We discuss Non-negative Matrix Factorization (NMF) techniques from the point of view of Intelligent Data Analysis (IDA), i.e. the intelligent application of human expertise and computational models for advanced data analysis. As IDA requires human involvement in the analysis process, the understandability of the results coming from computational models has a prominent importance. We therefore review the latest developments of NMF that try to fulfill the understandability requirement in several ways. We also describe a novel method to decompose data into user-defined — hence understandable — parts by means of a mask on the feature matrix, and show the method's effectiveness through some numerical examples.