ABSTRACT
Non-negative matrix factorization is really a class of decompositions whose members are not necessarily closely related to each other. They share the property that they are designed for datasets in which the attribute values are never negative – and it does not make sense for the decomposition matrices to contain negative attribute values either. Such datasets have attributes that count things, or measure quantities, or measure intensities. For example, documents cannot contain negative occurrences of words; images cannot contain negative amounts of each color; chemical reactions cannot involve negative amounts of each reagent, and so on.
