Introduction

In 2020, zenith year for social media, the WorldWideWeb proliferates with celebrities and influencers, showing off their incredible life online and seeking for followers as much as forty-niners were looking for nuggets during the California Gold Rush. Many of the social media users have used an analytical app at least once to manage their virtual activity and visualise statistics about their posts and friends. One in particular can end friendships: indeed these apps can indicate which of your online friends has deleted you from their friend’s list, or even unfollowed you. It is heartbreaking to discover that one of your close friends thought that you were not worth following anymore, and decided to cancel your virtual friendship.

It is almost impossible to precisely forecast the creation and deletion of particular social media friendships. Indeed it depends on too many real-life factors, including who you speak too, and who you meet, even randomly in a connection-free area. These factors making it difficult to use geo-localisation as friendship prediction tools. Nevertheless we believe that with the appropriate dataset, it must be possible to predict (or get close to) if a user will make or break friendships over a certain period.

Throughout this study, we used data from the social network Foursquare to build and train two different prediction models in order to determine whether friendships will be created or deleted a 22 month time period.

Foursquare is a location-based social network which database gathers 13+ billion check-ins, used by developers around the globe for localisation purposes. A check-in occurs when a user communicates their position, associated with a location category like a bakery, shops, boats, clubs, etc. We extracted a fraction of this database used in several papers exploring multiple aspects of friendship and mobility, and we will base our analysis on this dataset.

Initial Analysis

First, let’s talk about our data. As previously mentionned, we are using data from Foursquare which includes long-term global-scale check-in data collected from Foursquare (about 22 months from April 2012 to January 2014), and also two snapshots of user social networks before and after the check-in data collection period. After preprocessing, the check-in dataset contains 19,306,111 checkins by 71,188 users in 3,430,171 venues. The social network data contains 363,704 old and 607,333 new friendships.

Let’s find out where all of these beautiful users live! We adopt the same method as proposed in Friendship and Mobility: User Movement in Location-Based Social Networks by Jure Leskovec & al. [1]. We divide the world into 25km by 25km cells, we then determine the cell with the most check-ins for each user.

The average location of check-ins within this cell is defined as a user’s home. This method has proven to be 80% accurate in [1].

We can have a look at user home locations as well as check-in locations by country in the figure below.

By selecting Number of Homes in the dropdown menu, we can see that the users living in the United States and in Brasil are the ones who use the Foursquare application the most. In Europe, Asia, and Australia, there is also a large amount of users checking in on the application, whereas in Africa some countries don’t have any user homes in at all. Selecting Number of check-ins shows us a similar trend, however more countries are filled out this time.

Let’s dig a little deeper by looking at the 20 countries with the most users and figure out how the check-ins in these countries compare.

We observe a general correlation between the amount of homes per country and check-ins per country. The big exception here, that has a larger check-in number compared to other top countries as apposed to homes. Indeed japan is a very attractive country for tourists with over 30 million visitors a year, which would explain the large number of check-ins.

Foursquare defines a category hierarchy of multiple levels. Indeed each venue has a category, with perhaps a superior caterior, or even another uperior category! We define 5 category levels (0 to 5) with 0 being the most general. Let us look at the distribution of check-ins within each of the level 0 categories to get an idea on what our Foursquare users are up to.

Clearly the users love to eat!

Scoring Users

To create our prediction model, we need to give each check-in a certain Checkin Social Score: we want to know how social a check-in is! Indeed giving a social score to the 3,430,171 different venues is hard work. Giving a social score to the 506 unique proposed categories is slightly easier, but also not the best idea. Remember the Foursquare hierarchy? We can use the level 1 category to group all checkins into one of 275 categories now. Our social score is based on two main ideas, first of all that some places are less social than others, obviously a post office is less social than a nighclub. We define a coefficient C for each level 0 category, reflecting how social this category is (in general).

Second of all, we want to know if a check-in was performed during the peak hours of the venue category. For this we use level 1 categories to be slightly more precise in our categorisation. If a check-in is within the venue’s peak hours, we give it a score of S_peak = 2, if it isnt we give it S_peak = 2. Each check-in can now get a social score by multiplying the coefficient with the peak hour score: S = C*S_peak = 2.

Right, we have now given the check-ins social scores but not the users. We therefore give each user an individual social score that is equals to the mean value of S for each of their check-ins.

But we’re not done here… We also give each user two travel scores! We want to see if mobility influences friendships, therefore we can’t leave out travelling. First we notice that our friends at Foursquare have given us a level 0 category named Travel & Transport, our first travel score T_category is defined as the fraction of check-ins within this category over the total number of check-ins. Our second travel score T_distance uses a more scientific approach. By looking at the distribution of check-in distances from home. We see that the distribution follows a power law with a dip between 70 and 200km from home. We therefore use the upper value of 200km to define whether a check-in should be considered a Travel or not. We define T_distance as the fraction of Travel check-ins (further than 200km from home) over the total numver of check-ins.

The figure below shows three user’s with a high T_distance score in orange, and a low T_distance in purple. We can clearly see that our definition illustrates how far and how often a user with a high T_distance travels.

Prediction Models

We will try two methods in order to predict the number of friends that a specific user will gain or lose during the data collection period:

1. A model using the social scores and the travel scores that we have computed above
2. A model only using the check-ins of the users to determine the similarity between them

First of all we divide our data into a training set containing 80% of the users (45618 users), and a testing set containing 20% of the users (11405 users).
We then train our models on the training data, and predict the number of friends gained for the users in the testing set.

Let’s talk about the first model. After having computed social and traveler scores for every user in our training set, we normalise the scores and we use them to train a linear regression model. We then use this model to predict the number of friends gained for each user in the testing set, and we compare that value to the real number of friends gained. The figure below is a plot of the residual, or the subtraction of the predicted friendship gain and the true friendship gain.

We can see that with this simple regression model, the results already look pretty promising! In fact in 35% of the cases, we were able to determine with an error of less than 1 friends, the number of friends that a user has gained or lost.

Now what if we only use the the check-ins of the users in the testing set to determine to which user in the training set they are the most similar to?

For the second model, we use a similarity measurement technique between the users and then use this to predict how a user’s friendships have evolved. In this case, for each user in the testing set, we determine the 5 most similar users in the training set by using cosine similarity, taking only into account the frequency at which the users go to a specific location. With this information, we then determine which users are the most similar. The difference between the predicted number of friends and the real number of friends (aka the residual) can be seen in the density plot below.

Clearly, this method works a lot better than the model using the social and traveler scores of the users, which is something we were not expecting at all! In 60% of the cases, we are able to predict the number of friends a person will make (with an error of only 1 friend) simply by looking at the users to which this person is most similar. This clearly proves that users that go to similar places are similar in behaviour, and are most likely to make the same number of friends.

Conclusion

The main result of our analysis is that it is obviously difficult to make precise predictions on the evolution of friendships id users have a few friends on the social media. Indeed, little variations can have a higher impact on our model and affect its performances.

Nevertheless, we were able to predict the future number of friends of each user with acceptable trust ranges. The model of cosine similarity achieved 60% of accuracy while the other model did not exceed 35% of accuracy with an error of one friend.