With the rise of data mining techniques came across the problem of privacy disclosure, that is why it has become one of the top priorities as far as designing the data mining techniques is concerned. In this paper, we briefly discuss the Nonnegative Matrix Factorization (NMF) and the motivation behind using NMF for data representation. We provide the mathematical derivation for NMF with some additional constraints. Based on the mathematical derivations, we propose a couple of novel data distortion strategies. The first technique is called the Constrained Nonnegative Matrix Factorization (CMF) and the second one is Sparsified CNMF. We study the distortion level of each of these algorithms with the other matrix based techniques like SVD and NMF. K-means is used to study the data utility of the two proposed methods. Our experimental results show that, in comparison with standard data distortion techniques, the proposed schemes are very effective in achieving a good tradeoff between data privacy and data utility, and affords a feasible solution to protect sensitive information and promise higher accuracy in decision making. We investigate utility of the perturbed data based on the results from the original data.