The well known node2vec algorithm has been used to explore network structures and represent the nodes of a graph in a vector space in a way that reflects the structure of the graph. Random walks in node2vec have been used to study the local structure through pairwise interactions. Our motivation for this project comes from a desire to understand higher-order relationships by a similar approach. To this end, we propose an extension of node2vec to a method for representing the k-simplices of a simplicial complex into Euclidean space.
In this talk I outline a way to do this by performing random walks on simplicial complexes, which have a greater variety of adjacency relations to take into account than in the case of graphs. The walks on simplices are then used to obtain a representation of the simplices. We will show cases in which this method can uncover the roles of higher order simplices in a network and help understand structures in graphs that cannot be seen by using just the random walks on the nodes.
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- Applied Topology Seminar