How Much do Your Friends Tell About You? Reconstructing Private Information from the Friendship Graph Norbert Blenn
Christian Doerr
Nasireddin Shadravan
Piet Van Mieghem
Faculty of Electrical Engineering, Mathematics and Computer Science Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands
[email protected],
[email protected],
[email protected],
[email protected]
Abstract After the early land rush and fast exponential growth of online social networking platforms, concerns about how data placed in online social networks may be exploited and abused have begun to appear among mainstream users. Social networking sites have responded to these new public sentiments by introducing privacy filters to their site, allowing users to specify which aspects of their profile are visible to whom. In this paper, we demonstrate that such an approach to privacy and informational self-determination is largely futile: as we form social relations and build networks with those alike us, much of who we are and what we do can be reconstructed from unhidden parts of the social graph. Categories and Subject Descriptors K.4.1 [COMPUTERS AND SOCIETY]: Public Policy Issues—Privacy General Terms Security, Online Social Network Keywords Privacy, OSN, Friendship Graph
1.
Introduction
The recent boom of social networking platforms has lead to a dramatic shift in how people behave, spend their time and interact with others. The wealth of information registered users and visitors voluntarily place, curate and maintain within these platforms in combination with their enormous market reach has however also enabled a wide set of new applications beyond the initial usage propositions: Activities of users and their interactions with their friends are now analyzed to obtain personal profiles, which can be used for marketing activities, but also help companies determine whether a customer can be deemed “influential” and should consequently receive a better treatment than others [13]. In-
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. 5th Workshop on Social Network Systems EuroSys ’12 April 10, Bern. c 2012 ACM Copyright is held by the author/owner(s). SNS’12, April 10, Copyright � 2012, Bern, Switzerland. ACM 978-1-4503-1164-9/12/04.. . . $10.00
formation on relationships, personal habits and interests can be taken into account when assessing risks and rates when applying for health insurance [16], and face recognition performed on photos stored in online social media allows the re-identifications of persons in other contexts, such as identifying passerby’s in camera recordings to deliver targeted billboard advertisements [17]. As such technologies are developed and applied, concerns about the privacy of one’s personal data are increasingly gaining track. Indeed, privacy filter usage has become a mainstream practice: in case of the largest national social network site in the Netherlands, hyves.nl, 63% of the users have by now enabled privacy settings in their profile making their details invisible to the general public. In this paper, we demonstrate to what extent and at which accuracy level personal information can actually be reconstructed from a social network’s friendship graphs. The underlying justification our approach is driven by is the sociopsychological hypothesis, which was empirically verified for digg.com [5] and facebook.com [14], that users form social ties with those around them who are similar in socio-economic status, interests and opinions [15]. In consequence, knowing a user’s friends can therefore to a large degree tell us the individual tastes and choices of a social network user even when his profile page is hidden. The degree to which this technique can be successfully applied varies with the overall embedding of a particular user in the social graph as well as other attributes, such as the user’s personal characteristics, the overall diversity of the direct friends or the degree to which the friends are making use of privacy settings themselves. The remainder of this paper is structured as follows: Section 2 overviews previous work on privacy in social networking sites, section 3 outlines the platform Hyves.nl and the data acquisition used for this study. Section 4 demonstrates a study how hidden profile information can be extrapolated from the social friendship graph. Section 5 summarizes our findings and gives an outlook on future work.
2.
Related Work
Two major approaches, active and passive, are possible to access private information. Active approaches try to obtain data by directly attacking a particular user using fake profile information [2], surveys or third party applications that access the users profile in the OSN. In this paper we will investigate passive approaches which are based on statistical analyses of users and the friendship network. These passive approaches may be based on the profile information a user specifies, tracking the friendship network through third-party applications, or the combination of different data sources. Gross and Acquisti [7] analyzed patterns of information revelation in OSNs and privacy implications in the “early” stage of Facebook. An amazingly high number of 89% of users in their dataset provided their real name. Other attributes like phone number, birthday, home town, address etc. were also given by the majority of the users. Different techniques to infer private information like reidentification of users by analyzing the postal code and their birthday are presented. Face re-identification to identify users on different sites or even identity theft of the users social security number was shown to be feasible. The role of third party sites in tracking users of OSNs and obtaining private information is investigated by Krishnamurthy and Wills [9, 10]. In most cases, a user has no possibility to control all applications that track profile data. Users are not aware which data is accessed by them and what the different services do with this data. Because of the knowledge about friendships in OSN and the fact that those relations are mostly built between individuals having similar interests it is still possible to infer private attributes of a user from his friends even if the user has a profile which is not visible to everyone. McPherson et al. [11] discussed “homophily” as a concept that limits individuals to connect only to others having similar attributes. The strongest divisions are based on race and ethnicity followed by age, religion, education, occupation and gender. Hence, ties between non-similar users are either not constructed or dissolve at a higher rate. This leads to social niches in the social space. He et al. [8] constructed a Bayesian network assuming that direct neighbors have a higher overlap than users multiple hops away. It is shown that privacy can be indirectly inferred via social relations and mathematically over multiple hops. He et al. use an influence strength which is defined as the conditional probability (P (A|B)) that user A has a attribute given a friend (B) has the same attribute. By using friendship information and group attendance information, Zheleva and Getoor [19] showed for different OSNs that it is possible to infer private attributes using group and friendship information. Mislove et al. [14] claim that “you are who you know” because automatic community detection for multiple attributes
of the users led them infer private attributes with an accuracy of 80% inside those communities. This approach needs the knowledge of the topology of the social network in order to detect communities. Because of the dynamic nature of OSNs, standard crawling techniques take rather long to obtain the whole network, it is thus unfeasible for attackers to first crawl the network in order to detect communities.
3.
Hyves.nl
Hyves.nl is the largest Dutch Online Social Network founded in 2004 containing nearly 10.6 million accounts in 2011. Given the total population of the Netherlands (ca. 16.5 million), a large fraction of the inhabitants are registered. However, the total number of user accounts of Hyves.nl includes duplicates and orphan accounts as well as commercial pages. We obtained our dataset by screen scraping Hyves.nl using multiple parallel breadth first searches. Our dataset contains 2,971,261 user profiles. Out of those roughly one third are public viewable profiles. On a profile page, users have to define a username and a real name and they may provide birthday, age, hometown, relationship status, living situation, address, phone number and their email address. An example of a typical Hyves.nl profile page is shown in fig. 1. Additionally, users may join a large selection of groups. Those groups could be real world communities like sport clubs, schools or companies, famous people, bars and restaurants, books, movies Figure 1. Screenshot of a etc. Groups are orusers main profile page of ganized in 19 topics Hyves.nl namely: brands, hangouts, school, college, club, company, TV shows, books, food, film, gadgets, games, famous people, media, music, traveling, sport, TV programs and others. It is possible to join groups without invitation and a user may create a new group. Groups are displayed on the user’s profile page ordered by their topic. Every group has its own page, listing all members of this group, additional information like events, addresses or opening times. Friendship relations are set up by sending a friendship request via Hyves.nl to a user. If the request is accepted the two users are mutual friends. The average number of friends in our dataset equals 127. Users may also upload photos and tag people in these photos. We also crawled 446,868 images and people tagged in them resulting in 624,478 user names 1,311,423 relations. In terms of privacy control, Hyves.nl allows a user to change privacy settings to display each attribute to the public, viewable for everyone registered at Hyves.nl, friends of friends or only friends. Nearly one third of all profiles we
Reconstructing Users’ Profiles
In order to infer private attributes of a user who has his profile page set to private, we use statistical methods based on different sources of information. For some OSN’s like Hyves.nl, StudiVZ.de, Skyrock.com or Vkontakte.ru most users belong to the population of one country. Therefore, combining information from census bureaus of these countries constitutes a straightforward way of inferring attributes like the age, name, phone number or relationship of the user. We used association rule learning, trained on the dataset of publicly available information in order to reveal relations between user’s attributes and groups a profile page lists. A third approach is based on the theory of “birds of a feather flock together” describing that friends have similar interests. In general, the characteristics of a user can be classified into two groups: intrinsic attributes (such as name, age, city and the gender) and communities (school, college, university, company, sport club or interests). If a user has a private profile page it is still possible to uncover friendship relations because they are bidirectional. Therefore these friendships are listed on profile pages of friends having a publicly viewable profile page. Based on the average number of friends this indicates that on average every user has 42 friends having a publicly viewable profile page. As stated in Bonneau et al. [3] “eight friends are enough” to reveal the whole network of users of a OSN. We will show that a similarly small number of friends is sufficient to correctly infer most of a user’s characteristics. 4.1
“Birds of a Feather”
As described by McPherson et al. [11], friends tend to have similar interests because they know each other, live close to each other, met physically at places where they follow their hobbies or at places where they work together. Friendships in Online Social Networks do not necessarily follow this scheme as one may also create friendship relations towards users without knowing them in person. The hypothesis that personal preferences limit the possible number of users, still holds as online friendships are based on common interests as shown in [5, 11, 14, 15]. 4.1.1
Age
The age distribution of users in Hyves.nl shows an oversampling of young persons when comparing to the age of the Dutch population as shown in fig. 2. One assumption is that a user is as old as most of his friends. Hence, for every user in our dataset providing his age we used the most frequent age of his friends as an estimator. The results are shown in figure 3 given by the
Percentage of population
4.
difference between actual age of a user to the mode of the friend’s ages. As indicated by multiple traces (different markers, and colors) in fig. 3, the probability that most friends have the same age as a user is depending on the age group the user is in. The highest accuracy of this method (prediction rate) is found for the group of 16 to 20 year old users where 61% of friends of a user have exactly the same age as the user. When allowing up to ±1 year of difference the probability to predict the correct age of a user, by using the age of most friends, increases to 77%. This prediction probability decreases for older age groups. A reason for this high age overlap might be based on the fact that friendships in the group of 10 to 20 year old users are created in schools where the stuFigure 2. Comparison of the dents are in the same age of Hyves.nl users (blue) to class. Later in life, colthe population of the Netherleagues and friends are lands (red) not exactly the same age anymore. Another explanation for this trend is the decreasing average number of friends: In the group of 16-20 year old users 81, users at the age of 46-50 years have on average 14 friends. We also found a peak in the prediction error for users between 35 and 45 years which is around 20 years, indicating that quite a number of parents are befriended with their children. Percentage of Dutch inhabitants Percentage of Hyves.nl users
0.3
0.2
0.1
0.0
0-9
10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89
90-
Age group
1-5 6-10 11-15 16-20 21-25 26-30 31-35 36-40 41-45 46-50 51-
0.6
0.5
0.4
Probability to predict the exact age
collected, are publicly viewable, which means that the real name, groups, age, hometown and the list of friends is displayed. If a user has a private profile page, the real name, if entered by the user, is still displayed.
