Automatic identification of the relevant frames of references (or external task parameters) in programming by demonstration using the task-parameterized Gaussian mixture regression (TP-GMM) is addressed in this paper. While performing a given task, there may be several external task parameters, some of which are relevant to the specific task, while some others are not relevant. Identifying the irrelevant task parameters could help to automatize the selection of task parameters, construct a more compact model of the task and achieve better performances in the reproduction phase. At first, all the potential candidate frames of references will be taken into account, then, after identifying the irrelevant ones, they will be removed from the model, and only the relevant frames will be used for the reproduction. The performance of the approach is testified through an experiment, where the reproduction with only the relevant frames of references provides much better results compared to the case of including all candidate frames of references.