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Non-negative Matrix Factorization (NMF) is a method to obtain a representation of data using non-negativity constraints. These constraints lead to a part-based representation in the vector space because they allow only additive, not subtractive, combinations of original data. This is how NMF learns a part- based representation. This paper introduces briefly the theory and algorithm of NMF. Then a NMF ANN framework is presented to classify spontaneous EEG in five metal tasks. Several comparisons and experiments were carried out. The results showed that NMF lead more localized and sparse features than power spectrum method and principal component analysis method did, and that the NMF-ANN structure preserved the spatio-temporal characteristics of EEG signals. Its best cognition rate of five mental task pairs can achieves better than 88.0%. It may be a promising classifier for Brain Computer Interface (BCI) scheme.