The open set recognition task, most challenging among the biometric tasks, operates under the assumption that not all the probes have mates in the gallery. It requires the availability of a reject option. For face recognition open set corresponds to the watch list face surveillance task, where the face recognition engine must detect or reject the probe. The above challenges are addressed successfully in this paper using transduction, which is a novel form of inductive learning. Towards that end, we introduce the Open Set TCM-kNN algorithm, which is based upon algorithmic randomness and transductive inference. It is successfully validated on the (small) watch list task (80% or more of the probes lack mates) using FERET datasets. In particular, Open Set TCM-kNN provides on the average 96% correct detection / rejection and identification using the PCA and/or Fisherfaces components for face representation.