Who Is Missing? A New Pattern Recognition Puzzle

Consider a multi-class classification problem. Given is a set of objects, for which it is known that there is at most one object from each class. The problem is to identify the missing classes. We propose to apply the Hungarian assignment algorithm to the logarithms of the estimated posterior probabilities for the given objects. Each object is thereby assigned to a class. The unassigned classes are returned as the solution. Its quality is measured by a consistency index between the solution and the set of known missing classes. The Hungarian algorithm was found to be better than the rival greedy algorithm on two data sets: the UCI letter data set and a bespoke image data set for recognising scenes with LEGO parts. Both algorithms outperformed a classifier which treats the objects as iid.