0.3
0.6 0.5 0.4 0.3 0.2 0.1 0.0 1-5
6-10
11-15 16-20 21-25 26-30 31-35 36-40 41-45 46-50
50+
Agegroup
0.2
0.1
0.0 0
2
4
6
8
10
Figure 3. Prediction of the age of a user using mode of his friends age for different age groups. Inset: Probability to correctly guess the age of a user. 4.1.2
Location Determination
Another intrinsic value of a user is the hometown. The simplest assumption is that most friends of a user live in the same city the user lives in. Actually, based on our dataset 67% of a particular user’s friends who provided their hometown live in the same city as the user, and 91% of all friends live within 50 km of the users location. As already mentioned even private profile pages list the real name of a user. By accessing a database containing
the geographical distribution of names, for example phone books, this information can be combined to estimate the area or even the city of a user. Some census bureaus or universities also collect data on name distributions. In the Netherlands the Meertens Institute [1] lists how often and in which municipality a particular family name or first name occurs. Because no name is evenly geographically distributed, one can use the name of a user to guess his location. Fig. 4 shows the geographical distribution and the popularity of “Tim” as first name during the last 131 years. A similar geographical distribution can be obtained for family names. Comparing the geographical distributions of first and family name provides a rough estimate for the city of a user.
most users of this group, the average predictability increases to 86%. 4.1.3
Different Tastes in Age Groups
Groups do not only reveal location information but also information about the age of user. For example musical interests have a strong relation to the age of a particular user. We depict in figure 5 exemplarily the age of users who like different singers or music bands. Conversely these correlations suggest that the specified age of most users in our dataset is accurate. We found strong relations between interests and the age of a user for movies, music types and game consoles. 100
K3
90 80
ion Ce lin
eD
60 50
He
Green Day
10 0
rm an
U2
20
Ae 10
ith rosm
20
Sting 30
40
50
And re R ieu
30
Fin ke rs
40
nver John De
Percent of Interest
70
60
70
80
Age
Figure 4. The popularity of the first name Tim in the Netherlands. Inset: Geographical distribution of the name.
Figure 5. Probability users have a specific taste in music to the age of a user
Given the area distribution of names in fig. 4 and the distribution of the surname, we deduce that a user called “Tim Janssen”1 lives in Amsterdam with a probability of 32%, the Hague with a probability of 19% or Utrecht with a probability of 17% etc. Out of the 19 topic groups in Hyves.nl, some further strengthen location estimation. Topics like hangouts, schools, colleges, clubs, companies, food and sport contain implicit location information. Assuming that people like to visit bars, restaurants, spot clubs in the same city they live and work enables us to infer the city from these groups. By using Bayesian analysis [18] we calculated the probability a user has joined a specific group given he lives in a specific city. In this way we compared how many users attend a group in different cities. If the distribution shows no significant peaks (larger than 1 standard deviation), this means that the users in this particular group are homogeneously distributed in the Netherlands. An overrepresentation of a particular group in a city however is a good indicator that this group can be used to infer a users city. We identified 13,512 groups that can be used to predict the residence of a user. By analyzing all of those 13,512 groups with more than 5 users, we found that on average 64% of the members indeed live in the same city. This does not imply that the other 36% reside in different cities as some users simply do not provide their home town. When assuming that users, who did not enter a city in their profile, would live in the same city as
Every user joined on average 26.6 groups. Homophily suggests that friends have similar tastes which should result in a high overlap of group memberships between a user and his friends. Figure 6 depicts the probability the profile page of a user’s friend lists the same groups as the user. If all friends are taken into consideration only a small overlap (red points) can be found. When searching for the highest overlap of groups a user has with at least one friend we found that most users have at least one friend who joined nearly the same groups as the user (blue points). The difference in groups a user is a member of compared to his friends, can be seen as a similarity measurement between users. Based on this metric, only a fraction of all friends are close friends, whereas a high number of acquaintances appear in a user’s friendship network. The fact that only a few friends in the friendship graph are close friends is also described by [6] as the weak and strong ties and analyzed by [12]. Thus a way of identifying close friends could be by analyzing the information if the users are tagged on the same image. This would imply that the users physically know each other and the probability they are close friends increases.
1 Name
is randomly chosen.
4.2
Association Rules
Association rule learning is a popular method used in data mining in order to discover relations between attributes in datasets. Often utilized for market basket analysis the input dataset for association rule learning contains an item set of things a person has bought. A typical rule created out of a supermarket dataset could therefore be the following: If noodles and cheese are bought then the customer will also
-1
Probability friends of a user share cg percent of groups with the user
10
average overlap with all friends maximum overlap
-2
10
-14.4
f(o) = 0.011e -3
10
-4
10
(sport to brands to hangouts). A graph of rules illustrating these connections is shown in fig. 7. The colors indicate different networks where the nodes are groups with their corresponding id’s in our dataset. It is visible that most rules are between groups of the same topic (same color). For every topic there seems to be a few hubs standing for the largest groups in this particular topic that can be predicted by multiple Figure 7. Graph of associaother smaller groups. tion rules. Nodes are groups As association rule labeled by their group id’s. A learning seems to be link is drawn if a rule exist a good solution to obcontaining both groups. The tain global information links are labeled by the conabout group predictions fidence value of the rule. it is not an user-centric method. This means it is not possible to observe effects of the underlying topology of the friendship network. Therefore we calculated the “predictability” of a user using all rules. This predictability is defined by two values. One is the number of groups that can be inferred using all rules whereas the second is given by the average confidence of rules applied to all groups of a user. The latter gives insights in the “predictability” of this user. For every user we looked at all of his groups and calculated the average confidence of all rules that can be applied to its groups. Figure 8 depicts the predictability versus the fraction of predicted groups. A positive Pearson correlation can be found with a value of 0.537. 804
Brands Hangout Books Food Film Games Famous Media Music Others Travel Sport TV
54.4405
366
757
1329
671
8511
4441
2515 7214
755
50.3185
760
15942
1943
66.0366 6515
2485
1588
208
53.2931 63.5374 50.8848 65.7393 50.421 51.9334 54.391
