Effect Of Equality Constraints To Unconstrained Large Margin Distribution Machines

Unconstrained large margin distribution machines (ULDMs) maximize the margin mean and minimize the margin variance without constraints. In this paper, we first reformulate ULDMs as a special case of least squares (LS) LDMs, which are a least squares version of LDMs. By setting a hyperparameter to control the trade-off between the generalization ability and the training error to zero, LS LDMs reduce to ULDMs. In the computer experiments, we include the zero value of the hyperparameter as a candidate value for model selection. According to the experiments using two-class problems, in most cases LS LDMs reduce to ULDMs and their generalization abilities are comparable. Therefore, ULDMs are sufficient to realize high generalization abilities without equality constraints.