KIM et al.: GROWING A TREE FROM DECISION REGIONS OF A BOOSTING CLASSIFIER 1 Making a Shallow Network Deep: Growing a Tree from Decision Regions of a Boosting Classifier

This paper presents a novel way to speed up the classification time of a boosting classifier. We make the shallow (flat) network deep (hierarchical) by growing a tree from the decision regions of a given boosting classifier. This provides many short paths for speeding up and preserves the reasonably smooth decision regions of the boosting classifier for good generalisation. We express the conversion as a Boolean optimisation problem, which has been previously studied for circuit design but limited to a small number of binary variables. In this work, a novel optimisation method is proposed for several tens of variables, i.e. weak-learners of a boosting classifier. The method is then used in a two stage cascade allowing the speed-up of a boosting classifier with any larger number of weak-learners. Experiments on the synthetic and face image data sets show that the obtained tree significantly speeds up both a standard boosting classifier and Fast-exit, a prior-art for fast boosting classification, at the same accuracy. The proposed method as a general meta-algorithm is also shown useful for a boosting cascade, since it speeds up individual stage classifiers by different gains. The proposed method is further demonstrated for rapid object tracking and segmentation problems.