This paper presents a feature learning approach for speaker identification that is based on non-negative matrix factorisa-tion. Recent studies have shown that in methods such as non-negative matrix factorisation, the dictionary atoms can represent well the speaker identity and that Using speaker identity to induce group similarity can proven to improve further the performance. However, the approaches proposed so far fo-cused only on speakers variability and not on sessions variability. However, this later point is a crucial aspect in the success of the I-vector approaches that is now the state-of-the-art in speaker identification. This paper proposes an approach that relies on group-NMF and that is inspired that the I-vector training procedure. By doing so this approach intends to capture both the speaker variability and the session variability. Results on a small corpus prove the proposed approach to be competitive with the state-of-the-art I-vector approach.