How to learn a graph from smooth signals

@article{Kalofolias2016HowTL,
  title={How to learn a graph from smooth signals},
  author={Vassilis Kalofolias},
  journal={ArXiv},
  year={2016},
  volume={abs/1601.02513}
}
We propose a framework that learns the graph structure underlying a set of smooth signals. Given $X\in\mathbb{R}^{m\times n}$ whose rows reside on the vertices of an unknown graph, we learn the edge weights $w\in\mathbb{R}_+^{m(m-1)/2}$ under the smoothness assumption that $\text{tr}{X^\top LX}$ is small. We show that the problem is a weighted $\ell$-1 minimization that leads to naturally sparse solutions. We point out how known graph learning or construction techniques fall within our… CONTINUE READING

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