Adaptive Metric Dimensionality Reduction

@article{Gottlieb2013AdaptiveMD,
  title={Adaptive Metric Dimensionality Reduction},
  author={Lee-Ad Gottlieb and Aryeh Kontorovich and Robert Krauthgamer},
  journal={Theor. Comput. Sci.},
  year={2013},
  volume={620},
  pages={105-118}
}
We study adaptive data-dependent dimensionality reduction in the context of supervised learning in general metric spaces. Our main statistical contribution is a generalization bound for Lipschitz functions in metric spaces that are doubling, or nearly doubling. On the algorithmic front, we describe an analogue of PCA for metric spaces: namely an efficient procedure that approximates the data’s intrinsic dimension, which is often much lower than the ambient dimension. Our approach thus leverages… CONTINUE READING