55.3318 57.9372 56.882779.474 69.2469 61.5302 61.85952.3516 75.8847 55.1265 63.311 50.1241 58.0372 53.0582 13961 68.1167 71.1751
455
50.5253
52.1837
56.6164
460
51.4602 52.0696 105
-5
10
7617
58.8235
308677
4979
308100
3404
903 50.1705
7378521413 1414
8387
8889
52.1897 68.4464 57.9598 73.9833 69.7561
11109
52.7641
309573
304
52.2041
50.6272
61.8108 70.1148 54.9793
1502
1741
7356
69.4284
74.4017
60.803
52.9021
485
54.631
76.0581
901
415
259
56.3991
80.6117 62.1255 56.0125
3083 63.2841 61.8699
5227
54.1854
51.4684 57.2319 70.8705 64.1952
68.3005
58.4887 60.7494
3296
232
50.833
53.4291
7830
61.3982
271
0.0
0.2
0.4
0.6
0.8
1.0
50.2621
59.7929 55.1675
425
50.6323
2601
8970
35237
15358
55.3273
5061 77.3438 53.2639
63.3635 62.0813 50.4913 58.8645 54.683 52.8571
453858.7321 8735
75.0197 54.8251
50.6172
22023
8500
309845
5741
54.3645 51.0201
62.9971
68.3074
51.2168 50.59
815
52.2857
52.1565
1459
3607
52.2337
23350
18903
5504
65.0173
481
55.7573
50.3855
62.1456
53.9833586
480
58.7332
592 588 55.0978 58.9371 57.111 61.0896 63.1838 50.9467 54.8778 62.6287 63.1554 2579 55.8429
177464.3921 258
483
56.408
1415
67.0917
1660
57.523
63.8665
2580
27711
64.4743
4042
63.1991
62.9556
3332
51.2614
55.1902
71.0401
59.9688
81.834
63.0282
56.4382
66.3418
59.8769
61247
55.1402
50.5693 56.795
77.8147
4226
4043
5924
16412
62.2266
70.5139
77.6164 69.6988 82.1788 76.7065 86.2984
86.6168
637
1208
5211
64.6926
3334
54.7794
1083
414
51.9142
54.161
69.1866 59.5802
568
73.9234 53.2938 2718 70.4101 50.3453 73.082 62.4402 51.3796 75.311 62.3923 69.9114 51.5542 61.0526 75.4565 54.07351734 831 65.5423 52.9243 63.7799 56.5413 567 51.4835 74.2725 65.873 2719 54.2974 61.7703 56.4916 54.6889 62.8047 65.5024 51.0411 63.4921 68.8455 57.5832 52.3603 79.0675 59.3475 61.0287 54.5745 73.9893 896 70.3502 55.5881 53.8724 57.7629 63.0291 55.6386 65.6085 569 72.5359 58.7253 55.6061 73.8242 67.8426 57.7964 64.5172 51.7464 53.5136 50.933 53.8975 56.5044 64.146 72.5529 62.0714 60.9387 60.687854.3399 63.8486 566 66.5725 60.0412 51.9308 58.5317 53.5123 921 62.0705 51.4127 64.8495 54.728860.9569 52.5771 52.12770.7676 56.5934 55.286266.2496 57.1099 55.8961 64.268 71.2236 64.7487 64.4622 53.8278 1736 66.0316 65.0199 72.3178 74.0659 73.5968 52.0955 53.4526 58.2627 56.4507 57.1616 68.0863 55.0256 53.4866 64.2779 59.6081 899 54.5706 54.795 71.880564.344 53.8818 1706 50.1653 63.0892 68.209161.8917 58.5437 68.0559 68.7466 62.6309 64.3116 50.0449 51.1073 53.4923 57.0768 3265 62.2482 50.9569 55.6967 51.2287 173953.7195 62.2374 71.5735 51.6875 64.2258 59.5004 56.241364.562 52.177 61.0803 65.064 71.3936 53.6469 69.2788 53.0423 55.6174 62.4158 61.1601 54.496 75.3818 63.4123 51.1432 50.5716 57.3024 66.7943 64.2105 50.7098 51.5616 51.8519 52.3684 898 71.9491 57.9467 54.055552.1085 66.8284 57.9979 56.8202 55.0256 65.7777 64.7156 54.0675 57.693 52.1114 65.623 50.0725 63.7568 63.7321 66.964355.622 52.2948 58.0386 5816 173875.5624 50.942562.9376 4092 52.7577 63.4391 58.328 59.4651 55.4567 50.1905 62.3569 51.7095 64.6825 70.6349 53.3972 75.0965 62.8077 56.0371 69.4596 52.9256 288 60.9606 75.5989 173554.2134 62.9287 58.263860.3242 58.9176 70.9211 56.3509 62.3977 52.3137 50.3518 59.951666.0921 70.2159 53.1663 52.0555 53.2746 57.0029 1737 57.5051 55.8516 56.9434 50.4259 57.3797 52.2273 50.6709 51.7148 50.4827 56.2682 53.0948 54.1099 1707 10150 59.3533 73.0546 58.4051 51.5521 59.0909 53.293465.1522 57.4578 61.0449 60.9881 56.2748 54.326 52.1276 50.5334 66.2522 62.6091 60.3886 60.8421 1733 56.5868571 56.9563 58.4228 54.5046 55.8523 52.1587 61.8564 74.0653 74.6581 52.9996 51.6197 52.9182 713 51.8286 65.8139 66 51.817 62.0644 54.8855 52.3194 60.3772 51.7453 51.9431 54.5818 57.2128 51.4186 50.9611 50.0994 52.4725 60.8927 3792 56.1645 58.4588 67 56.1451 287 59.051550.5299 54.2348 54.902556.1516 58.1 6551.2058 54.2348 1705 897 50.7818 64.0515 57.698450.3566 50.3026 50.3369 55.5353 290 56.6004 565 53.765973.3148 53.933 56.555 56.4985 58.945 57.805 56.2422 51.731454.6392 70.8253 56.7128 71.984 66.8245 59.3666 67.2615 70.158 69.7757 61.5441 62.4363 50.6055 53.3534 52.3981 50.4365 52.8583 69.2932 65.9141 63.8497 65.2925 55.0659 65.8316 66.6412 67.3152 59.4199 60.9406 58.6595 62.8597 59.1127 5502 63.78953.98 58.3284 51.142 53.1198 1825 53.2891 52.866 52.1401 52.0151 58.6372 50.8578 61.6486 59.8524 51.1091 59.177 5817 57.3312 62.3959 63.8771 58.1295564 5797 53.8803 55.6934 56.0087 50.1663 54.0872 62.5728 3604 54.4704 67.5568 60.8311 62.0186 54.6667 57.7379 50.5349 57.2868 54.601 53.9813 56.96258.3873 53.7158 51.2168 60.0991 51.2424 51.8877 59.3233 55.0331 61.7177 54.8554 75.7207 73.5991 55.9636 68.4444 57.4645 59.18 1829 58.799 75.226 65.0516 59.4462 60.4824 70.8423 61.9107 51.6121 57.1864 53.3742 59.5091 56.4749 57.9738 50.7415 53.4134 56.800267.1775 55.0914 54.6654 59.2427 51.3827 51.3507 69.5287 51.6466 52.3641 55.652368.0262 4671 50.862 56.4457 60.1238 73.8533 52.9269 57.5562 52.5229 58.5353 59.8369 62.8673 52.7279 51.8816 51.1103 78.371 5822 50.6555 53.7821 1819 51.9746 76.1864 68.7065 51.4567 53.0387 50.3058 57.7886 71.2279 79.2914 55.3532 77.5234 51.3761 54.78 58.5366 58.624 50.7057 63.024 68.3032 52.9324 8962 53.5072 73.4712 77.1097 51.1232 829 69.9638 1827 51.1703 50.7597 3222 55.2137 52.3927 1273 79.3008 50.1498 70.2762 1828 53.882 74.9085 5703 50.5471 56.3249 54.7862 1768 56.7735 9645 52.2774 54.8165 791 65.4607 1090 57.9555 1732 56.905 2545 6671 177050.6295 11785
471
52.381
71.3114 62.6516114659.5935 71.1985
54.6043 57.6664
54.0185
5481
274
50.386
54.7161
58.6798
53.9851
422
61.1655
1704
7433
31047
1808
87.2574
51.1987
58.42
55.2076
5818
50.7084
1866
65.0847 54.0625
81.0692 80.8861 80.9227 70.6064 55.5776 66.2174 70.1329
1822
76.0762
830
63.1893 72.8946
280
58.5881 58.2561 72.9718
1830
291
570 102013498
2328
64.1344
52.8412
53.4444
50.8797
2140
52.8959
80.2967
60.2458
715
91.22 56.8111 50.9709 54.8062 54.8333 51.661 56.8216 52.9663 57.6238 1809 51.2864 58.499 56.6128 52.4942 90.761376.4906 84.8547 35706 52.0445 60.5993 58.9876 7746
2141
51.9915
4625 5087
65.4915
23776 61.5507
7888 75.1592
61.2887
22406
63.0747 78.7797
58.0339
4622
75.1155
82.73 68.3095
52.5403 58.8722 59.4723
629
76.1282
31835
11176 50.8925 54.0096 53.4785 9638 58.8333 54.1667 63.1737 2756 51.1447 9526 19164 50.823254.0021
54.0316 59.8316 59.3709
60.5764 59.4075 54.9327 59.5238 58.670259.3196 59.8254 59.209 26077 60.4997
58.8724
35235
1804
68.1553 24449 52.2033 19028 67.4077 65.0132
53.1432 66.4458
67.5665
13117
19659
14442
50.2482 51.3634
1807
7747
50.2256
3625
62.6037
1811
29254
1296
516
7560 65.2572 717 64.8916 51.3594 69.1601 63.5141 54.0592 2152 8736 57.1849 51.42 71.1057 60.8008 1184 56.8506 714 77.5669 61.1092 71.2889 30944 517 53.5328 78.6774 66.558 6888 80.0033 70.8504
1689
52.1746 1812 51.1405 53.7152 3335 54.7348 55.9618 61.0314 56.1106 50.2862 59.5745 54.2047 69.5882 55.0952 6720 19448 61.1142 53.9167 56.9524 66.9381 1802 59.3124 62.127 54.115 56.2082 61.5505 56.8896 51.2538 53.0126 51.3927 59.1587 69.3016 9639 55.799 63.7619 55.1614 55.7396 5954 52.0546 54.2885 61.2969 19658 19447 62.070356.8479 58.612 63.203658.2146 18653 54.9206 54.8258
1813
53.8706 52.2459 60.6777
51.9044
70.0447
3710
9637
631
13422
2142
13425
57.3514 59.2973 56.5854 31015 62.3171 56.7568 69.3937 4628 57.8378 69.4668 59.939 51.1146 60.6649 52.4324 62.1477 59.6951 65.3762 4627 52.5211 70.0671 53.4756 69.6129 67.5851 66.264 57.4837 59.7516 67.7289 8179 55.036869.6077 67.9344 71.5884 55.5329 75.4925 63.9117 67.5077 55.8389 77.8679 57.8549 65.4219 68.8951 671972.1992 76.5933 56.8357 72.836 62.734 13421 68.6559 4623 67.0816 74.1731 55.551 71.1618 72.1323 56.5378 52.8501 76.6252 66.2913 57.7303 55.1809
13423
13424
716
51.0373
8180
2290
50.7636
1260 2547 56.5757 3572 1468
518 2546
7094
56.5217 58.1098
7787
828
