods．By using integration of equalities,a novel expression of label propagation algorithm was proposed．We used the label propagation result as the initial value mapping,and then found the best approximation to it in the graph spectral space．The experiment shows that our semi-supervised dimensionality reduction method can achieve smooth data mapping that is closer to the ideal effect.

Key words: Semi-supervised learning,Manifold learning,Label propagation,Spectral graph theory