Users in online networks exert different influence during the process of information propagation, and the heterogeneous influence may contribute to personalized recommendations. In this paper, we analyse the topology of social networks to investigate users’ influence strength on their neighbours. We also exploit the user-item rating matrix to find the importance of users’ ratings and determine their influence on entire social networks. Based on the local influence between users and global influence over the whole network, we propose a recommendation method with indirect interactions that makes adequate use of users’ relationships on social networks and users’ rating data. The two kinds of influence are incorporated into a matrix factorization framework. We also consider indirect interactions between users who do not have direct links with each other. Experimental results on two real-world datasets demonstrate that our proposed framework performs better than other state-of-the-art methods for all users and cold-start users. Compared with node degrees, betweenness, and clustering coefficients, coreness constitutes the best topological descriptor to identify users’ local influence, and recommendations with the measure of coreness outperform other descriptors of user influence.
As the amount of information available online increases exponentially, it becomes more difficult for users to find the relevant information or contents in which they are interested, thereby resulting in an information overload problem. Recommender systems play an important role in tackling the problem of information overload and have attracted more attention in both academia and industry in recent years [
Collaborative filtering (CF) is one of the most popular techniques in recommender systems. Some CF methods that use only user-item ratings for recommendation confront cold-start problems. More specifically, for a new user in such recommender systems, because he/she has given few ratings, these CF algorithms perform poorly for the user. The situation is similar for a new item in recommender systems.
Given the rapid increase of online social networks and applications, users participate in online activities and produce a lot of social relationships, such as social friendships and trust relationships. In the real world, we always ask our trusted friends for movie and book recommendations. Social relationships provide an independent source of information for recommender systems in addition to user-item rating information. Social relationships among users can be incorporated into memory-based CF methods and matrix factorization methods in the recommendation process. Social influence theory in [
Some work has been done to exploit social relationship networks of users in recommender systems and improve the performance of recommender systems [
In this paper, we investigate users’ influence on their neighbours and the entire network, and we incorporate the influence into recommender systems. We exploit the topology of social networks to determine the local influence of each user and determine his/her global influence based on the number of his/her ratings. Both local and global influences are applied in the matrix factorization framework. In addition to the effect of trusted friends, we consider indirect interactions from users that have a high reputation. Experimental results demonstrate that our proposed algorithm outperforms other state-of-the-art recommendation models. Within this framework, the main contributions of this work include the following. We explore the topological influence of users according to their roles on social networks and incorporate the topological influence into recommendations. In addition to the influence between socially linked users, we also consider the influence of indirect interactions among users, which can improve the recommendation performance. Our proposed recommendation framework reduces recommendation errors, particularly for cold-start users.
The rest of this article is organized as follows. In Section
In this section, we review several approaches for recommender systems, including
Collaborative filtering is a widely used recommendation method. Generally, it is based on the assumption that similar users have similar preferences on common items. CF contains memory-based collaborative filtering [
Based on the assumption that users’ tastes can be represented by a small number of latent factors, the MF method in [
Recently, some social recommendation methods based on matrix factorization techniques have been proposed to directly use trust relationships among users to provide better recommendations. These methods show substantial improvements [
One more effective way to utilize social relations, as discussed in [
A few works have been done based on heterogeneous friends’ influence in social recommendations [
In the majority of cases, the influence between two users only takes effect at the local scale [
Based on this definition of
The distribution of coreness in different datasets.
Epinions
Ciao
In the Epinions dataset, most nodes’ coreness is smaller than 10, and the proportion is 94.75%. This distribution may be because this network fits the power-law distribution and a large long tail of users has a very small coreness. The smallest coreness is 0 and the biggest coreness is 26 in the Epinions dataset. Unlike the Epinions dataset, in the Ciao dataset, the proportion of nodes in which coreness is smaller than 10 is 65.05%, implying different network hierarchies and influence distributions of the two chosen datasets. The smallest coreness is 0 and the biggest coreness is 32 in the Ciao dataset.
We define a user
If user
A user’s global influence indicates his/her reputation in the whole network. The user’s reputation is a sort of status that gives additional powers and capabilities in recommender systems [
In the real world, in addition to asking our friends for suggestions, we tend to take into account the suggestions of some persons who have high reputations in the community, even if they are not our friends and we have no direct interactions with them. In online networks, a celebrity’s opinion is likely to affect the actions of other users even if they do not follow the celebrity. Indirect interactions between users will also affect users’ actions, so indirect or implicit user connections should be emphasized [
With
The parameter
As previously discussed, recommendations from users with high global influence are more likely to be trustworthy and reliable. Therefore, we use the values of users’ global influence to weight the importance of their recommendations so as to incorporate global influence into MF. In the MF framework, the weight of
The method incorporates two kinds of social influence into recommendation to improve the performance of recommender systems. The optimization problem minimizes the sum-of-squared-error objective function shown in the following:
A local minimum of the objective function given by (
Three steps are designed to train our proposed model.
