Non-uniqueness of NMF was addressed using sparsity constraints. Currently, the most popular bag-of-visual-words representation suffers from sparsity and high dimensionality. Using those definitions, a matrix will be sparse when its sparsity is greater than 0.5. More control over the non-uniqueness of NMF is obtained with sparsity constraints. The first one is sparsity, which requires the signal to be sparse in some domain. From linear programming, GAMS learned that exploitation of sparsity was key to solving large problems. This sparsity is problematic for any method that requires statistical significance. It can be shown that the formula 54 norm induces sparsity. Collaborative filtering approaches often suffer from three problems&colon; cold start, scalability, and sparsity. It handles the sparsity of the original matrix better than memory based ones. They provide one way of overcoming the data sparsity problem found with conventional "n"-gram analysis. This sparsity of activation can be achieved by formulating the penalty terms in different ways. Data sparsity is a major problem in building language models. Other graph families not characterized by their sparsity can also be described in this way. One typical problem caused by the data sparsity is the cold start problem.