Non-link Preserving Network Embedding using Subspace Learning for Network Reconstruction

Learning meaningful vector representations of nodes of a network has been a subject of intense study in the past few years, with various objectives such as node or link labeling, preserving higher order structures, etc. In this paper, we focus on reconstruction of adjacency matrix, which also leads to preservation of higher order structures, through spectral distance. Methodologically, existing techniques focus on construction of various neighborhoods based on the link-structure, but do not explicitly give importance to nonlinks. Our method, called the subspace learning method (SLM), is based on a simple observation that in addition to representations of neighbors sharing a common subspace, representations of non-neighbors should lie in each others' null-space. We devise an efficient, negative sampling based algorithm for learning the node representations. Experimental results on many real world benchmark networks show surprising improvement in both reconstruction error and spectral distance over state of the art methods. Moreover, we show that the representations given by SLM perform better than state of the art representations on the tasks of community detection and link prediction.