Semi-supervised manifold regularization with adaptive graph construction

Abstract

Manifold regularization (MR) provides a powerful framework for semi-supervised classification (SSC) learning. It imposes the smoothness constraint over a constructed manifold graph, and its performance largely depends on such graph. However, 1) The manifold graph is usually pre-constructed before classification, and fixed during the classification learning process. As a result, independent with the subsequent classification, the graph does not necessarily benefit the classification performance. 2) There are parameters needing tuning in the graph construction, while parameter selection in semi-supervised learning is still an open problem currently, which sets up another barrier for constructing a “well-performing” manifold graph benefiting the performance. To address those issues, we develop a novel semi-supervised manifold regularization with adaptive graph (AGMR for short) in this paper by integrating the graph construction and classification learning into a unified framework. In this way, the manifold graph along with its parameters will be optimized in learning rather than pre-defined, consequently, it will be adaptive to the classification, and benefit the performance. Further, by adopting the entropy and sparse constraints respectively for the graph weights, we derive two specific methods called AGMR_entropy and AGMR_sparse, respectively. Our empirical results show the competitiveness of those AGMRs compared to MR and some of its variants.