It is to generate the user-user trust matrix with trust relationships and then calculate coreness of each node in the trust network from the trust matrix. We normalize the values of coreness and then calculate the values of local influence according to (
It is to generate the user-item rating matrix with rating data. We use the user-item rating matrix to calculate the number of ratings for each user. We then normalize the numbers of users’ ratings and calculate the global influence using (
It is to use stochastic gradient descent to find the optimal user feature matrix
The details of the steps are shown in Algorithm
dimensionality of user feature vector and item feature vector parameters influence vector calculate calculate calculate calculate calculate calculate update update
The main cost in learning
In this section, we conduct several experiments to compare the recommendation qualities of our approach with other state-of-the-art recommendation models.
We chose two real-world datasets to evaluate our proposed method: Epinions and Ciao. Each dataset has a trust network. The two datasets were collected from the websites
Epinions is an online product review website where users can read reviews about a variety of products (such as books, articles for daily use, cars, and home appliances) to help them make decisions on what to purchase. Users can also post a review after rating a product with integer scores from 1 to 5. Every member of Epinions establishes social relationships (i.e., trust relationships) with others to show his/her attitude to other users.
Ciao is an online shopping portal website in Europe. The site provides a network platform where registered users can review items and share their opinions on various products to help others make decisions. These reviews are available to the general public. Each user on Ciao also maintains a trust list to indicate his/her attitude to others.
The two datasets are crawled by Jiliang Tang et al. from two popular product review sites Epinions and Ciao in the month of May, 2011. The raw Epinions dataset contains 27 categories of items and the Ciao dataset contains 28 categories of items. These two datasets are published at Jiliang Tang’s homepage at “
Some statistics of these datasets are presented in Table
Statistics of datasets.
Epinions | Ciao | |
---|---|---|
# of Users | 7411 | 7267 |
# of Items | 8728 | 11211 |
# of Ratings | 276116 | 149147 |
Rating Density | 0.0043 | 0.0018 |
# of Social Relationships | 52982 | 110755 |
Social Relationship Density | 0.00096 | 0.0021 |
We choose four well-known metrics to measure the performance of our proposed approach in comparison with other collaborative filtering and trust-aware recommendation models. They are mean absolute error (MAE), root mean square error (RMSE), precision, and recall. The metric MAE is defined as
The metric precision is defined as
The metric recall is defined as
In this section, to show the effectiveness of our proposed recommendation approach, we compare our recommendation method RDISI with the following representative models.
Probabilistic Matrix Factorization (PMF) [
RSTE [
SoRec [
SocialMF [
SoReg [
For our method, we select optimal parameters for both datasets. Because the two datasets have different data statistics, different parameters are needed for training. The parameter
Parameter settings of compared recommendation methods.
Datasets | Algorithms | Parameters |
---|---|---|
Epinions | PMF | |
RSTE | | |
SoRec | | |
SocialMF | | |
SoReg | | |
| ||
Ciao | PMF | |
RSTE | | |
SoRec | | |
SocialMF | | |
SoReg | |
We randomly select 80% of data for each dataset as training data to verify our proposed method. The experiment results are shown in Table
Performance comparisons (MAE and RMSE).
Dataset | Metrics | PMF | SoRec | RSTE | SocialMF | SoReg | RDISI |
---|---|---|---|---|---|---|---|
Epinions | MAE | 0.8680 | 0.8467 | 0.8564 | 0.8651 | 0.8232 | |
RMSE | 1.0922 | 1.1105 | 1.1475 | 1.1903 | 1.0655 | | |
| |||||||
Ciao | MAE | 0.8841 | 0.7991 | 0.7786 | 0.7858 | 0.7491 | |
RMSE | 1.1353 | 1.1071 | 1.0859 | 1.1230 | 0.9904 | |
As shown in Table
As discussed in Section
The effect of parameter
Epinions
Ciao
Parameter
The impact of parameter
Epinions
Ciao
To verify whether coreness is more effective than other indicators (e.g., node betweenness, node degrees, and clustering coefficients) on determining local influence in recommender systems, we conduct experiments to compare the performance of RDISI using betweenness, degrees, clustering coefficients, and coreness to determine users’ local influence, respectively. In these comparison experiments, we merely replace
Performance comparisons with other indicators (dimensionality=20).
