  The problem of quickest growing dynamic anomaly detection in sensor networks
is studied. Initially, the observations at the sensors, which are sampled
sequentially by the decision maker, are generated according to a pre-change
distribution. At some unknown but deterministic time instant, a dynamic anomaly
emerges in the network, affecting a different set of sensors as time
progresses. The observations of the affected sensors are generated from a
post-change distribution. It is assumed that the number of affected sensors
increases with time, and that only the initial and the final size of the
anomaly are known by the decision maker. The goal is to detect the emergence of
the anomaly as quickly as possible while guaranteeing a sufficiently low
frequency of false alarm events. This detection problem is posed as a
stochastic optimization problem by using a delay metric that is based on the
worst possible path of the anomaly. A detection rule is proposed that is
asymptotically optimal as the mean time to false alarm goes to infinity.
Finally, numerical results are provided to validate our theoretical analysis.
