• Corpus ID: 6730046

A Locally Adaptive Normal Distribution

@inproceedings{Arvanitidis2016ALA,
  title={A Locally Adaptive Normal Distribution},
  author={Georgios Arvanitidis and Lars Kai Hansen and S{\o}ren Hauberg},
  booktitle={NIPS},
  year={2016}
}
The multivariate normal density is a monotonic function of the distance to the mean, and its ellipsoidal shape is due to the underlying Euclidean metric. We suggest to replace this metric with a locally adaptive, smoothly changing (Riemannian) metric that favors regions of high local density. The resulting locally adaptive normal distribution (LAND) is a generalization of the normal distribution to the "manifold" setting, where data is assumed to lie near a potentially low-dimensional manifold… 
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