Dataset | Metrics | Betweenness | Degree | Clustering Coefficient | Coreness |
---|---|---|---|---|---|
Epinions | MAE | 0.8155 | 0.8139 | 0.8060 | 0.8011 |
RMSE | 1.0605 | 1.0581 | 1.0466 | 1.0392 | |
| |||||
Ciao | MAE | 0.7382 | 0.7335 | 0.7336 | 0.7308 |
RMSE | 0.9818 | 0.9763 | 0.9762 | 0.9721 |
The results in Table
In the Epinions and Ciao datasets, some users have rated lots of items, but most users have rated only a few items. We select those users who have rated no more than 10 items in the training set as cold-start users. We conduct experiments to verify whether our method RDISI performs better than other state-of-the-art recommendation models. In addition to coreness, node’s
The comparison results for MAE and RMSE on cold-start users are shown in Figure
Performance comparisons of cold-start users (dimensionality=20).
MAE
RMSE
Inspired by [
Performance comparisons using different generation functions.
Dataset | Generation function of local influence | Generation function of global influence | Performance (MAE) |
---|---|---|---|
Epinions | | | 0.8011 |
| | 0.8056 | |
| | 0.8042 | |
| |||
Ciao | | | 0.7308 |
| | 0.7348 | |
| | 0.7319 |
In trust networks, in general, relational information is not static. The effect of the emergence of new influencers and new trends should be discussed. Specifically, the number of the users in a social network is increasing, and new trust relationships among users have been emerging. To verify the performance of our proposed algorithm with the effect of the emergence of new influencers and new trends, we conduct a new experiment. In this experiment, we use a larger Epinions dataset which is named Epinions_ext dataset. The Epinions_ext dataset contains 390732 ratings of 13209 users for 14027 items and 145927 trust relations among users. Specifically, the Epinions dateset we used and described in Section
Performance comparisons (dimensionality =20).
Dataset | Metrics | PMF | SoRec | RSTE | SocialMF | SoReg | RDISI |
---|---|---|---|---|---|---|---|
Epinions_ext | MAE | 0.9230 | 0.8923 | 0.8580 | 0.8559 | 0.7571 | |
RMSE | 1.1543 | 1.1982 | 1.1567 | 1.1903 | 1.0087 | |
When we conduct experiments on the Epinions_ext dataset, we get smaller MAE and RMSE, which means that our proposed model even performs better when the social relationships and the number of users in the network are increasing. It is also noticeable that our proposed model gets larger improvement than the comparison methods when using the Epinions_ext dataset and our proposed model is scalable with the size of the dataset.
Our proposed model is focusing on rating prediction so that we select the metrics MAE and RMSE to evaluate the performance of our proposed recommendation model. To verify whether our proposed method is effective in the ranking, which is another task of recommender systems, we conduct extended experiments to verify the performance of our proposed method in the ranking task by using the metrics precision and recall that are both defined in Section
Performance comparisons (precision and recall).
Dataset | Metrics | PMF | Social | SoReg | RSTE | SoRec | RDISI |
---|---|---|---|---|---|---|---|
Epinions | precision | 4.8e-4 | 5.5e-4 | 5.8e-4 | 6.2e-4 | 6.7e-4 | |
recall | 0.0065 | 0.0072 | 0.0072 | 0.0081 | 0.0091 | | |
| |||||||
Ciao | precision | 1.8e-4 | 2.2e-4 | 2.2e-4 | 2.4e-4 | 2.6e-4 | |
recall | 0.0038 | 0.0046 | 0.0044 | 0.0047 | 0.0054 | | |
| |||||||
Epinions_ext | precision | 0.0011 | 0.0014 | 0.0015 | 0.0016 | 0.0016 | |
recall | 0.0257 | 0.0267 | 0.0287 | 0.0303 | 0.0307 | |
Our proposed model and the comparison methods in this paper are focusing on rating prediction so that these methods do not perform well in the ranking task of recommender systems, which can be verified by the values of precision and recall. However, our proposed method performs better than the comparison partners in ranking task.
With the popularization of online social networks, exploiting social relationships provides a reliable source that can be utilized to improve the performance of recommender systems. In this paper, we exploited users’ trust relationships and calculated each user’s coreness, which determines the user’s local influence on social networks. A user’s global influence is determined by the number of ratings he/she has given. Incorporating local and global influence, we propose the recommendation method RDISI. In addition to direct influence, the method also considers indirect interactions between users who do not have direct links. Experimental results from the real-world datasets Epinions and Ciao demonstrate that our method performs better than some state-of-the-art social recommendation models. Moreover, as analysed beforehand and shown in Figure
In this paper, we only investigate how trust relationships affect users’ preferences and how they can be fused into the MF recommendation model to make better recommendations. However, distrust relationships in social networks are also critical in the social recommendation process. Even very few distrust links can have a great impact on social recommendations. Thus, it is worth conducting research using a dataset that contains both trust and distrust relationships as some networks allow users to express distrust of others.
The data used to support the findings of this study are available from “
The authors declare that they have no conflicts of interest.
This work has been supported by the National Natural Science Foundation of China under Grant 61872033, the Humanity and Social Science Youth Foundation of Ministry of Education of China under Grant 18YJCZH204, and the Beijing Natural Science Foundation under Grant 4184084.