50.0391
272
3363
3367
5032
1105
64.5868
53.4253
51.2596
4672
1153 1824
1451
1823
627
4220
2433
55.5121
58.6181 74.307
82.3084 58.8292 69.0625 68.886 60.9134 78.885462.3913 50.781275.1499442862.041 62.9102 76.9299
1868
1805
5950
65.1562
19592 65.6584
54.798 53.5919 1869 59.1655
1826
964 5805 63.3599
1261
56.0594
53.8462
76.8363
1803
52.8821
1867
139
51.5436
53.135 51.343
51.4322 56.3361 54.7868 57.9549
6502
90052.8652
56.8413 63.0977
52.187560.2167
63.8281 54.8198
56.3184
1262
11615
53.8381
58.9827
51.311
76.1163
52.5781
1529
63.6587
3372
52.1618
55.0679
1806
53.7872
66.965 62.5772 66.0971 77.1452 66.8085 70.9091 632 57.4423 52.5441 7476 64.233 76.0831 62.6963 52.8308 51.0744 82.2605 75.0902 86.6634 74.2281 6504 50.9504 70.7758 72.5295 14935 72.9476 78.0284 74.8688 71.1983 81.6657 251 59.1322 74.0429 60.203478.9967 60.269 62.0197 59.2948 53.2876 55.5899 250 75.9843 51.7245 64.793 4780 61.0029 59.7446 63.754450.9407 59.6694 19394 71.3987 50.0 60.7407 64.0496 69.8055 252 77.4554 61.008 70.3807 66.304 54.5002 66.5702 57.7592 56.2066 71.6997 64.6117 50.3906 66.2581 59.334 50.5781 253 53.6581 60.5999 61.8728 57.5098 56.5641 64.7134 2327 64.2233 51.916 51.7224 1659 58.9301 56.6374 50.4729 53.7484 4937 53.9301 53.2269 633
2170
66.492
54.9906 53.1657
6374
50.0739 1817 2020
3501
55.1891 59.5064
53.2994
61.9803
16230
50.6238
50.224
58.2498 62.8014 52.1048 61.5235 51.3564
70.2962 54.3181 51.2697 1277 64.5869 60.6354 71.6239 57.2504 65.1916 64.6829 53.3142 51.9278 72.8815 95758.1151 73.4375 61.4761 64.1768 58.3784 128059.43941278 50.1834 59.2994 50.6063 61.9747 53.1276 56.5786 72.0632 62.2051 70.8118 51.761 69.2384 58.0015 80.3881 50.1251 66.78278.4332 58.6632 75.8507 58.0261 53.0049 52.957 62.632 69.4622 64.6372 79.7573 60.53 64.8955 60.3067 62.4118 69.2278 51.5953 59.9666 56.1259 74.4515 58.7242 57.2219 56.6557 57.3508 71.4762 57.7571 66.1912 66.9781 69.0575 59.1326 54.7432 51.6383 67.2744 50.2982 69.104 52.4889 62.2047 53.7634 50.3325 72.8082 62.9751 991 65.924 61.7741 76.2366 55.6201 50.1966 60.2478 475 51.2193 78.3284 2781 62.98 50.4727 50.059.9078 51.5745 67.2638 79.3412 61.1674 62.9763 54.5238 60.5165 60.1972 67.0559 63.7918 55.0163 59.2725 50.8609 51.1055 78.5655 73.6448 59.5496 2019 71.2988 55.5577 58.3499 66.7632 68.871 50.5534 69.7248 1275 57.2753 76.7381 74.7217 66.2219 57.204 56.6334 14680 55.1798 61.2713 51.8766 4659 72.0776 66.3827 52.8834 58.6481 70.128 53.9542 58.4444 58.4815 70.9423 61.4399 63.1336 75.3962 67.8955 630 68.4379 52.4166 55.2425 59.9078 59.601 52.6868 59.3765 52.5384 53.7442 70.8236 65.0542 51.0237 54.7076 58.508 54.1102 1555 58.679 53.6098 60.3837 50.2496 51.848 62.9751 67.7969 56.7706 72.8858 55.1187 62.2994 50.839 54.8162 60.1334 68.6763 5081 4256 67.1275 53.2679 57.3394 59.5636 52.1803 55.3327 57.11 58.1898 66.3099 60.7539 68.126 66.7133 66.05565.0542 58.987260.806 5092 64.8441 64.2202 58.8326 4660 51.6484 68.8244 59.726 51.1401 58.1618 53.8433 57.8022 65.6682 51.8766 59.3828 54.2439 69.2771 57.9948 50.4587 4539 58.4842 54.8058 59.05468.356461.1367 57.548 62.4575 55.8758 51.3761 56.3983 68.6636 54.4547 5095 50.55436540 50.384 61.7517 58.0192 51.1489 55.1249
12437
53.7698
54.332
344
64.352
572
68.7586
14835
58.2294 59.1184
73.261
1554
53.7016 53.0646 61.3553
50.8874 58.2649
57.7465
602
186484.1727
53.6805 57.9633 57.8308 55.9863
7688
4221
470
54.3532
4037
1528
88.1442
64.888
71.9041
63.5764 61.7685
57.638
51.8561
16875
53.1741
26989
17516
61.1655
84.9913 82.561 80.7999
51.8407 53.7523
6479
56.8201
50.2871
52.838
53.1613
81.8015
1865
52.9237
412
58.2956
469
869
51.0387
2513
80.1931
63.1579 75.7232
601
1687
20628
51.9071
71.5123
1694
50.6358
5041
4537
8759
1690
58.1075
55.6202 63.96 62.9457 69.4287 70.2181 56.0329 52.6109 51.2246 638
63.5921 1696 54.3478
51.764
50.841
60.0095 57.7356 56.4609 51.7258 61.1025 60.7919
1161
55.3675
8884
466
50.4086 52.1346 52.7084 244254.6097 69.7654 56.3084 73.5906 58.6111 72.553 1557 68.0261 60.3013 61.3295 72.4784 82.7351 2884 57.8313 56.1654 57.8915 74.3722 79.897356.023 61.3252 57.6419 56.3442 57.0526 68.9995 54.2734 51.6298 69.4343 2572 51.353351.5797 57.3592 49819 54.577561.435 67.651450.2029 62.4148 2573 34427 56.8182 50.18 71.7604 75.4461 67.6254 79.1076 57.0494 64.1177 69.8576 52.6168 65.0815 62.434 57.8579 59.236951.037 54.4958 3462 61.7671 60.3109 61.7261 79.934 68.3907 59.1194 73.9056 57.3447 1556 60.1767 60.5796 73.2104 54.8544 53.6097 56.0895 63.8908 69.6412 60.2133 53.0388 60.5028 75.1943 51.824 55.8313 75.6311 62.9855 467 67.1618 58.6604 1558 61.7557 53.9147 69.0693 55.6366 71.1684 51.7048 56.4576 55.3528 3520 54.6246 69.3374 474 80.0 63.5046 53.2435 51.8574 50.7242 56.605 57.7064 59.7916 58.0788 65.6359 56.8756 50.6576 52.9738 62.1993 73.9468 53.2236 62.8249 63.2619 62.1909 67.5915 50.515 52.6729 54.2204 72.040572.6089 54.0442 63.5933 4702 69.418 1559 51.2315 152662.3309 68.4052 61.6735 51.7125 57.2856 67.2002 58.6037 52.5298 50.094758.3933 55.9896 55.5196 53.2692 59.1715 60.11351103 53.6745 52.4826 65.3309 50.0728 73.7462 53.3491 53.0757
52.6099
52.7262 53.7123
71.6221
61.5006
53.1652
56.4516
59.038
55
62.065
67.045 343 83.3052 63.6329 53.5621 240 65.7387
70.2167
4704
51.7579
3994
8885
60.4823
8762
60.2419 67.2951
79.4492 80.4635
51.4197 51.9655
77.1796 54.4086 50.8916
35603562
1145
9802
11509
5951
59.7384
51.8908
52.919 53.5415
52.7843 2169 468
51.5395
57.5359 51.004 53.3394
473
51.2363
411
50.0
50.8357
55.6575 50.4305 52.5353 257 23059 59.1275 53.967 6254 50.6766 54.4779 60.5315 72.5116 837 51.9246 53.6082 57.2536 61.2094 52.2968 81.4653 50.1446 55.673 50.9413 58.2596 1777 55.3265 58.7523 2729 57.9956 52.5811 59.417 62.0725 58.361 1457 51.8377 50.3913 78.4187 54.9291 52.2324 56.0625 50.834 56.3239 55.4267 58.3812 52.9824 53.8931 58.6149 878 52.8548 50.3126 52.921 52.0619 51.9888 3580 55.1105 54.485 77.344252.7963 54.156
62.4159 55.2029
5952
53.2143 54.6132 1816 58.2123 60.833351.3966 51.2202 57.9254 57.6802 58.7176 51.9248 50.0548 64.134151.994 57.9888 50.1647 62.886 1815 55.0423 55.2744 10477 56.0276 54.9853 57.933 51.5495 56.9813 55.7556 60.2385 51.5548 62.4947 58.7716 54.2361 58.75612606 52.6643 58.3509 64.0093 873758.8704 56.0829 71.4767 5953 56.4808 9797
4920
3712
57.2758 55.1181
279
56.2743
2483
50.6084
52.9824
4426
68.7439
51.4773 52.5736 50.1131 50.788 917 50.3911
7440
3561
56.4193 51.5469 60.0412 70.6419 4095 62.2215
55.338970.239 57.7842 51.0447
51.40478887 888852.4038 52.6683 8886
54.848
71.9293
59.0971
308097
52.583 53.3675 51.4528 55.5048 58.8977 247 59.7724 54.038 53.5249 53.7599 916 1008 51.502 52.3181 51.9155 71.899154.7727 52.9471 50.1292 51.4567 52.65 62.5822 339 60.8455 60.9826 59.3118 58.7512 71.5575 52.0137 62.1512 50.0625 341 72.5502 53.8043 77.2281 52.8938 59.6592 76.9125 76.0735 63.7472 53.8098 51.695 69.2933 51.8234 2936 50.7663 421 51.273 54.6622 62.036 50.1415 1889 71.7694 77.5123 5278 72.3331 71.2398 335 55.1033 51.8895 60.0603 67.392 64.327 61.3603 60.5957 63.7947 53.0456 873 63.844 55.1111 55.1178 64.9483 50.2038 59.1587 50.878 59.5393 55.588 56.0844 55.2732 64.9519 54.4723 50.962 81.2035 51.7781 65.6306 78.011259.7925 75.2376 77.0435 52.3067 80.2682 59.0012 80.0888 57.8759 59.3448 1890 51.111255.1619 57.395664.3288 51.7594 65.3118 69.1886 70 59.165 61.1094 59.3812 77.431 54.1933 57.8802 61.9385 68.3726 245 50.241152.2466 62.2385 54.6952 57.3444 68.1731 64.0564 60.8724 86251.7903 56.8833 56.2025 51.1762 57.2371 59.0628 50.207 55.2633 55.7591 7004 71.0044 70.1462 67.760870.8329 54.2287 56.9044 57.9861 62.2969 57.0632 51.0772 51.6044 54.696851.9462 50.2032 50.542 60.0777 58.2612 60.7351 53.2699 69.0711 51.8288 56.1132 51.485 51.4215 58.011 57.063 66.166 56.2093 56.2092 54.8925 53.0407 52.1327 60.6057 52.274556.982755.7947 80.381454.6967 71.4661 51.7642 634 