Because balanced constraints can overcome the problems of trivial solutions of data classification via minimum cut method, many techniques with different balanced strategies have been proposed to improve data classification accuracy. However, their performances have not been compared comprehensively so far. In this paper, we investigate seven balanced classification methods under the discrete non-local total variational framework and compare their accuracy performances on graph. The two-class classification problem with equality constraints, inequality constraints and Ratio Cut, Normalized Cut, Cheeger Cut models are investigated. For cases of equality constraint, we firstly compare the Penalty Function Method (PFM) and the Augmented Lagrangian Method (ALM), which can transform the constrained problems into unconstrained ones, to show the advantages of ALM. The other cases are all solved using the ALM also. In order to make the comparison fairly, we solve all models using ALM method and using the same proportion of fidelity points and the same neighborhood size on graph. Experimental results demonstrate ALM with the equality balanced constraint has the best classification accuracy compared with other six constraints. 200 words.