Links between binary classification and the assignment problem in ordered hypothesis machines

Ordered Hypothesis Machines (OHM) are large margin classifiers that belong to the class of Generalized Stack Filters which were originally developed for non-linear signal processing. In previous work we showed how OHM classifiers are equivalent to a variation of Nearest Neighbor classifiers, with the advantage that training involves minimizing a loss function which includes a regularization parameter that controls class complexity. In this paper we report a new connection between OHM training and the Linear Assignment problem, a combinatorial optimization problem that can be solved efficiently with (amongst others) the Hungarian algorithm. Specifically, for balanced classes, and particular choices of parameters, OHM training is the dual of the Assignment problem. The duality sheds new light on the OHM training problem, opens the door to new training methods and suggests several new directions for research.