64.3553 1112 62.1656 52.9204 60.836 338 60.9309 61.7595 70.1805 77.3755 56.1684 87.0569 61.9589 61.7635 52.1068 72.8755 54.2414 241 51.4341 58.6564 54.6316 60.3667 52.5902 56.3198 70.13 51.0829 51.7943 54.2103 66.0206 63.5866 56.6759 50.6758 56.2124 59.6514 53.6195 58.7177 53.4983 57.2768 57.0087 64.2885 56.1304 57.0426 54.896 8712 57.3687 55.5491 69.6118 61.8019 67.3637 60.7012 59.9848 55.1313 57.5993 51.8345 72.4978 54.83859.0584 72.2428 872 62.9644 61.4025 70.5864 52.6272 65.5005 55.5521 1881 61.5897 52.877 52.6698 51.7299 65.2912 51.6323 63.3858 54.9046 50.4332 58.4241 55.1248 50.5585 58.8164 50.2598 55.8261 56.2233 68.648 84.1915 54.8336 52.9609 63.209468.6042 54.0026 55.0455 55.9102 336 55.1287 61.805860.3969 59.714 58.5248 50.0415 51.5954 52.3638 58.0325 51.2045 60.7533 66.5123 65.388 55.059 58.136 60.0282 52.0205 51.968451.1816 55.462865.3926 636 57.0383 51.4923 64.0799 52.9861 78.5913 50.0037 66.6538 65.7905 60.2458 60.1254 76.9747 62.8283 54.1928 74.1977246 54.378 62.4893 69 56.3494 55.3835 57.3935 60.8121 67.1963 50.0067 54.5703 54.6077 54.1841 50.1799 64.3281 66.2906 59.4433 62.5831 56.1175 1530 51.9433 55.0205 64.7001 52.3932 60.5804 59.7615 53.5574 50.1848 72.0896 60.8144 61.8361 55.4155 50.557 50.2519 53.5873 60.9185 51.7415 69.0694 63.173 58.131 59.1778 56.0905 242 67.4079 13831 65.8203 51.5478 69.186 55.8044 67.5075 56.7441 2853 1417 58.4469 56.1991 56.3016 55.1898 55.6468 51.3374 56.9205 55.4672 58.464 51.36 51.8922 53.1108 52.6869 57.3102 60.8443 53.2796 50.8622 51.4329 55.813 77.992 54.2399 70.3227 82.554 50.6324 57.6892 64.2581 51.3726 66.136 53.3752 58.1624 55.629 53.2548 52.6001 50.5642 69.463 57.315666.0223 61.8577 50.208 56.7391 52.284 57.7697 58.7276 635 54.9977 5507 248 51.5343 50.615669.2248 51.3785 59.2318 55.8679 72.295 54.5257 65.3643 54.2479 52.0824 68.4721 50.0 64.7991 60.2055 50.5743 70.551 50.1449 50.5883 57.0254 61.8771 60.5424 51.8259 57.7053 547 50.8349 52.7583 53.2633 53.8034 1763 56.4981 51.783 77.3171 53.5625 55.2019 53.2245 58.2174 67.5999 21408 8711 50.7364 1181 64.7336 64.9792 67.3213 60.9029 53.49252.022 51.5656 66.9455 57.816 56.3346141 53.773 57.8261 52.0716 59.0126 56.3565 55.3365 60.7106 54.9094 52.548 57.2145 61.897 66.6279 54.2808 50.597 55.0946 251152.2093 51.7877 50.5606 51.9545 55.2738 53.4977 63.7276 337 53.9717 55.6011 55.9289 51.8414 50.6562 51.2287 55.8164 2576 65.5916 7003 50.5599 54.5748 62.2007 59.5849 66.3598 61.1137 56.9547 57.8889 51.1978 50.3373 55.7907 60.6345 65.0323 50.3318 70.0465 59.992 52.3451 57.9867 55.1214 53.4318 52.6636 52.4899 54.5049 65.4173 56.9938 423 59.254352.4736 50.6083 51.0627 61.2846 52.8195 66.615 62.2388 60.1733 54.8819 60.5946 140 56.4281 53.8818 64.3627 68.4924 52.5414 51.6151 1160 52.5803 65.5256 62.4799 59.0735 8709 55.9318 51.2836 54.9376 57.4031 50.9554 50.6951 52.1697 69.2666 52.1252 1418 58.0277 74.9075 62.3079 63.1783 61.3178 55.6376 53.0579 70.4947 55.8158 57.7907 14837 55.9692 52.5161 56.099351.3749 52.7287 51.0962 334 55.1418 52.3981 74.631156.3362 51.0408 61.935550.3595 51.248 61.5414 1110 50.4639 55.957 50.6955 5776 53.8925 2657 8795 61.1878 63.234 56.4949 53.9653 55.8498 2656 54.3023 50.6182 62.0993 56.8671 55.6523 76.0293 67.5474 60.8527 69.8566 50.6927 50.0443 66.2229 54.3944 11567 50.6545 63.4906 7006 57.6744 64.7282 54.9209 62.7029 53.3763 1111 83.616752.9433 59.3236 62.8425 1182 50.780158.8623 51.3426 50.9071 56.938 74.4807 9947 64.0039 12073 57.7204 54.0821 63.59 16461 56.167 55.6855 4443 8796 60.2201 127184.5054 59.358 53.9244 82.2377 58.9514 53.5054 51.8217 51.1828 342 61.7477 53.5682 81.1437 76.5391 50.7342 75.0329 73.9533 66.1848 52.3451 13552 53.4919 50.5301 81.9392 53.9995 66.0389 50.8946 51.699190.1082 77.7235 76.2985 56.9552 4084 69.4183 62.237 50.3561 1318 282 73.8577 54.5726 51.0064 53.0454 51.3082 50.0113 53.682254.2048 51.2681 59.1936 57.5937 13832 51.882 53.0323 90.2628 80.5824 53.1376 51.66157005 68.3975 76.0519 71.9026 142 69.1446 52.2581 58.7597 62.2488 71.5653 50.9731 72.83 68.7386 53.5785 50.3091 52.1537 61.181 50.0738 50.1938 90.1468 57.4724 67.0415 61.7959 60.8602 73.1789 59.2508 283 13830 50.634456.3178 56.9767 52.3871 51.0256 875 52.0178 74.269 51.0078 55.1163 61.75823709 59.3978 68.629 50.0 24356.9032 51.3178 1697 62.1529 58.5376 340 51.619 58.4086 55.0538 1493756.0078 244 77.5618 50.440953.0267 281 61.8265 53.8495 54.0645 50.657 78.295 53.164 73.2413 57.4319 2512 333 83.8339
62.6422
54.8442 52.1345 58.2982
55.8872
13427
55.6701
11568
54.1284 60.2205 67.4689
36940
53.0105
427
50.3157 54.3649 51.22650.1463
51.2608
54.6079
56
50.6952
50.2085 52.613 50.2638
4044
58.3297
56.4089 70.1122 58.1725
8062
1106
13150
69.6507 51.9246 65.0399 67.4739
84.7345
53.741977.5811
8185
61.0423 61.1044 8495 60.48760.598 54.3886 50.8398 60.5239 67.4236 56.2208 61.5581 17312 56.1028 50.3197 52.4562 54.8154 17313 60.5179 63.5659 51.4844 59.2391 50.0468 62.015566.3446 50.6672 63.0774 11707
450
11514
308791
59.3944 10478 50.0065 50.9398
66.6954 67.933
413
77.1685 51.5458
5175
70.4393 62.9904
600
308637 309430
1148
9409
70.9204
13853
56.3978
55.3884
84.0862
54.2969 56.6884
4427
53.6232 61.3468
273
83.1865
54.3435
51.9088
65.3977
51.1846
62.9976
1104
16700 57.0569 54.7096
2114
57.1429
3366
42533
52.1193
3374
100 Average confidence of applied rules
buy bolognese sauce with a confidence of α percent where all products appear in β percent (support) of all purchases. The confidence α corresponds to the fraction of the support of all items in the rule to the support of the requisites. The naive way of calculating simple co-occurrences would result in a very large co-occurrence matrix because of ca. 1.1 million groups in our dataset. Given the groups of all users as input, association rule learning will still calculate rules in a reasonable time, for a given minimum support and confidence. We used an implementation called apriori [4] to calculate association rules with a given minimum support of 0.1% and a minimum confidence of 50%. The exact number of groups in our dataset was 1115558. The support of 0.1% means that 1116 user profiles should list a group in order to include the group in the rule. The calculated rules had a maximum length of 4 resulting that at most 3 groups lead to a consequence. Longer rules are clear subsets of shorter ones having a higher confidence but smaller support. An example for such a rule is the following. We found that users that are interested in the soccer club “Ajax Amsterdam” are also interested in the “Amsterdam Arena” with a support of 0.203% and a confidence of 58%. But if a user is interested in “Ajax Amsterdam” and “Adidas” he is more likely to be interested in the “Amsterdam Arena” with a confidence if 83% but the rule has a support of only 0.113%. Because it is possible to set the privacy settings for groups to only show groups out of selected topics, association rules learning helps to infer others. By knowing only a few groups of a user it is possible to directly apply a rule with a high confidence to infer other groups of the user. The same holds for the earlier mentioned age prediction as shown in figure 5 based on different groups. For example the probability to be 11 years old if a user likes the movie “Finding Nemo” is 70%. If we know that the user additionally likes “Happy Feet” this probability increases to 87% as the rule gets more specific. Interestingly the given example of soccer fans already depicts that group predictions work across different topics
74.7471 440
54.1254
11089
54.7647
50.0637
52.6469
Figure 6. The percentage to which extend lists of groups between friends are similar. Red, the average overlap between all friends of a user. Blue, the maximal overlap with at least one of the friends.
