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Statistics > Methodology
Title: On the Selection of Tuning Parameters for Patch-Stitching Embedding Methods
(Submitted on 14 Jul 2022 (v1), last revised 18 Oct 2023 (this version, v2))
Abstract: While classical scaling, just like principal component analysis, is parameter-free, other methods for embedding multivariate data require the selection of one or several tuning parameters. This tuning can be difficult due to the unsupervised nature of the situation. We propose a simple, almost obvious, approach to supervise the choice of tuning parameter(s): minimize a notion of stress. We apply this approach to the selection of the patch size in a prototypical patch-stitching embedding method, both in the multidimensional scaling (aka network localization) setting and in the dimensionality reduction (aka manifold learning) setting. In our study, we uncover a new bias--variance tradeoff phenomenon.
Submission history
From: Ery Arias-Castro [view email][v1] Thu, 14 Jul 2022 22:04:00 GMT (4308kb,D)
[v2] Wed, 18 Oct 2023 03:48:23 GMT (6397kb,D)
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