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Nonnegative matrix factorization (NMF) approximates a nonnegative ma-trix by the product of two low-rank nonnegative matrices. Since it gives semanti-cally meaningful result that is easily interpretable in clustering applications, NMF has been widely used as a clustering method especially for document data, and as a topic modeling method. We describe several fundamental facts of NMF and introduce its optimization framework called block coordinate descent. In the context of clustering, our frame-work provides a flexible way to extend NMF such as the sparse NMF and the weakly-supervised NMF. The former provides succinct representations for better interpretations while the latter flexibly incorporate extra information and user feed-back in NMF, which effectively works as the basis for the visual analytic topic mod-eling system that we present. Using real-world text data sets, we present quantitative experimental results showing the superiority of our framework from the following aspects: fast con-vergence, high clustering accuracy, sparse representation, consistent output, and user interactivity. In addition, we present a visual analytic system called UTOPIAN (User-driven Topic modeling based on Interactive NMF) and show several usage scenarios. Overall, our book chapter cover the broad spectrum of NMF in the context of clustering and topic modeling, from fundamental algorithmic behaviors to practical visual analytics systems.