64.3856
50.0444 53.7426
16006
55.5172 1692 1693
14145
Predictability of a users groups based on the groups of all friends cg
72.8737
63.9099
54.7369
442
23820
59.049
52.4011
70.7525 57.0496 54.2646 67.4461
50.0023 61.5554
57.4702 50.7888
60.1676
434
50.4853 74.7913
58.0742
955
834
61.4827 56.2909 366658.3084 60.3022 55.0432 3665
51.2233
52.4945 52.2417
72.629 66.8707
51.099
54.661 426 70.1111
59.9641 54.558780.7901 67.3967 51.1466 50.3258 61.3291 52.3331 56.8665 54.1646 51.1346 54.1346 58.3365 58.1866 5176 53.100861.0817 63.7905 55.7054 53.3774 59.7843 84.4511 67.3604 60.8704 1875 56.5785 57.9276 64.614759.2193 1609 82.2968 54.7744 66.6334 58.7486 57.7572 56.7797 53.7057 63.1381 8753 59.9235 81.6006 83.1524 51.8204 55.2328 52.5725 51.0517 64.5185 66.2014 50.2534 71.1502 58.0481 6859 428 88.3467 59.159 58.8529 75.0353 53962.0712 55.6994 10603 2599 54.1262 55.6733 51.3611 55.605553.0128 55.9925 53.1289 54.5636 64.6487 55.9011 57.4726 53.1527 85.439385.7554 432 53.9876 67.2401 53.9153 62.3054 56.0581 57.4825 57.2917 66.7125 53.9651 57.7367 70.226 58.4208 83.5752 55.8654 55.4725 50.2061 77.9764 60.2588 3711 57.8428 62.0169 59.442661.7856 56.9275 50.1055 58.2544 55.6731 61.2009 445 70.666283.4072 64.43 52.2596 51.3796 50.2298 50.6422 53.0288 62.4283 441 58.6664 67.4596 69.066470.5583 58.5512 62.3523 59.800564.38966.4099 55.1136 60.1078 50.9615 7179 44765.8814 56.4343 50.6779 55.782 51.0393 51.25 53.2558 51.9015
446
295
284
291470 57.9802 52.8259 309763 311863
3810
57.2846 50.8116 53.3083
345
57.6771 65.6954 53.8325 51.6962 51.8772 63.7645 60.4978 51.9328 1107 52.9615 832 54.351251.8067 74.2858 585 55.9013 51.8303 54.9445 3579 54.3057 58.6014 53.7922 51.692 59.9807 55.4997 54.3194 53.939 52.3232 75.7349 72.5089 53.3426 50.0713 63.166 58.848 53.5372 52.5308 53.5078 52.3059 51.352 53.5009 1082 50.3101 541 814 64.7068 57.8979 68.5332 590 53.5614 57.824 52.8152.7298 61.503261.5426 51.0926 3790 58.1621 70.7174 52.2648 51.7251 51.0853 70.075 53.67 54.5605 72.5554 50.1696 50.0447 59.6744 55.4358 66.8461 73.795 66.2198 56.5544 73.651756.2826 1394 53.6355 53.0748 62.3662 59 51.926 918 2022 51.0516 50.612752.3679 542 58.6964 65.8038 68.3081 63.5809 67.2801 53.7955 60.9787 51.2834 66.362 57.2264 71.3515 50.3876 60.2199 56.0604 237 50.8208 58.7207 51.2967 56.6086 54.3183 50.9279 63.8159 76.8289 75.3007 50.2473 54.0354 78051.1934 82.0046 52.0888 63.2967 56.8758 68.4601 61.4239 59.7681 19194 52.6193 54.0439 57.5939 50.4532 56.6379 67.8977 66.1014 52.176 62.2387 58.4399 91953.4197 66.1653 63.2364 63.5457 584 56.2103 59.6222 50.4514 50.0 50.1212 69.7709 2023 50.7958 77.2698 65.7233 61 72.0868 80.4391 65.4391 62.8972 52.7887 52.8242 55.0668 54.2088 3300 55.9633 56.4948 53.00697432 63.7671 58.07460.9786 51.6586 51.3017 64.773 57.6706 2392 33738 56.8164 53.3038 63.2311 57.4409 51.1552 52.6461 57.9443 51.3789 920 23347 50.14 57.7874 55.75651.5908 52.4159 52.0901 68.2149 64.4446 53.8206 62.8866 60.0545 58 52.507669.3897 63.4182 58.306 51.8276 62.60853.749 56.9375 77.588150.2271 55.5556 65.5455 70.721 51.89 51.3975 57.7447 51.6427 50.7853 51.9731 50.6435 60.1893 57.502 55.9653 50.1231 589 50.7226 62.7028 2688 58.0734 1691 18333 64.453750.41 1204 2659 50.6699 76.5443 58.8399 4705 541152.6212 55.7401 52.3959 51.249 82.3421 51.0327
1990
59.3749 61.515
429
51.1497
70.6448 56.9221
626
1144
74.0619 55.8414
60.4346
54.1401
52.1839
17134
13010
57
55.530965.276
52.8926
4999
50.0
12572 54471.6138 50.2836
1870 5412 1196 60.29262.5296 500055.5571
52.1429 52.1091
275 59.7907 51950 61.9315 52.7155 56.2232 66.4237 50.1676 53.0289 51.3795 1986 54.0864 55.1264 5174 50.9912 50.7903 59.7043 5956 1814 67.9183 51.9411 55.2679 2917 58.3084 51.4521 57.5597 58.1093 65.4914 58.6946 77.3174 69.906 59.5472 58.9336 54.7384 55.2499 57.8771 56.5641 58.5557 67.6647 54.9887 56.7179 67.4535 60.9578 57.2049 71.8646 64.3382 57.6353 57.8928 67.9943 8755 56.8486 64.0116 52.281 68.5757 2608 70.4043 51.5379 51.3878 68.5885 56.6285 66.891 72.7894 70.3159 63.0908 53.2947 50.9051 64.7638 61.1988 73.0122 52.0237 77.8454
6730 10592
51.5288
436
52.1918
58.4357
6493
54.1889
86.5419
3295
54.1036 66.0039 53.9168 3301
782
63.7833
56.2676 70.4369 61.9359 65.4908
543
64.3916
833
540
5410
8217 51.9685 50.8062
50.04252.1005 52.4937 60.4495 53.0598 53.2661 51.8849 50.9233 50.3721 58.0808 50.3998 52.6838 67.6729 53.0773
835 54.8311
587
58.7559 1764 52.2594 50.2503 54.6464
60
19446
628
2919
72.1682
68.454
52.6222 60.8756 65.0424 65.4107 51.4537
6041
57.9741
1010
482
1458
8754
51.526
60.1567
51.0486
291471 73.728875.0565 64.9778 309286
8074
593
2481 57.5651
2720
52.5464
60.8089
55.7914
591
4928
10604
52.2277
71.0222 72.6285
55.3543
50.7572
54.5838 58.8112
520
52.7749
51.6964
51.6361
577
53.3716
50.026
451
788
53.4301
2117
781
519
52.7895 51.5574 50.0179
5409
5632
53.6944 52.4329 56.5973 68.9845 58.0944 65.6868
3624
1199
8211
58.6819
17948 69.7363 15698 73.978 65.3296 53.05319245
7646
10741
50.1559
53.4
779
778
54.1418
50.0687
1213
55.0035 52.9661 51.9216
64.4745
59.1081
50.8847 54.4847 74.4772
574
576
59.4876 59.8793
3299
1023
743
3147
69.7085
56.1538 55.9439 55.8805
68.8791 66.9976 66.7491
12312
297
52.0627
1665
73.2656
75.6619
6723
60.4225
239
478
58.5403
479 58.9898
4479
52.4463 65.1566
68.3341 52.4807 52.2457 51.2253 59.2006 61.1174 52.8797 52.4367 72.7134
296
328
877
78.1588
4089 58.0327 575
67.4821
52.2076
14330
56.0584
1324
6001
231
1644
77.8916
264
73.2283
309740
4703
55.1417
52.8291
62.5277 56.47
7002
53.8144
310554
50.0598
2544
5408
-6
10
50.9992 57.4681 51.5403
1390
2330
57.528 70.2877
309288
70.634
101
78.131 55.321
54.6095
11525
53.593
1431
79.9011 75.7798 78.7402
81.9199 64.3479 51.2402
58.9711
416
51.4387
70.4365
53.4219 51.1514 308098 64.9985
476
310450
55.7089
53.9052 57.6484 50.5055 83.1429 75.3626 84.3956 80.0371 71.6706 81.4403 81.810472.565 82.3371 72.7912 68.5332 66.748 74.878 71.7363 59.3858 71.011 66.637469.187 68.5121 64.7074 60.2595 52.6192 57.4393 66.2008 54.8019 58.224
308099
5796
52.7108 55.8646
1937
4956
6666
51.4704
71.7347 55.711 60.8351 52.9742 87.1301
58.601455.6756 59.8519 76.0294 486 59.3496 60.0444 30808683.3302 78.7332 285 84.0314 546 73.170753.721 77.3984 64.5138 87.59863.382 65.7764 86.4814 62.8455 69.7569 83.2603 68.871751.4085 72.8455 55.0063 70.5691 75.5285 66.764859.8512 69.4613 68.377 53.4952 63.532659.8388 52.8411 52.8634 260 74.2019 68.9314 65.3123 50.7654 56.9214 1599469.9187 75.6911 51.9008 58.9657 74.3089 67.9675 8388 60.3252 64.4319 56.8309 51.756470.7858 308096 71.0208 308085 23785 55.3727 55.0322
57.9213 57.6897
1776
639
55.563459.187 52.2183 57.1127
56.2676 51.1972
1958
74.0619
58.6293 1560
54.9072
1141
53.232 86.103 80.3592 84.4492 63.1315 51.5658 58.2463 86.461472.538 85.429477.3273 87.0406 73.0037 67.3725 52.0325 86.4797 52.6931 65.6996 614 60.0614 60.882 69.7219 63.5369 52.3701 69.6679 55.6935 57.1497 55.746 78.3451 52.6494 51.3821 54.398655.1292 54.4354 50.9295
55.2465
63.0045
54.9105
3151
92.0374
26587
615
25080
2155
52.9241
1177
55.2652 50.0939 62.436 461 60.8553
965
44
