Node2vec

Node2vec (Grover and Leskovec, 2016) is a method that can learn the continuous feature representation of each node in the network. It can map the node to low-dimensional feature space and preserve the network neighborhood of the node to the maximum. Node2vec provides a biased random walk method to obtain the nearest neighbor sequence of vertices, effectively combining DFS (Depth First Search) and BFS (Breath First Search). We assume that node v is the current vertex, then the probability of accessing the next vertex x is:

where π is a vertex v and not normalized transition probability between x, Z is a normalized constant. c is the node in the walk and initial c = u.

Consequently, two super parameters p and q are introduced to control the strategy of the random walk. It is assumed that the current random walk reaches the vertex v after passing the edge (t, v). Here, the unnormalized transition probability is set as π_vx = α_pq(t, x)·w_vx, where:

which w is the weight of the edge between the vertices v and x, d is the shortest path distance between vertex t and vertex x.