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This research introduces a class of random polytopes that generalizes existing constructions while maintaining computational efficiency, offering a new trade-off between data description accuracy and processing speed. The authors leverage these geometric properties to enhance classification and clustering tasks in data analysis, with the paper's focus shifting significantly toward stochastic geometry rather than standard machine learning pipelines.

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Random Polytope Descriptors

arXiv24 septembrie 20261 min de cititArticolul și perspectiva sunt în engleză.

arXiv:2009.13987v3 Announce Type: replace Abstract: We introduce a class of random polytopes which simultaneously generalizes several known constructions. While being fairly general, these polytopes are also computationally exceptionally benign. We indicate how these properties can be exploited for classification and clustering tasks in data analysis. Crucially, our construction lets users smoothly trade off between a tighter description of the data and faster computation.

Abstract:We introduce a class of random polytopes which simultaneously generalizes several known constructions. While being fairly general, these polytopes are also computationally exceptionally benign. We indicate how these properties can be exploited for classification and clustering tasks in data analysis. Crucially, our construction lets users smoothly trade off between a tighter description of the data and faster computation.

19 pages (v3); major rewrite (new title, more stochastic geometry, less machine learning); experiments reworked from scratch; code and data available on zenodo, doi:https://doi.org/10.5281/zenodo.22913313

Machine Learning (cs.LG); Metric Geometry (math.MG); Machine Learning (stat.ML)

arXiv:2009.13987 [cs.LG]

(or arXiv:2009.13987v3 [cs.LG] for this version)

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