71.2123 75.9229 51.1614 56.4013 77.1546 55.8106 463 221 52.9136 73.6217 27 50.177 54.0701 61.5279 1795 52.007260.4057 57.442566.7625 4 54.3912 456 51.747 51.3975 761 69.755 756 68.647262.117 53.4473 54.9849 63.4008 51.0565 71.3845 948 59.8717 66.9626 52.9241 52.5033 56.6103 68.9013 56.4312 57.1654 930 53.4285 54.4056 54.8522 50.1846 1051 555 55.8852 58.9716 53.1065 190 51.61 68.9888 63.2951 64.486 58.4221 50.1521 63.4802 58.7935 93 401 64.7593 912 66.9367 82 50.3141 50.8127 102 457 58.6397 50.6135 58.0076 53.7438 68.4339 67.96 52.2018 61.6367 65.059163.1781 2856 8 462 50.7853 70.7099 670 55.698650.553963.1339 58.200151.4916 74.021 358 60.2453 50.0119 67.5417 785 50.7346 55.6936 59.0089 62.0878 65.18 88 66.5526 50.2637 51.7321 50.8616 52.8714 51.4763 50.2005 53.1772 50.8212 55.141 57.4775 57.0509 796 62.9779 51.0999 61.1388 58.3381 53.5747 640 58.2242 57.232 51.7303 50.1103 51.5234 56.3821 784 53.6947 65.8065 50.5395 50.471 50.1979 52.6656 51.6991 1092 53.3805 54.8829 58.8669 57.5945 62.123 53.1453 51.1939 51.6678 55.428 60.4837 52.1255 56.6954 51.5754 459 58.1852 94 50.1451 55.1941 57.1818 51.5754 55.285250.4198 50.0517 57.21 58.309 96 59.3026 225 51.4226 526 53.216 50.5485 51.4418 52.3047 52.7213 55.1364 51.3759 50.9999 52.4821 61.2572 57.6897 52.2381 50.131 737504 59.8905 50.848750.1897 53.1125 464 58.1966 55.0596 929 55.9699 58.1528 53.1602 558 52.1589 50.3223 53.1419 56.0475 26 54.17 50.1896 62.266755.9764 51.8935 738755 60.2693 55.6776 50.0499 52.3492 50.7781 60.4945 55.3985 56.9388 54.1317 54.5901 55.4011 60.8869 54.2675 1050 57.7406 60.0489 57.1949 42 58.1407402 57.3537 758 50.1162 53759.9115 54.4455 352 56.7018 60.4065 50.430657.5342 52.3241 54.5234 52.3497 53.0356 56.0206 56.6793 58.275 100 52.2031 52.9525 69.7412 54.7521 56.7749 52.3856 57.8773 52.9789 57.6095 54.1123 50.994952.8265 53.353855.757 693 62.9513 55.0412 57.6431 60.0088 51.1842 59.3677 56.1814 59.2576 60.0718 2496 196 55.0205 50.2213 56.4827 50.1141 50.270551.9248 58.1087 54.7264 66.5872 4153 364 53.7393 55.6807 50.9643 458 53.9574 64.03 55.1922 50.6416 51.5538 404 53.506 25 55.6783 50.2738 53.8121 53.8121 50.7969 50.0246 54.3532 57.2516 55.2878 51.2056 52.6294 58.4665 50.5719 51.9178 50.468 54.6178 52.1908 54.9946 53.0907 52.9403 53.4688 20156.7233 68.7823299 50.0616 50.9592 51.2937 50.5268 60.7477 68.814952.7712 54.2683 53.6119 53.9408 66.109251.7037 6 50.106 50.9426 56.347 4047 63.223560.9062 55.1349 57.2921 54.0811 60.5029 52.9789 50.8716 56.4737 50.277 59.6125 55.035752.065 50.5958 51.4049 50.5412 52.589 3576 51.345558.107 51.5785 68.4145 69.8083 52.2906 54.1759 50.7781 53.7946 15422 529 59.0809 53.3532 57.3045 63.7413 61.4876 55.1706 59.0809 8993 58.6289 95 52.4066 51.8713 74154.1761 63.6006 51.1067 53.4434 62.9893 54.2233 51.6616 50.0174 55.9891 52.4041 50.2486 55.9798 55.277857.4397 63.9101 52.0165 57.5531 67.2332 63.7608 55.0966 55.2878 60.1082 50.4278 51.2525 53.8274 1759 3326 1037 55.0081 56.3543 60.5509 59.8893 51.3931 56.496 35 56.1338 66.9194 59.7437 60.4992 63.3546 795 58.1246 3534 57.0873 54.6898 301 53.7629 51.6161 67.4974 56.0037 53.4348 50.0805 60.1265 50.7463 59.3741 55.8106 55.7445 59.4899 51.4677 62.82 71.4963 504 54.3533 53.702954.070951.7115 53.1202 51.4034 51.896 52.2822 50.57 68.0383 63.1474 52.192 56.0475 50.4125 57.2638 744 1760.981 64.6559 56.267652.3533 50.0246 51.6451.795456.124 50.0422 57.2678 53.1548 1263 54.9197 56.9161 54.3967 64.043 58.7013 53.6456 53.7629 63.7482 211 52.1514 57.7585 67.1294 55.043 55.0412 58.618 55.87850.8305 51.0041 75950.8128 51.2714 59.8596 911 62.7816 52.4503 55.7319 57.316656.3256 59.763 54.5993 64.5626 87 50.7371 53.1836 62.2263 51.005 50.9356 53.8669 530 59.1829 58.9669 50.3749 53.8625 32 60.053 51.8053 61.4814 54.7044 347 59.7325 65.1274 56.3699 92 1948 51.6405 52.4666 55.5674 52.2559 50.6674 69.3277 76.7123 50.7303 60.6156 50.1242 50.1952 527 2235 97 52.7319 55.8214 53.5662 50.0624 57.7281 58.01 60.8189 52.577856.025654.9151 66.1869 51.554660.698554.464 57.7023 83 50.5784 59.8052 50.6889 62.0408 74.159 52.6303 33054.231253.8407 63.2068 53.2473 55.075 69.2459 64.6818 52.5115 59.4776 64.2805 62.4448 50.0194 1987 51.9287 55.667 65.1746 71.9591 55.5573 50.3423 53.9498 54.2658 64.5638 50.5705 57.2287 51.4608 50.7983 56.9186 50.293 54.1744 60.4335 2264 53.9374 50.4673 50.0664 58.9308 66.1104 58.7053 53.0314 54.966559.4807 51.629 63.0839 62.1478 3016 62.9991 58.1407 58.2362 60.7673 417654.3227 51.7182 50.4673 63.7035 1603 54.9313 52.2381 62.7796 71.392 55.2246 31 57.3798 50.2571 680 60.555761.4085 2239 69.5631 72.1444 51.5315 64.7468 55.085 66.0319 51.6203 50.8444 51.6847 55.2739 66.3458 37 50.3666 52.0901 51.2968 66.7978 52.5588 57.0329 58.1109 59.5618 51.0945 68.8703 58.8157 58.34965.6932 57.4403 59.3698 348 768 65.9557 55.3993 57.4305 59.384934 55.26 54.5007 50.8049 53.517 52.8502 50.3326 50.4175 59.543 51.2154 51.0384 64.7571 56.9407 53.8512 267 64.9973 56.665 64.0086 63.1258 52.0952 51.7267 51.0355 56.8626 6939 62.6894 65.948 61.303 52.4077 65.1884 60.1817 56.0144 60.9227 61.9682 69.6451 60.9756 8471 55.8851 50.9105 71.1219 69.9514 58.0533 67.2277 54.3433 55.3733 52.7387 51.7801 50.0283 64.061477.8536 51.9248 51.4511 55.5764 50.3121 52.0929 55.5093 54.0849 54.4957 51.4058 66.6667 50.0458 51.0261 63.271863.6795 55.8067 56.1962 52.4525 60.4545 1535 61.7284 54.0433 57.4041 58.148 72.002 71.269 63.3959 59.0997 61.7394 66.1814 59.8012 1265 1115 51.6359 60.1186 58.5923 58.6329 58.9009 57.5342 50.4181 50.2481266 64.9441 50.2721 62.684 56.5621 61.9705 66.4452 51.9921 57.3295 52.9267 57.7472 65.0636 56.558556.4746 59.7656 61.616 59.4286 50.773 53.37 56.523 63.0943 56.3864 63.334 52.3597 62.6986 58.7841 64.5799 6414 55.6829 51.7401 52.0607 66.6436 71.463769.4405 54.2643 53.4124 52.3685 65.5678 51.8015 60.5888 70.6156 54.0557 51.4236 74.7054 50.2169 57.9474 59.4909 59.5392 56.5761 62.1033 52.1884 54.6539 51.4332 63.6932 54.0312 68.9531 54.4131 57.7878 69.6786 62.9213 71.6235 53.1592 62.0502 71.4514 50.1457 50.717659.4344 62.484 57.3482 62.9409 765 65.7549 767 56.7877 53.2385 55.810956.1109 69.7623 65.5725 52.6022 59.1267 51.5194 62.8475 1427 65.1254 61.7697 89 51.3151 370 51.5217 54.4625 53.8403 63.6503 67.8225 57.2869 54.956 57.9652 54.0344 50.664 71.0361 53.334 65.3142 69.4888 60.0158 51.3482 62.0567 60.846 61.6822 83.4153 62.4744 53.8604 57.742651.9996 56.5486 55.9925 53.3084 73.4524 61.714 63.9206 50.4687 66.0379 58.0869 59.9403 61.8965 50.8879 56.2599 62.1914 56.0599 59.8509 58.7296 61.7285 60.4065 66.3653 55.6424 52.3448 60.7952 56.1157 57.3021 50.6624 53.9374 140953.3653 40 62.2502 74.9429 74.2745 53.7818 62.8833 55.3137 51.1182 63.009256.098 50.9789 1521 57.3102 1389 50.6407 60.6804 51.0084 57.6369 61.4363 53.380270.3704 50.7624 493 51.5749 62.3414 53.3537 58.9769 54.6134 51.9284 52.663756.8835 53.6736 70.5954 58.8394 220 61.4037 55.1186 55.9739 56.1636 56.0717 61.1365 65.3222 53.3745 55.5556 63.7003 53.0765 51.8718 54.3894 61.5347 70.1587 69.3981 61.407356.3359 67.2277 50.8322 51.8332 52.151 50.0993 56.2401 66.2583 52.999451.4191 60.3611 54.1576 56.4725 60.7749 50.3979 58.2605 58.7606 63.8521 53.7933 57.8805 69.8918 71.1091 60.2435 64.7523 58.6107 60.1729 61.9282 52.3259 70.0295 54.3968 58.3076 80 53.5315 57.3129 54.8135 62.9069 58.9542 56.783 57.7801 54.7208 50.9919 51.4997 61.1378 64.3529 50.8652 57.3799 65.6133 55.6988 52.108 68.3719 52.1425 56.7388 59.6374 65.0444 63.5022 50.7874 55.2699 51.9898 58.5828 54.8288 50.4433 51.7478 1393 50.0913 69.5793 58.0766 641 50.2511 64269.2765 77.4449 55.4429 72.2729 52.1071 2963.6261 51.1974 36 52.1416 54.8178 43 50.1942 64.1359 56.1888 53.2316 66.3942 50.3149 61.3449 52.8781 50.0144 54.7809 52.5824 51.0954 62.9089 3102 62.9165 56.2395 56.4713 51.1141 56.1637 54.9716 57.4623 57.618 58.2969 68.9307 51.5986 59.8453 58.9569 60.618 53.1762 64.3419 56.6568 50.6761 54.0477 57.2309 50.5477 67.0438 55.7249 57.4693 55.8631 56.3284 56.5264 50.1825 58.3845 51.5646 61.837 65.6732 51.9252 51.2814 52.3289 71.5998 56.4191 52.037 60.4069 55.878 63.1141 61.4471 1461 50.0457 59.0456 50.520252.809 60.9642 52.3962 55.9272 64.6574 59.3323 279022 51.8759 51.5738 60.9689 51.4728 57.6072 64.0156 59.9348 51.5974 66.552 66.3199 55.0708 63.1918 53.2621 65.8603 59.7005 56.3382 56.2098 52.9333 56.6748 54.0294 19955.7441 71.3065 75.2358 50.5854 559 51.5115 50.5846 50.3633 57.5125 185 53.2296 51.9921 60.6001 61.6193 57.7724 51.809 58.2932 56.459 66.2473 226 52.9673 54.0105 59.5394 59.9194 63.8957 57.8248 54.632 53.7338 53.3248 30 56.4611 50.0663 57.8997 64.0456 58.4893 64.7106 51.3475 56.793676 54.2548 54.101553.3344 50.1313 51.5803 57.5994 54.0356 60.340554.7902 59.1244 50.6149 60.3891 54.6865 50.2897 55.4353 55.6529 50.0738 60.5117 56.7865 66.5867 50.4013 557 50.2546 58.9622 54.9011 66.4702 57.3444 403 62.0637 50.5996 59.0599 50.824 56.4717 62.9799 50.7881 60.5604 50.0235 58.2975 66.184 50.1303 58.4006 50.6346 51.4108 39 55.6079 58.1626 52.1712 57.9754 61.9957 53.7592 61.0123 560 