Consider the two related problems of sensor selection and sensor fusion. Inthe first, given a set of sensors, one wishes to identify a subset of thesensors, which while small in size, captures the essence of the data gatheredby the sensors. In the second, one wishes to construct a fused sensor, whichutilizes the data from the sensors (possibly after discarding dependent ones)in order to create a single sensor which is more reliable than each of theindividual ones. In this work, we rigorously define the dependence amongsensors in terms of joint empirical measures and incremental parsing. We showthat these measures adhere to a polymatroid structure, which in turnfacilitates the application of efficient algorithms for sensor selection. Wesuggest both a random and a greedy algorithm for sensor selection. Given anindependent set, we then turn to the fusion problem, and suggest a novelvariant of the exponential weighting algorithm. In the suggested algorithm, onecompetes against an augmented set of sensors, which allows it to converge tothe best fused sensor in a family of sensors, without having any prior data onthe sensors' performance.
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