Signed network representation is a key problem for signed network data. Previous studies have shown that by preserving multi-order signed proximity (SP), expressive node representations can be learned. However, multi-order SP cannot be perfectly encoded using limited samples extracted from random walks, which reduces effectiveness. To perfectly encode multi-order SP, we have innovatively integrated the informativeness of infinite samples to construct high-level summaries of multi-order SP without explicit sampling. Based on these summaries, we propose a method called SPMF, in which node representations are obtained using low-rank matrix approximation. Furthermore, we theoretically investigate the rationality of SPMF by examining its relationship with a powerful representation learning architecture. In sign inference and link prediction tasks with several real-world datasets, SPMF is empirically competitive compared with state-of-the-art methods. Additionally, two tricks are designed for improving the scalability of SPMF. One trick aims to filter out less informative summaries, and another one is inspired by kernel techniques. Both tricks empirically improve scalability while preserving effective performance. The code for our methods is publicly available.

Signed network embedding (SNE) has received considerable attention in recent years. A mainstream idea of SNE is to learn node representations by estimating the ratio of sampling densities. Though achieving promising performance, these methods based on density ratio estimation are limited to the issues of confusing sample, expected error, and fixed priori. To alleviate the above-mentioned issues, in this paper, we propose a novel dual-branch density ratio estimation (DDRE) architecture for SNE. Specifically, DDRE 1) consists of a dual-branch network, dealing with the confusing sample; 2) proposes the expected matrix factorization without sampling to avoid the expected error; and 3) devises an adaptive cross noise sampling to alleviate the fixed priori. We perform sign prediction and node classification experiments on four real-world and three artificial datasets, respectively. Extensive empirical results demonstrate that DDRE not only significantly outperforms the methods based on density ratio estimation but also achieves competitive performance compared with other types of methods such as graph likelihood, generative adversarial networks, and graph convolutional networks. Code is publicly available at https://github.com/WHU-SNA/DDRE.

Social media sites are now becoming very important platforms for product promotion or marketing campaigns. Therefore, there is broad interest in determining ways to guide a site to react more positively to a product with a limited budget. However, the practical significance of the existing studies on this subject is limited for two reasons. First, most studies have investigated the issue in oversimplified networks in which several important network characteristics are ignored. Second, the opinions of individuals are modeled as bipartite states (e.g., support or not) in numerous studies, however, this setting is too strict for many real scenarios. In this study, we focus on social trust networks (STNs), which have the significant characteristics ignored in the previous studies. We generalized a famed continuous-valued opinion dynamics model for STNs, which is more consistent with real scenarios. We subsequently formalized two novel problems for solving the issue in STNs. In addition, we developed two matrix-based methods for these two problems and experiments on realworld datasets to demonstrate the practical utility of our methods.

Developing effective network embedding methods for social trust networks (STNs) is a non-trivial problem because two key pieces of information need to be preserved simultaneously: a user's relations to latent factors and the trust transfer patterns that govern what type of relationship will form. In this study, we propose a novel social trust network embedding method (STNE) to address these issues. Specifically, we present a modified Skip-Gram model with negative sampling to jointly learn latent factor features, along with the trust transfer pattern features. Moreover, we define a flexible notion about a user's latent relationships with other users, which generates reliable negative samples for optimization. Extensive experiments on several real-world networks demonstrate the efficacy of the proposed STNE.

Link prediction in signed social networks is an important and challenging problem in social network analysis. To produce the most accurate prediction results, two questions must be answered: (1) Which unconnected node pairs are likely to be connected by a link in future? (2) What will the signs of the new links be? These questions are challenging, and current research seldom well solves both issues simultaneously. Additionally, neutral social relationships, which are common in many social networks can affect the accuracy of link prediction. Yet neutral links are not considered in most existing methods. Hence, in this paper, we propose a s igned l atent f actor (SLF) model that answers both these questions and, additionally, considers four types of relationships: positive, negative, neutral and no relationship at all. The model links social relationships of different types to the comprehensive, but opposite, effects of positive and negative SLFs. The SLF vectors for each node are learned by minimizing a negative log-likelihood objective function. Experiments on four real-world signed social networks support the efficacy of the proposed model.