Open-set recognition (OSR) is a more realistic approach than traditional multiclass classification in many real-world scenarios where an unforeseeable number of classes may arise at inference time. Specifically, OSR aims to recognize whether an instance belongs to one of the classes used for the training or not. In case it is, the instance is also categorized accordingly. On the contrary, when not recognized, OSR labels it with a generic class label indicating the rest of the world. Similarly to text classification, OSR approaches suffer from the curse of dimensionality and feature reduction could be beneficial. In this paper, inspired by previous evidence on text classification, we claim that Non-negative Matrix Factorization (NMF) of the tf-idf term-document matrix can also improve OSR accuracy on text data. Preliminary results on benchmark datasets prove our claim is correct and paves the way for future developments.