A novel unsupervised machine learning algorithm for single channel source separation is presented. The proposed method is based on nonnegative matrix factorization, which is optimized under the framework of maximum a posteriori probability and Itakura-Saito divergence. The method enables a generalized criterion for variable sparseness to be imposed onto the solution and prior information to be explicitly incorporated through the basis vectors. In addition, the method is scale invariant where both low and high energy components of a signal are treated with equal importance. The proposed algorithm is a more complete and efficient approach for matrix factorization of signals that exhibit temporal dependency of the frequency patterns. Experimental tests have been conducted and compared with other algorithms to verify the efficiency of the proposed method.