text: To enjoy more social network services, users nowadays are usually involved in multiple online social networks simultaneously. The shared users between different networks are called anchor users, while the remaining unshared users are named as non-anchor users. Connections between accounts of anchor users in different networks are defined as anchor links and networks partially aligned by anchor links can be represented as partially aligned networks. In this paper, we want to predict anchor links between partially aligned social networks, which is formally defined as the partial network alignment problem. The partial network alignment problem is very difficult to solve because of the following two challenges: (1) the lack of general features for anchor links, and (2) the "one-to-one @math " (one to at most one) constraint on anchor links. To address these two challenges, a new method PNA (Partial Network Aligner) is proposed in this paper. PNA (1) extracts a set of explicit anchor adjacency features and latent topological features for anchor links based on the anchor meta path concept and tensor decomposition techniques, and (2) utilizes the generic stable matching to identify the non-anchor users to prune the redundant anchor links attached to them. Extensive experiments conducted on two real-world partially aligned social networks demonstrate that PNA can solve the partial network alignment problem very well and outperform all the other comparison methods with significant advantages.
  @cite_44: This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or @math -way array. Decompositions of higher-order tensors (i.e., @math -way arrays with @math ) have applications in psycho-metrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors.
  @cite_38: Online reviews are valuable sources of information for a variety of decision-making processes such as purchasing products. As the number of online reviews is growing rapidly, it becomes increasingly difficult for users to identify those that are helpful. This has motivated research into the problem of identifying high quality and helpful reviews automatically. The current methods assume that the helpfulness of a review is independent from the readers of that review. However, we argue that the quality of a review may not be the same for different users. For example, a professional and an amateur photographer may rate the helpfulness of a review very differently. In this paper, we introduce the problem of predicting a personalized review quality for recommendation of helpful reviews. To address this problem, we propose a series of increasingly sophisticated probabilistic graphical models, based on Matrix Factorization and Tensor Factorization. We evaluate the proposed models using a database of 1.5 million reviews and more than 13 million quality ratings obtained from Epinions.com. The experiments demonstrate that the proposed latent factor models outperform the state-of-the art approaches using textual and social features. Finally, our experiments confirm that the helpfulness of a review is indeed not the same for all users and that there are some latent factors that affect a user's evaluation of the review quality.
  @cite_27: Clustering by integrating multiview representations has become a crucial issue for knowledge discovery in heterogeneous environments. However, most prior approaches assume that the multiple representations share the same dimension, limiting their applicability to homogeneous environments. In this paper, we present a novel tensor-based framework for integrating heterogeneous multiview data in the context of spectral clustering. Our framework includes two novel formulations; that is multiview clustering based on the integration of the Frobenius-norm objective function (MC-FR-OI) and that based on matrix integration in the Frobenius-norm objective function (MC-FR-MI). We show that the solutions for both formulations can be computed by tensor decompositions. We evaluated our methods on synthetic data and two real-world data sets in comparison with baseline methods. Experimental results demonstrate that the proposed formulations are effective in integrating multiview data in heterogeneous environments.
summary: Tensor has been widely used in social networks studies. @cite_38 propose to apply extended tensor factorization model for personalized prediction of review helpfulness. @cite_27 present a tensor-based framework for integrating heterogeneous multi-view data in the context of spectral clustering. A more detailed tutorial about tensor decomposition and applications is available in @cite_44 .