1349 1056 52.2146 52.8906 52.8253 57.619 50.9287 60.0558 50.552 54.7185 51.1067 58.6704 52.8512 53.2071 55.3647 63.4698 54.2707 50.328 51.3891 62.301 60.6682 61.9234 54.557153.7274 57.8068 51.8116 52.7501 72.7127 53.6476 50.4055 54.1232 51.0432 58.4282 68.7979 57.3468 52.4502 51.7955 8556.1407 61.8834 51.0858 53.7685 41 50.878 53.1737 57.6551 56.319 54.9238 53.4444 57.867 56.9851 50.6138 58.6873 53.4177 61.8425 59.3791 60.1134 55.2421 58.8902 52.1271 61.6944 52.0741 55.9779 50.0013 62.8277 1400 52.147 50.9058 50.6987 55.7334 51.3615 57.5501 59.7187 52.2198 54.0887 70.9187 57.8661 56.8168 59.5498 58.3995 56.0483 65.1688 362 54.4333 62.7357 50.4499 53.4088 62.1416 51.8173 72.7519 52.2261 71.3985 57.4323 57.2133 556 51.2119 57.0846 57.4833 51.138 57.5305 74 54.6473 90 60.849 55.4606 57.7792 56.2819 54.2191 51.2534 52.715 50.3732 58.3412 28 51.3958 52.815 52.2724 53.7249 55.043 57.2411 51.2784 50.8583 57.3839 59.076 57.0729 65.497 62.4108 50.2459 53.4604 67.1103 55.271 58.1456 53.3141 57.1267 56.7699 51.9432 55.5194 61.5539 58.4752 300 64.9628 99 50.2603 50.326356.5199 329 53.2762 66.4311 53.1252 54.8276 54.8435 68.3068 53.6164 50.627 58.644765.6019 60.9913 56.1627 53.2877 52.027 66.4082 52.6625 64.0828 65.3574 58.2432 56.9327 669 55.7551 50.343 51.4544 65.1668 55.1269 54.791 52.3612 54.0627 51.2099 57.969 50.7655 52.9936 58.6766 50.2687 55.352 63.4635 166352.0155 679 68.3828 54.9683 398 56.8064 53.0349 203 54.5316 9151.2455 67.1753 66.2638 73.9265 53.5508 54.6792 399 51.7299 56.3033 51.5421 56.7379 50.8338 24 51.8795 53.9462 50.8938 70.5785 56.4736 56.6709 51.8674 58.4922 54.4512 53.0789 54.6412 50.4956104 50.324 50.2746 56.909 53.195 58.1933 54.4208 866 60.8696 55.0055 103 51.8139 53.6537 57.8364 57.081 62.8681 53.5257 54.2933 38 215 50.2115 57.4967 52.1661 2846 400 57.8235 51.0521 50.3494 84 62.5903 62.595 55.043 1321 55.8676 51.5122 799 6402 60.6955 50.5442 1130 59.2159 55.3037 56.6956 61.1315 81 1360 79 14095 688 1100 52.0827 54.0897
742
50
90
40
80
30
70
20
60
10
50
0 0.0
0.2
0.4
0.6
0.8
Percentage of groups possible to predict
Figure 8. Joint 2D histogram of the percentage of groups that can be revealed using association rules versus the average confidence of the applied rules. The color indicates the number of users the rules apply to. The Pearson correlation of the age of a user towards its predictability is slightly negative with -0.15 which in turn is based on the fact that the number of users in our dataset decreases for older users. As previously shown groups may have a certain dependency on the age which means that the groups, older people follow do not reach the required
minimum size of 1116 users to be included as a result of association rule learning. By comparing the predictability of a user with the predictability of the friends of this user we found a positive correlation value of 0.29. This indicates that users with a high predictability are connected to others having also a high predictability. By correlating the number of friends that have a publicly viewable profile to the predictability we found no significant relation, which means that a small number of friends having an open profile are already enough to guess the groups a user attends.
5.
Conclusion
We showed that the friends of young users are in most cases as old as the user itself. In contrast if the age of the friends has a large variation the user is most probably an older one. However by looking at interests of users, or the friends interest the predictability of older users can be raised again to a percentage of 78%. We also showed that the number of friends needed to infer private attributes is relatively small. Close friends have a very high overlap in terms of their groups they like and the city they live in. Most of the acquaintances of a user have dispersed attributes and only a small overlap. By identifying these few close friends a high prediction accuracy can be reached. We showed in a case study how to infer private attributes of a user in an Online Social Network. By using statistical analysis were we were able to calculate rules that allowed us to reconstruct most of the interests of a user even if he has a private profile which is not viewable by everyone. We connected this information with information of friends of a user and showed that basic attributes like age and hometown can be derived with a very high accuracy. We also used data from statistical institutes to further increase the prediction rate. Our findings lead to the conclusion that the common practice in privacy regulation is not practical at all. For most users in our dataset we were able to estimate private attributes.
Acknowledgments This work was partly funded by the Trans-sector Research Academy for complex Networks and Services (TRANS).
References
Listings. In Proceedings of Second ACM Workshop on Social Network Systems, Mar. 2009. [4] C. B. Department and C. Borgelt. Efficient Implementations of Apriori and Eclat, 2003. [5] C. Doerr, S. Tang, N. Blenn, and P. Van Mieghem. Are friends overrated? a study for the social news aggregator digg.com. In NETWORKING 2011, Part II, Lecture Notes in Computer Science 6641, pages 314–327. IFIP International Federation for Information Processing, 2011. [6] M. S. Granovetter. The strength of weak ties. American Journal of Sociology, 78(6):pp. 1360–1380, 1973. ISSN 00029602. [7] R. Gross and A. Acquisti. Information revelation and privacy in online social networks. In Proceedings of the 2005 ACM workshop on Privacy in the electronic society, WPES ’05, pages 71–80, New York, NY, USA, 2005. ACM. [8] J. He, W. Chu, and Z. Liu. Inferring Privacy Information from Social Networks. In Intelligence and Security Informatics, volume 3975 of Lecture Notes in Computer Science, pages 154–165. Springer-Verlag, Berlin/Heidelberg, 2006. [9] B. Krishnamurthy and C. E. Wills. Characterizing privacy in online social networks. In Proceedings of the first workshop on Online social networks, 2008. [10] B. Krishnamurthy and C. E. Wills. On the leakage of personally identifiable information via online social networks. SIGCOMM Comput. Commun. Rev., 40:112–117, Jan. 2010. ISSN 0146-4833. [11] M. McPherson, L. S. Lovin, and J. M. Cook. Birds of a Feather: Homophily in Social Networks. Annual Review of Sociology, 27(1):415–444, 2001. doi: 10.1146/annurev.soc. 27.1.415. [12] M. Mcpherson, L. Smith-lovin, and M. E. Brashears. Social isolation in america: Changes in core discussion networks over two decades. American Sociological Review, 71:353– 375, 2006. [13] A. Miller. Untangling the social web. The Economist, September 2 2010. [14] A. Mislove, B. Viswanath, K. P. Gummadi, and P. Druschel. You are who you know: Inferring user profiles in online social networks. In Proceedings of WSDM, 2010. [15] K. Raynes-Goldie. Pulling sense out of today’s informational chaos: Livejournal as a site of knowledge creation and sharing. First Monday, 8(12), 2004. [16] L. Scism and M. Maremont. Insurers test data profiles to identify risky clients. Wall Street Journal, Novmber 10 2010. [17] N. Singer. Face recognition makes the leap from sci-fi. New York Times, November 12 2011.
[1] The meertens institute. Website, 2012. http://www. meertens.knaw.nl/cms/en/meertens-institute.
[18] P. Van Mieghem. Performance Analysis of Communications Networks and Systems. Cambridge University Press, 2006.
[2] L. Bilge, T. Strufe, D. Balzarotti, and E. Kirda. All your contacts are belong to us: Automated identity theft attacks on social networks. In 18th International World Wide Web Conference, pages 551–551, April 2009.
[19] E. Zheleva and L. Getoor. To join or not to join: The illusion of privacy in social networks with mixed public and private user profiles. In 18th International World Wide Web Conference, pages 531–531, April 2009.
[3] J. Bonneau, J. Anderson, R. Anderson, and F. Stajano. Eight Friends are Enough: Social Graph Approximation via Public
