This paper addresses the problem of mapping high-dimensional data to a low-dimensional space, in the presence of other known features. This problem is ubiquitous in science and engineering as there are often controllable/measurable features in most applications. To solve this problem, this paper proposes a broad class of methods, which is referred to as conditional multidimensional scaling (MDS). An algorithm for optimizing the objective function of conditional MDS is also developed. The convergence of this algorithm is proven under mild assumptions. Conditional MDS is illustrated with kinship terms, facial expressions, textile fabrics, car-brand perception, and cylinder machining examples. These examples demonstrate the advantages of conditional MDS over conventional dimension reduction in improving the estimation quality of the reduced-dimension space and simplifying visualization and knowledge discovery tasks. Computer codes for this work are available in the open-source cml R package.

翻译：本文研究了在存在其他已知特征的情况下，将高维数据映射到低维空间的问题。该问题在科学和工程领域普遍存在，因为大多数应用中通常存在可控或可测量的特征。为解决此问题，本文提出了一类广泛适用的方法，称为条件多维缩放（MDS）。同时，本文还开发了一种用于优化条件MDS目标函数的算法，并在较弱假设下证明了该算法的收敛性。条件MDS方法通过亲属关系术语、面部表情、纺织品面料、汽车品牌感知以及气缸加工等实例进行了说明。这些实例表明，与传统降维方法相比，条件MDS在提升低维空间估计质量、简化可视化及知识发现任务方面具有显著优势。本工作相关计算机代码已开源发布在cml R包中。