提出两种新点嵌入方法，解决向量图中新增数据的难题
Out-of-Sample Embedding with Proximity Data: Projection versus Restricted Reconstruction
- 基于投影与受限重构两类策略，统一框架下推导多种方法
- 受限重构需解非线性优化，可简化为一维搜索，精度更高
- 适合需要高保真嵌入的场景，如生物数据、社会网络分析
1968年J.C. Gower首次研究了利用邻近性（相似或相异）数据将新点加入向量图的问题。此后，众多方法——主要是核方法——被提出，统称为‘外部样本嵌入’问题。本文综述了所遇各类核方法，表明其均可归因于两种竞争策略：投影或受限重构。投影类似于主成分分析中加点的经典公式；受限重构则要求在保持已有向量图不变的前提下，最佳近似重新执行整个多变量分析，形成非线性优化问题，可通过一维搜索简化求解。不同情形下，投影或受限重构各有优势。
原文摘要 · Abstract (English)
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.
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