Optimal decision rules for distributed binary decision tree classifiers

We consider the problem of recognizing M objects using a fusion center with N parallel sensors. Unlike conventional M-ary decision fusion systems, our fusion system breaks a complex M-ary decision fusion problem into a sequence of simpler binary decision fusion problems. In our system, a binary decision tree (BDT) is employed to hierarchically partition the object space at all system elements. The traversal of the BDT is synchronized by the fusion center. The sensor observations are assumed conditionally independent given the unknown object type. We use a greedy performance criterion in which the probability of error is minimized at individual nodes. Using this performance criterion, we characterize the optimal fusion rules and the optimal sensor rules. We compare our results with some important results on conventional one-stage binary fusion.