Learning Semi-Supervised Representation Towards a Unified Optimization Framework for Semi-Supervised Learning

State of the art approaches for Semi-Supervised Learning (SSL) usually follow a two-stage framework -- constructing an affinity matrix from the data and then propagating the partial labels on this affinity matrix to infer those unknown labels. While such a two-stage framework has been successful in many applications, solving two subproblems separately only once is still suboptimal because it does not fully exploit the correlation between the affinity and the labels. In this paper, we formulate the two stages of SSL into a unified optimization framework, which learns both the affinity matrix and the unknown labels simultaneously. In the unified framework, both the given labels and the estimated labels are used to learn the affinity matrix and to infer the unknown labels. We solve the unified optimization problem via an alternating direction method of multipliers combined with label propagation. Extensive experiments on a synthetic data set and several benchmark data sets demonstrate the effectiveness of our approach.