Inductive and flexible feature extraction for semi-supervised pattern categorization

•A flexible graph-based semi-supervised embedding is proposed.•A kernel version of the linear semi-supervised algorithm is also proposed.•They simultaneously estimate a non-linear embedding and its out-of-sample extension.•Classification performance after embedding is assessed on ten benchmark datasets.•We use KNN, SVM, and two phase test sample sparse representation as classifiers.

This paper proposes a novel discriminant semi-supervised feature extraction method for generic classification and recognition tasks. This method, called inductive flexible semi-supervised feature extraction, is a graph-based embedding method that seeks a linear subspace close to a non-linear one. It is based on a criterion that simultaneously exploits the discrimination information provided by the labeled samples, maintains the graph-based smoothness associated with all samples, regularizes the complexity of the linear transform, and minimizes the discrepancy between the unknown linear regression and the unknown non-linear projection. We extend the proposed method to the case of non-linear feature extraction through the use of kernel trick. This latter allows to obtain a nonlinear regression function with an output subspace closer to the learned manifold than that of the linear one. Extensive experiments are conducted on ten benchmark databases in order to study the performance of the proposed methods. Obtained results demonstrate a significant improvement over state-of-the-art algorithms that are based on label propagation or semi-supervised graph-based embedding.