Non-negative tensor factorization (NTF) is a relatively new technique that has been successfully used to extract significant characteristics from polyadic data, such as data in social networks. Because these polyadic data have multiple dimensions (e.g., the author, content, and timestamp of a blog post), NTF fits in naturally and extracts data characteristics jointly from different data dimensions. In the standard NTF, all information comes from the observed data and end users have no control over the outcomes. However, in many applications very often the end users have certain prior knowledge, such as the demographic information about individuals in a social network or a pre-constructed ontology on the contents, and therefore prefer the extracted data characteristics being consistent with such prior knowledge. To allow users’ prior knowledge to be naturally incorporated into NTF, in this paper we present a novel framework— FacetCube—that extends the standard non-negative ten...