How Long will She Call Me?

Introduction

Analysis of mobility-based usage patterns can not only help understand users' requirements but also reveal underlying patterns behind user behaviors. The discovered patterns can be used to evaluate traffic demand and forecast call volumes, and also as a tool for infrastructure monitoring. Call duration analysis is a key issue for understanding underlying patterns of (mobile) phone users.

In this paper, we study the extent to which a call between two users can be predicted in a dynamic mobile call network.

First, we examine the dynamic properties of data distributions of the mobile network including periodicity and demographics.
Then we study several important social theories in the call network including strong/weak ties, link homophily, opinion leader and social balance. We find several interesting phenomena such as people with strong ties tend to make shorter calls and young females tend to make long calls, in particular in the evening.
Finally, we present a time-dependent factor graph model to model and infer call duration between pairwise users. The model incorporates our discoveries in the distribution analysis and the social theory analysis. Experiments show that the presented model can achieve much better predictive performance compared to several baseline methods.

Our study offers evidences for social theories and also unveils several different patterns in the call network from online social networks.

Mobile Data

The data set used in this paper is made of a large collection of non-America call data records provided by a large mobile communication company. The extracted network contains around 272,345 nodes and 521,925 edges, which represent 3.9 million call records during two months (December and January). For privacy reason, we can only publicize one-week anonymous CDR data [CDR].

Furthermore, the results data in observations also are public, including: [Social Tie] (Figure 3 (a)(b) in Section 3), [Link Homophily] (Figure 3 (c)(d) in Section 3), [Opinion leader] (Figure 4 in Section 3), [Social Balance] (Figure 5 in Section 3).

The input for prediction model is [Model Input].

When you use the data sets for publications, please kindly cite the following paper.

@inproceedings{DongTang:13PKDD,

author = {Yuxiao Dong, Jie Tang, Tiancheng Lou, Bin Wu, Nitesh Chawla},

title = {How Long will She Call Me? Distribution, Social Theories and Duration Prediction},

booktitle = {ECML/PKDD'13},

year = {2013},

} [PDF Download]

Why do You Call for 59s?

We investigate the interplay of human call behaviors and social theory and answer the question: how social theories i:e:, social tie, homophily, social balance theory etc. influence duration of people's call. More specifically, we connect call duration to four basic social psychological theories and focus our analysis on the network based correlation via the following statistics:

0. Demographics: How long do people with different gender and age call?

1. Strong/weak Ties. How long do people with a strong or weak tie call?

2. Link homophily. Do similar users tend to call each other with long or short duration?

3. Opinion leader. Would opinion leaders have a similar or diffierent call behavior patterns with ordinary users?

4. Social balance. How does the duration-based network satisfy the social balance theory? To which extent?

How Long will She Call You?

Call Duration Prediction Problem. Given a dynamic call network G = (V, E, X, Y), the goal of the prediction is to learn a mapping fuction f: (G, Y) --> Yt+1 to predict the call duration in the next time stamp.

Social Time-dependent Factor Graph Model. Tang et. al. [PKDD11]first proposed a partially labeled factor graph model to infer social tie, and a triad based factor graph model was presented in [TKDD12] for reciprocal relationship prediction in Twitter network. In this work, we come up with a dynamic factor graph model based on previous partially labeled and triad factor graph model. The dynamic factor graph model incorporates both the correlations among latent variables in different timestamps and other social or attribute features for modeling and prediction. The name of this model is derived from the idea that we incorporate social theory into the factor graph model. The detailed information and codes of this model can be seen at KEG-Factor-Graph page.

**Table 1. Duration Prediction Performance**
	Next Call Duration Prediction					Average Call Duration Prediction
Method	SVM	LRC	BNet	CRF	STFG	SVM	LRC	BNet	CRF	STFG
Precision	0.5057	0.6184	0.5812	0.5865	0.6501	0.4869	0.6143	0.5943	0.6085	0.6695
Recall	0.5021	0.5548	0.5705	0.5886	0.6375	0.4875	0.6044	0.5902	0.6054	0.6707
F1-Measure	0.5042	0.5173	0.5692	0.5871	0.6393	0.4847	0.5996	0.5873	0.6049	0.6692

Prediction Results. Our goal here is to predict the next call duration and the average duration of calls in next time stamp based on historic call detail records. We use the first 7 week call detail records as historic data, the first call in the 8th week as next call duration and the average duration of calls in the 8th week as average call duration. We quantitatively evaluate the performance of inferring call duration in terms of Precision, Recall and F1-Measure. Table 1 shows the results for binary duration prediction next call duration prediction and average call duration prediction, set under the threshold. From Table 1, we see that our method clearly outperforms the baseline methods on both cases. For next call duration prediction, the STFG achieves a 5-13% improvement compared with SVM, LRC, BNet, CRF methods in terms of F1-Measure.

Distribution factor contribution analysis. Now, we analyze how different distribution factors: gender (G), age (A), week periodicity (W), day periodicity (D), can help infer future call duration. We first remove the gender factor (denoted as STFG-G), followed by further removing the age factor (STFG-GA), week periodicity (STFG-GAW), and finally removing day periodicity (STFG-GAWD). Figure 7 (a) shows the F1-Measure of the different STFG models. Obviously, we can observe clear drops on the performance when removing each of the factors. The result indicates that our model works well by combining the dynamic properties of data distribution, and each factor in our model contributes improvement in the performance.

Social factor contribution analysis. In STFG, we also consider five different social factors: social balance theory (B), social tie (T), link homophily (H) and opinion leaders (O). Here, we take the analysis to evaluate the contribution of different social factors for the prediction performance. With the same removing operations, we also can see clear drops in F1-Measure score in Figure 7 (b). For both two cases, we can find that there is a quick drop when ignoring social tie or link homophily factors. Figure 7 (b) also shows that the other social factors contribute to the prediction of call duration in two cases.

Reference

Yuxiao Dong, Jie Tang, Tiancheng Lou, Bin Wu, Nitesh V. Chawla. How Long will She Call Me? Distribution, Social Theories and Duration Prediction. ECML/PKDD' 13, Prague, Sep. 2013.