An important task in network modeling is the prediction of relationships between classes of objects, such as friendship between persons, preferences of users for items, or the influence of genes on diseases. Factorizing approaches have proven effective in the modeling of these types of relations. If only a single binary relation is of interest, matrix factorization is typically applied. For ternary relations, tensor factorization has become popular. A typical application of tensor factorization concerns the temporal development of the relationships between objects. There are applications, where models with n-ary relations with n > 3 need to be considered, which is the topic of this paper. These models permit the inclusion of context information that is relevant for relation prediction. Unfortunately, the straightforward application of higher-order tensor models becomes problematic, due to the sparsity of the data and due to the complexity of the computations. In this paper, we discuss two different approaches that both simplify the higher-order tensors using coupled low-order factorization models. While the first approach, the context-aware recommendation tensor decomposition (CARTD), proposes an efficient optimization criterion and decomposition method, the second approach, the context-aware regularized singular value decomposition (CRSVD), introduces a generative probabilistic model and aims at reducing the dimensionality using independence assumptions in graphical models. In this article, we discuss both approaches and compare their ability to model contextual information. We test both models on a social network setting, where the task is to predict preferences based on existing preference patterns, based on the last item selected and based on attributes describing items and users. The experiments are performed using data from the GetGlue social network and the approach is evaluated on the ranking quality of predicted relations. The results indicate that the CARTD is superior in predicting overall rankings for relations, whereas the CRSVD is superior when one is only interested in predicting the top-ranked relations.
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Normalization takes care that all entries are non-zero and are smaller than one. Incidentally, this step turns out to be unnecessary in the regularized reconstruction, since after matrix completion all entries already obeyed these constraints. A second step ensures that the sum over matrix entries is equal to one.
A link from the last movie to movie might appear more plausible. If one does that change, the link between user and movie would need to point from movie to user, such that no collider (more than one link pointing to the same node) appears. With a collider one would need to use a tensor model as a local model.
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Rettinger, A., Wermser, H., Huang, Y. et al. Context-aware tensor decomposition for relation prediction in social networks. Soc. Netw. Anal. Min. 2, 373–385 (2012). https://doi.org/10.1007/s13278-012-0069-5
- Relation prediction
- Tensor matrix decomposition
- Graphical model
- Social media analysis