Convergence rates for ordinal embedding

Jordan S. Ellenberg; Lalit Jain

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arXiv · 1904.12994

Convergence rates for ordinal embedding

Jordan S. Ellenberg·Lalit Jain

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Abstract

We prove optimal bounds for the convergence rate of ordinal embedding (also known as non-metric multidimensional scaling) in the 1-dimensional case. The examples witnessing optimality of our bounds arise from a result in additive number theory on sets of integers with no three-term arithmetic progressions. We also carry out some computational experiments aimed at developing a sense of what the convergence rate for ordinal embedding might look like in higher dimensions.

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Jordan S. Ellenberg, Lalit Jain. 2019-04-30. Convergence rates for ordinal embedding. https://arxiv.org/abs/1904.12994

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