Semi-supervised dimensionality reduction based on local estimation error

Abstract

The construction of a graph is extremely important in graph-based semi-supervised learning. However, it is unstable by virtue of sensitivity to the selection of neighbourhood parameter and inaccuracy of the edge weights. Inspired by the good performance of the local learning method, this paper proposes a semi-supervised dimensionality reduction based on local estimation error (LEESSDR) algorithm by utilising local learning projections (LLP) to semi-supervised dimensionality reduction. The algorithm sets the edge weights through minimising the local estimation error and can effectively preserve the global geometric structure as well as the local one of the data. Since LLP does not require its input space to be locally linear, even if it is nonlinear, LLP maps it to the feature space by using kernel functions and then obtains its local estimation error in the feature space. The effectiveness of the proposed method is verified on two popular face databases with promising classification accuracy and favourable robustness.