# Evolutionary Features for Dynamic Link Prediction in Social Networks
## 3 Network Datasets and Experimental Settings  
Considering two different time intervals \((t_{1},t^{\prime})\), \((t_{t},t_{1}^{\prime})\) where \(t_{1}<t^{\prime}<t_{1}^{\prime}\) and a finite set of discrete time points within the range \([t_{1}-t^{\prime}]\) as \(T=t_{1},(t_{1}+\tau),(t_{1}+2\tau),\ldots,\)\((t_{1}+n\tau),\ldots,(t^{\prime}-\tau),t^{\prime}\), where \(\tau\) denotes the temporal sampling interval, a dynamic social network \(G_{T}=(V,E_{T})\) consists of a set of uniquely labeled actors \(V=\{v_{1},v_{2},v_{3},\ldots,v_{n}\}\), and \(E_{T}=\{e_{t}(v_{i},v_{j},t)|v_{i},v_{j}\in V;t\in T\}\), where \(t\) represents the timestamp of a link \(e\) between a pair of actors \((v_{i},v_{j})\). In addition, dynamic networks can be undirected, where \(e=(v_{i},v_{j})\) and \(e=(v_{j},v_{i})\) denote identical or directed links where these two links are not the same. Thus, the dynamic network is composed of an evolutionary sequence of network snapshots \(G_{T}=\{G_{t_{1}},G_{t_{1}+\tau},G_{t_{1}+2\tau}\ldots G_{t_{1}+n\tau}\ldots G _{t^{\prime}-\tau},G_{t^{\prime}}\}\) known as short-interval networks (SIN). Fluctuations in the total number of actors are taken into consideration across the time series of network snapshots. Any link may appear in multiple network snapshots at different timestamp(s). Considering this temporal sequence of network snapshots \(G_{T}=\{G_{t_{1}},G_{t_{1}+\tau},G_{t_{1}+2\tau}\ldots G_{t_{1}+n\tau}\ldots G _{t^{\prime}-\tau},G_{t^{\prime}}\}\), for a given pair of actors \((v_{i},v_{j})\), dynamic link prediction attempts to predict the link probability between them during the interval \((t^{\prime},t_{1}^{\prime})\) in \(G_{T+1}\) by analyzing the link formation and the temporal information in \(G_{T}\) at timestamp \([t_{1}-t^{\prime}]\) as \(T=t_{1},(t_{1}+\tau),(t_{1}+2\tau),\ldots,(t_{1}+n\tau),\ldots,(t^{\prime}- \tau),t^{\prime}\). Here, \(G_{T}[t_{1},t^{\prime}]\) and \(G_{T}[t^{\prime},t_{1}^{\prime}]\) are considered as the networks in the training and testing phase, respectively. Traditional link prediction in the static network generally emphasizes the presence or absence of the links and simultaneously considers topological information to construe the similarity between actors. It does not consider the temporal information or the evolutionary dynamicity associated with all actors that vary in existence across network snapshots as well as in their associated links. A key aspect in dynamic link prediction is to generate dynamic similarity metrics (i.e., dynamic features) considering the evolutionary changes incident to actors. Therefore, this study attempts to develop such dynamic similarity metrics where the \(i\)th metric will assign a score \(sim_{i}(v_{i},v_{j})\) to non-connected actor pairs \((v_{i},v_{j})\) considering the similarity/proximity of their evolutionary information in \(G_{T}\). These scores will measure the likelihood of future links that emerge in \(G_{T+1}\). In (Table 1), we summarized five dynamic similarity metrics/dynamic features constructed in this study to measure the similarity/proximity between non-connected actor pairs.