arXiv Machine Learning By Michael W. Trosset, Kaiyi Tan, Minh Tang, Carey E. Priebe

Out-of-Sample Embedding with Proximity Data: Projection versus Restricted Reconstruction

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The paper reviews methods for adding a new point to a vector diagram using proximity data, a problem first examined by J.C. Gower in 1968. It classifies existing kernel-based approaches into two strategies: projection, analogous to adding a point in principal component analysis, and restricted reconstruction, which seeks to re‑optimize the multivariate analysis while keeping the existing diagram fixed. The authors show that each method can be derived from one of these two strategies and discuss when each strategy may be preferable.

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