Learning Matching Score Dependencies for Classifier Combination

The integration of recognition algorithms into a single document processing system might involve different available modules suitable for a single task. For example, we might possess few character or word recognition algorithms which all can be used in the system. One possible approach is to test these algorithms and to choose the one with the best performance. But practice shows that better approach is to try to use all available algorithms and to combine their outputs in order to achieve a better performance than any single algorithm. The combination problem consists in learning the behavior of given algorithms and deriving best possible combination function. We assume that both the combined algorithms and the result of combination are classifiers. Thus a finite number of classes are distinguished in the problem, and the task is to find a class, which corresponds most to the input. As examples, classes might be a character set, a word lexicon, a person list, etc. Usually classifiers output the numeric matching scores corresponding to each class, and we will assume that these scores are available for combination. The combination algorithm is a function producing a final combined score for each class, and the final classifier selects class with the best combined score. The purpose of this chapter is to investigate the different scenarios of combining classifiers, to show the difficulties in finding the optimal combination algorithms, and to present few possible approaches to combination problems. Generally, the classifier combination problem can be viewed as a construction of postprocessing classifier operating on the matching scores of combined classifiers. For many classifier combination problems, though, the number of classes or the number of classifiers and, consequently, the number of matching scores is too big, and applying generic pattern classification algorithms is difficult. Thus some scores are usually discarded from combination algorithm, or simplifying assumptions on score distributions are made and used in the combination algorithm. Though the dependency between classifiers is usually learned by the combination algorithms, the dependency between scores assigned to different classes by the same classifier is discarded. In this work we will show that accounting for score dependencies is essential for proper com