Machine learning algorithms based on semi-supervised strategies have drawn the attention of researchers due to their ability to work with limited labeled data making use of huge number of unlabeled samples. Graph based semi-supervised algorithms make an assumption of similarity of examples in lower dimensional manifold and use an objective that ensures similarity of labels as enforced by the similarity graph. Such methods typically make use of a L2 regularization term to avoid over-fitting. Regularization term further ensures convexity of the overall objective leading to efficient learning algorithms. Addressing the problem of low-supervision and high class imbalance, prior work has shown state-of-the-art results for anomaly detection and other important classification problems by using a convex-concave objective. The current work analyses such performance improvements of convex-concave objective thoroughly. Our study indicates that a KL-Divergence based loss function for semi-supervised learning has performed much better than the convex-concave objective based on L2-Loss. It is also seen that the one-versus-rest setting for multi-class classification using convex-concave objective is performing much weaker compared to the naturally multi-class KL-Divergence based multi-class classification setting.