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While classical scaling, just like principal component analysis, isparameter-free, other methods for embedding multivariate data require theselection of one or several tuning parameters. This tuning can be difficult dueto the unsupervised nature of the situation. We propose a simple, almostobvious, approach to supervise the choice of tuning parameter(s): minimize anotion of stress. We apply this approach to the selection of the patch size ina prototypical patch-stitching embedding method, both in the multidimensionalscaling (aka network localization) setting and in the dimensionality reduction(aka manifold learning) setting. In our study, we uncover a new bias--variancetradeoff phenomenon.

On the Selection of Tuning Parameters for Patch-Stitching Embedding Methods