FacetCube: a general framework for non-negative tensor factorization

Non-negative tensor factorization (NTF) 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 traditional NTF, all information comes from the observed data, and therefore, the 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 data characteristics extracting by NTF being consistent with such prior knowledge. To allow users' prior knowledge to be naturally incorporated into NTF, in this paper, we present a general framework-FacetCube-that extends the standard NTF. The new framework allows the end users to control the factorization outputs at three different levels for each of the data dimensions. The proposed framework is intuitively appealing in that it has a close connection to the probabilistic generative models. In addition to introducing the framework, we provide an iterative algorithm for computing the optimal solution to the framework. We also develop an efficient implementation of the algorithm that consists of several techniques to make our framework scalable to large data sets. Extensive experimental studies on a paper citation data set and a blog data set demonstrate that our new framework is able to effectively incorporate users' prior knowledge, improves performance over the traditional NTF on the task of personalized recommendation, and is scalable to large data sets from real-life applications.