Ordinal embedding is the task of computing a meaningful multidimensional representation of objects, for which only qualitative constraints on their distance functions are known. In particular, we consider comparisons of the form “Which object from the pair (j, k) is more similar to object i?”. In this paper, we generalize this framework to the case where the ordinal constraints are not given at the level of individual points, but at the level of sets, and propose a distributional triplet embedding approach in a scalable learning framework. We show that the query complexity of our approach is on par with the single-item approach. Without having access to features of the items to be embedded, we show the applicability of our model on toy datasets for the task of reconstruction and demonstrate the validity of the obtained embeddings in experiments on synthetic and real-world datasets.

中文翻译：

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从集合中学习序数嵌入

序数嵌入是计算对象的有意义的多维表示的任务，对于它们的距离函数只有定性约束是已知的。特别是，我们考虑了“(j, k) 对中的哪个对象与对象 i 更相似？”形式的比较。在本文中，我们将此框架推广到顺序约束不是在单个点级别给出的情况，而是在集合级别，并在可扩展的学习框架中提出了一种分布式三元组嵌入方法。我们表明我们的方法的查询复杂性与单项方法相当。无需访问要嵌入的项目的功能，