SCIENCE CHINA Information Sciences, Volume 60, Issue 11: 110104(2017) https://doi.org/10.1007/s11432-017-9243-7

## Integrating a weighted-average method into the random walk framework to generate individual friend recommendations

• AcceptedSep 8, 2017
• PublishedOct 13, 2017
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### Abstract

Friend recommendation is a fundamental service in both social networks and practical applications, and is influenced by user behaviors such as interactions, interests, and activities. In this study, we first conduct in-depth investigations on factors that affect recommendation results. Next, we design Friend+, a hybrid multi-individual recommendation model that integrates a weighted average method (WAM) into the random walk (RW) framework by seamlessly employing social ties, behavior context, and personal information. In Friend+, the first plus signifies recommending a new friend through network features, while the second plus stands for using node features. To verify our method, we conduct experiments on three social datasets crawled from the Sinamicroblog system (Weibo). Experimental results show that the proposed method significantly outperforms six baseline methods in terms of recall, precision, F1-measure, and MAP. As a final step, we describe a case study that demonstrates the scalability and universality of our method. Through discussion, we reach a meaningful conclusion: although common interests are more important than user activities in making recommendations, user interactions may be the most important factor in finding the most appropriate potential friends.

### Acknowledgment

This work was supported by National High Technology Research and Development Program of China (863 Program) (Grant No. 2015AA124102), Hebei Natural Science Foundation of China (Grant No. F2015203280), Open Project Program of the State Key Laboratory of Mathematical Engineering and Advanced Computing (Grant No. 214125), National Natural Science Foundation of China (Grant No. 61303130), Graduate Innovation Funded Program of Yanshan University (Grant No. 2017XJSS028), and Innovation Zone Project Program for Science and Technology of China's National Defense (Grand No. 2017-0001-863015-0009).

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• Figure 1

(Color online) Architecture of Friend+.

• Figure 2

Results for user behavior statistics.

• Figure 3

Analysis results for DS1, DS2, and DS3. (a) Results of IN analysis; (b) results of IA analysis; (c) results of ID analysis.

• Figure 4

Trend of $\alpha$ for $u_{1}$, $u_{2}$, and $u_{3}$.

• Figure 5

Trends of MAP, Recall, and F1-Measure with changes in weight $a\_{\rm weight}$ in (a) DS1, (b) DS2, and (c) DS3.

• Figure 6

Values of Macro-average F1-Measure on DS1, DS2, and DS3.

• Figure 7

(Color online) Screenshots and descriptions of Xunweiyou whose Chinese meaning is “Looking for Weibo friends".

• Figure 8

(Color online) Results of Xunweiyouapplication.

•

Algorithm 1 Random-walk-with-restart algorithm

$\tilde{W}\Leftarrow$ The normalized matrix;

$r_{0}\Leftarrow$ the initial vector;

${\rm iterator} = 0.000001$;

M$\Leftarrow$ the state transition matrix;

Initialize $r_{\left ( k \right )}^{\left ( 0 \right )}=\left ( r_{\left ( 1 \right )}^{\left ( 0 \right )},r_{\left ( 2 \right )}^{\left ( 0 \right )},\ldots, r_{\left ( n \right )}^{\left ( 0 \right )} \right )$ , $m$=1;

for $i=1,2,\ldots, N$

$\phi _{i}^{(m-1)}=\frac{r_{i}^{(m-1)}}{ \| r_{i}^{(m-1)} \|}_{1}$;

$A^{(m-1)}\Leftarrow$ the aggregation matrix;

$(A^{(m-1)})_{ij}=\phi_{i}^{m-1}M_{ij}e_{j}$;

$\zeta ^{(m-1))}\Leftarrow$ characteristic vector;

$\zeta ^{(m-1))}=\zeta^{(m-1)}A^{(m-1)}+c_{1\times N}$ (constant vector);

if $r^{(m)}_{(k)}-r^{(m-1)}_{(k)}$)$\leq$ iterator then

$r^{(m)}_{(k)}=(\zeta ^{(m-1)}_{1}\phi^{{(m)}}_{1}, \zeta ^{(m-1)}_{2}\phi^{{(m)}}_{2}, \times , \zeta ^{(m-1)}_{N}\phi^{{(m)}}_{N})$;

else

$m \Leftarrow m+1$;

end if

end for

$r \Leftarrow$Stationary distribution probability;

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