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0111 · Nov 201419922001200920172026
3 results for Degree-Scaling

We analyze directed, unweighted graphs obtained from xiRdx_i\in \mathbb{R}^d by connecting vertex ii to jj iff xixj<ε(xi)|x_i - x_j| < ε(x_i). Examples of such graphs include kk-nearest neighbor graphs, where ε(xi)ε(x_i) varies from point to point, and, arguably, many real world graphs such as co-purchasing graphs. We ask whethe…

2014-11-20abs ↗pdf ↗

This paper studies node embeddings of networks, revealing their geometric properties.

problem Understanding the geometric properties of node embeddings in random networks.
method Characterization of ergodic limits, generalization, and convex relaxations of random walk node embedding objectives.
result The optimal node embedding Grammians have rank 1 for a nuclear norm relaxation of the non-randomized objective.