The use of unlabeled data to aid classification is important as labeled data is often available in limited quantity. Instead of utilizing training samples directly into semi-supervised learning, energy function incorporating the conditional probability of classification is adopted. The semi-supervised learning is posed as the optimization of both the classification energy and the cluster compactness energy. The resulting integer programming is relaxed by a semi-definite relaxation where efficient solution can be obtained. Furthermore, the spectral graph methods provide improved energy minimization via the incorporation of additional criteria. Results on UCI datasets show promising results.