Approximating Higher-Order Distances Using Random Projections

Ping Li, Michael Mahoney, Yiyuan She
Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, PMLR R8:319-328, 2010.

Abstract

We provide a simple method and relevant theoretical analysis for efficiently estimating higherorder lp distances. While the analysis mainly focuses on l4, our methodology extends naturally to p = 6, 8, 10..., (i.e., when p is even). Distance-based methods are popular in machine learning. In large-scale applications, storing, computing, and retrieving the distances can be both space and time prohibitive. Efficient algorithms exist for estimating lp distances if 0 < p $\leq$2. The task for p > 2 is known to be difficult. Our work partially fills this gap.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR8-li10b, title = {Approximating Higher-Order Distances Using Random Projections}, author = {Li, Ping and Mahoney, Michael and She, Yiyuan}, booktitle = {Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence}, pages = {319--328}, year = {2010}, editor = {Grünwald, Peter and Spirtes, Peter}, volume = {R8}, series = {Proceedings of Machine Learning Research}, month = {08--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r8/main/assets/li10b/li10b.pdf}, url = {https://proceedings.mlr.press/r8/li10b.html}, abstract = {We provide a simple method and relevant theoretical analysis for efficiently estimating higherorder lp distances. While the analysis mainly focuses on l4, our methodology extends naturally to p = 6, 8, 10..., (i.e., when p is even). Distance-based methods are popular in machine learning. In large-scale applications, storing, computing, and retrieving the distances can be both space and time prohibitive. Efficient algorithms exist for estimating lp distances if 0 < p $\leq$2. The task for p > 2 is known to be difficult. Our work partially fills this gap.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Approximating Higher-Order Distances Using Random Projections %A Ping Li %A Michael Mahoney %A Yiyuan She %B Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2010 %E Peter Grünwald %E Peter Spirtes %F pmlr-vR8-li10b %I PMLR %P 319--328 %U https://proceedings.mlr.press/r8/li10b.html %V R8 %X We provide a simple method and relevant theoretical analysis for efficiently estimating higherorder lp distances. While the analysis mainly focuses on l4, our methodology extends naturally to p = 6, 8, 10..., (i.e., when p is even). Distance-based methods are popular in machine learning. In large-scale applications, storing, computing, and retrieving the distances can be both space and time prohibitive. Efficient algorithms exist for estimating lp distances if 0 < p $\leq$2. The task for p > 2 is known to be difficult. Our work partially fills this gap. %Z Reissued by PMLR on 04 October 2026.
APA
Li, P., Mahoney, M. & She, Y.. (2010). Approximating Higher-Order Distances Using Random Projections. Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R8:319-328 Available from https://proceedings.mlr.press/r8/li10b.html. Reissued by PMLR on 04 October 2026.

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