Temporal relation co-clustering on directional social network and author-topic evolution

Analyzing three-way data has attracted a lot of attention recently because such data have intrinsic rich structures and naturally appear in many real-world applications. One typical type of three-way data is multiple two-way data/matrices with different time periods, for example, authors' publication key terms and people's email correspondence varying with the time. We propose to use the PARATUCKER model to analyze three-way data. The PARATUCKER model combines the axis capabilities of the Parafac model and the structural generality of the Tucker model and thus can be viewed as the combination of Tucker and Parafac. It does not require the symmetry of the data nor the same dimensionality of mode 1 and mode 2. However, no algorithms have been developed for fitting the PARATUCKER model, especially for obtaining non-negative solutions that are intuitive to understand and explain. In this paper, we propose TANPT: a three-way alternating non-negative algorithm to fit the PARATUCKER model. We apply the algorithm to temporal relation co-clustering on directional social network and author-topic evolution. Experiments on real-world datasets (DBLP and Enron Email datasets) demonstrate that our proposed algorithm achieves better clustering performance than other well-known methods and also discovers some interesting patterns.