SCIENCE CHINA Information Sciences, Volume 61, Issue 11: 112103(2018) https://doi.org/10.1007/s11432-017-9334-3

## Correlations multiplexing for link prediction in multidimensional network spaces

• AcceptedDec 28, 2017
• PublishedJun 8, 2018
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### Abstract

In social networks, link establishment among users is affected by diversity correlations. In this paper, we study the formation of links, map correlations into multidimensional network spaces and apply their behavioral and structural features to the problem of link prediction. First, by exploring user behavioral correlation and network structural correlation, we map them into three network spaces: following space, interaction space and structure space. With a hierarchical process, the coupling relationship between the spaces can be reduced and we can analyze the correlation in each space separately. Second, by taking advantage of the latent Dirichlet allocation (LDA) topic model for dealing with the polysemy and synonym problems, the traditional text modeling method is improved by Gaussian weighting and applied to user behavior modeling. In this way, the expression ability of topics can be enhanced, and improved topic distribution of user behavior can be obtained to mine user correlations in the following space and the interaction space. Moreover, the method can be extended using the hidden naive Bayesian algorithm which is good at reducing attribute independence. By quantifying the dependencies between common neighbors, we can analyze user correlations in the structure space and multiplex the correlations of the other two spaces to link prediction. The experimental results indicate that the method can effectively improve link prediction performance.

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• Figure 1

• Figure 2

(Color online) Multidimensional network spaces.

• Figure 3

Graphic model.

•
 Symbols Description Symbols Description $N$ Number of the users in $G$ ${f_{x,n}},{i_{x,n}}$ The $n$-th followed or interacted user of ${u_x}$ ${N_x},N_x'$ Number of followed or interacted users about $u_x$ ${l_{xy}}$ Existence of link between $u_x$ and $u_y$ ${N_f},{N_i}$ Number of followed or interacted users in $G$ ${s_q}$ The $q$-th common neighbor between $u_x$ and $u_y$ $K$ Number of interest topics ${\eta~_q}$ Independent dependency weight of the $q$-th common neighbor between $u_x$ and $u_y$ ${\gamma~_i},\gamma~_i'$ Gaussian weight of the $i$-th followed or interacted user in $G$ ${\pi~_q}$ Joint dependency weight of the $q$-th common neighbor between $u_x$ and $u_y$ ${Q_{xy}}$ Number of common neighbors between $u_x$ and $u_y$ ${R_1}$ Set of correlation in following space ${G^f}$ ${\boldsymbol{\alpha~}},{\boldsymbol{\beta~}},{{\boldsymbol{\alpha~}}'},{{\boldsymbol{\beta~}}'}$ Dirichlet priors ${R_2}$ Set of correlation in interaction space ${G^i}$ ${{\boldsymbol{\theta~}}_{\boldsymbol{x}}},{\boldsymbol{\theta~}}'_{\boldsymbol{x}}$ A topic distribution of $u_x$ ${R_3}$ Set of correlation in structure space ${G^s}$ ${{\boldsymbol{\psi~}}_{\boldsymbol{k}}},{\boldsymbol{\psi~}}'_{\boldsymbol{k}}$ A behavior distribution of topic $k$ $\tau~$ Learning rate for driving mechanism ${z_{x,n}},z_{x,n}'$ The $n$-th interest topic of $u_x$ $Y$ Set of the existence of links in $G$
•
 Dataset Sina micro-blog Twitter Users 49556 97632 Relationships 61880 6883144 Activity 3057635 167420 Forward 506765237 91142 Review 185079821 62986
•
 Algorithm Accuracy Precision Recall F1-measure LDA 0.716 0.719 0.626 0.669 CN+LDA 0.820 0.857 0.634 0.729 RA+LDA 0.826 0.861 0.638 0.733 VSM 0.834 0.839 0.605 0.703 CF 0.831 0.836 0.592 0.693 RW 0.843 0.877 0.612 0.721 HNB 0.847 0.881 0.608 0.719 WAODE 0.851 0.893 0.629 0.738 Proposed method ($K{\rm{~=~}}10$) 0.874 0.913 0.649 0.759 Proposed method ($K{\rm{~=~}}15$) 0.858 0.895 0.636 0.744
•
 Algorithm Accuracy Precision Recall F1-measure LDA 0.709 0.725 0.719 0.722 CN+LDA 0.775 0.801 0.743 0.771 RA+LDA 0.783 0.809 0.751 0.779 VSM 0.768 0.792 0.735 0.762 CF 0.761 0.784 0.726 0.754 RW 0.796 0.813 0.754 0.782 HNB 0.809 0.828 0.763 0.794 WAODE 0.818 0.834 0.793 0.813 Proposed method ($K{\rm{~=~}}10$) 0.836 0.848 0.784 0.825 Proposed method ($K{\rm{~=~}}15$) 0.821 0.831 0.774 0.803

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