This paper presents supervised feature learning approaches for speaker identification that rely on nonnegative matrix factorisa-tion. Recent studies have shown that group nonnegative matrix factorisation and task-driven supervised dictionary learning can help performing effective feature learning for audio classification problems. This paper proposes to integrate a recent method that relies on group nonnegative matrix factorisation into a task-driven supervised framework for speaker identification. The goal is to capture both the speaker variability and the session variability while exploiting the discriminative learning aspect of the task-driven approach. Results on a subset of the ESTER corpus prove that the proposed approach can be competitive with I-vectors. Index Terms— Nonnegative matrix factorisation, feature learning , dictionary learning, online learning, speaker identification