better distinguish between the different link types. Firstly, we define the global similarity as the Twitter similarity over Foursquare distance as:

$$sim_{GNij} = \frac{sim_{ij}^a}{dist_{ij}^b}$$

where $sim$ can be replaced with any type of similarity, which is the mass or sum of that similarity for a pair of users, and $a,b$ are exponents which can be tuned to optimise the features. Figure \[fig:mult2\] shows how this feature captures the different levels of links (a=2, b=1). We additionally frame a feature which captures the complete interaction across layers of social networks:

$$int_{GNij} = \sum_\alpha^M |int^\alpha_{ij}|$$

where $int$ can be any type of interaction of layer $\alpha$, this can be further refined by giving a weight to each interaction but in our case, we consider the coefficient to be equal to 1 and use colocations from the Foursquare layer and mentions from the Twitter layer to express the global interaction of two users in the multilayer network. This feature allows us to capture the levels of different link types significantly better as shown in Figure \[fig:mult1\].

[0.22]{} ![Interaction features for the different link types.[]{data-label="fig:interactions"}](log_men.pdf "fig:"){width="\textwidth"}

[0.22]{} ![Interaction features for the different link types.[]{data-label="fig:interactions"}](log_hasht.pdf "fig:"){width="\textwidth"}

[0.22]{} ![Interaction features for the different link types.[]{data-label="fig:interactions"}](log_colocs.pdf "fig:"){width="\textwidth"}

