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We introduce a non-negative matrix factorization technique which learns speech features with temporal extent in the presence of non-stationary noise. Our proposed technique, namely Sparse convolutive robust non-negative matrix factorization, is robust in the presence of noise due to our explicit treatment of noise as an interfering source in the factorization. We derive multiplicative update rules using the alpha divergence objective. We show that our proposed method yields superior performance to sparse convolutive non-negative matrix factorization in a feature learning task on noisy data and comparable results to dedicated speech enhancement techniques.