Which Spatial Partition Trees Are Adaptive to Intrinsic Dimension?
Abstract
Recent theory work has found that a special type of spatial partition tree -- called a random projection tree -- is adaptive to the intrinsic dimension of the data from which it is built. Here we examine this same question, with a combination of theory and experiments, for a broader class of trees that includes k-d trees, dyadic trees, and PCA trees. Our motivation is to get a feel for (i) the kind of intrinsic low dimensional structure that can be empirically verified, (ii) the extent to which a spatial partition can exploit such structure, and (iii) the implications for standard statistical tasks such as regression, vector quantization, and nearest neighbor search.
Cite
Text
Verma et al. "Which Spatial Partition Trees Are Adaptive to Intrinsic Dimension?." Conference on Uncertainty in Artificial Intelligence, 2009.Markdown
[Verma et al. "Which Spatial Partition Trees Are Adaptive to Intrinsic Dimension?." Conference on Uncertainty in Artificial Intelligence, 2009.](https://mlanthology.org/uai/2009/verma2009uai-spatial/)BibTeX
@inproceedings{verma2009uai-spatial,
title = {{Which Spatial Partition Trees Are Adaptive to Intrinsic Dimension?}},
author = {Verma, Nakul and Kpotufe, Samory and Dasgupta, Sanjoy},
booktitle = {Conference on Uncertainty in Artificial Intelligence},
year = {2009},
pages = {565-574},
url = {https://mlanthology.org/uai/2009/verma2009uai-spatial/}
}