Spectral Methods for Linear and Non-Linear Semi-Supervised Dimensionality Reduction

We present a general framework of spectral methods for semi-supervised dimensionality reduction. Applying an approach called manifold regularization, our framework naturally generalizes existent supervised frameworks. Furthermore, by our two semi-supervised versions of the representer theorem, our framework can be kernelized as well. Using our framework, we give three examples of semi-supervised algorithms which are extended from three recent supervised algorithms, namely, “discriminant neighborhood embedding”, “marginal Fisher analysis” and “local Fisher discriminant analysis”. We also give three more semi-supervised examples of the kernel versions of these algorithms. Numerical results of the six semi-supervised algorithms compared to their supervised versions are presented.