• Corpus ID: 9716414

Metric recovery from directed unweighted graphs

  title={Metric recovery from directed unweighted graphs},
  author={Tatsunori B. Hashimoto and Yi Sun and T. Jaakkola},
We analyze directed, unweighted graphs obtained from $x_i\in \mathbb{R}^d$ by connecting vertex $i$ to $j$ iff $|x_i - x_j| < \epsilon(x_i)$. Examples of such graphs include $k$-nearest neighbor graphs, where $\epsilon(x_i)$ varies from point to point, and, arguably, many real world graphs such as co-purchasing graphs. We ask whether we can recover the underlying Euclidean metric $\epsilon(x_i)$ and the associated density $p(x_i)$ given only the directed graph and $d$. We show that consistent… 

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