Out-of-Sample Embedding with Proximity Data: Projection versus Restricted Reconstruction
Abstract
The problem of using proximity (similarity or dissimilarity) data for the purpose of "adding a point to a vector diagram" was first studied by J.C. Gower in 1968. Since then, a number of methods -- mostly kernel methods -- have been proposed for solving what has come to be called the problem of *out-of-sample embedding*. We survey the various kernel methods that we have encountered and show that each can be derived from one or the other of two competing strategies: *projection* or *restricted reconstruction*. Projection can be analogized to a well-known formula for adding a point to a principal component analysis. Restricted reconstruction poses a different challenge: how to best approximate redoing the entire multivariate analysis while holding fixed the vector diagram that was previously obtained. This strategy results in a nonlinear optimization problem that can be simplified to a unidimensional search. Various circumstances may warrant either projection or restricted reconstruction.
Cite
@article{arxiv.2505.06756,
title = {Out-of-Sample Embedding with Proximity Data: Projection versus Restricted Reconstruction},
author = {Michael W. Trosset and Kaiyi Tan and Minh Tang and Carey E. Priebe},
journal= {arXiv preprint arXiv:2505.06756},
year = {2025}
}
Comments
19 pages, 2 figures