Laplacian pair-weight vector projection for semi-supervised learning

Abstract

Semi-supervised learning is a new challenge that exploits the information of unlabeled instances. In this paper, we propose a novel Laplacian pair-weight vector projection (LapPVP) algorithm for semi-supervised classification. LapPVP consists of two stages: projection and classification. In the projection stage, LapPVP integrates a within-class scatter, a between-class scatter and a Laplacian regularization together and formulates a pair of optimization problems. The goal of LapPVP is to maximize the between-class scatter and minimize the within-class scatter on the basis of labeled data, and simultaneously maintain the geometric structure of labeled and unlabeled data in the projected subspace. The optimization problems of LapPVP are identical to generalized eigenvalue ones. Thus, it is easy to obtain the optimal solutions to LapPVP. In the classification stage, LapPVP adopts a minimal distance classifier to implement tasks in the projected subspace. The proposed LapPVP can find a better separability using the geometric information embedded in labeled and unlabeled instances and the discriminative information embedded in labeled instance. Experiments on artificial datasets and UCI datasets validate the feasibility and effectiveness of the proposed algorithm.