Given a set of relative similarities between objects in the form of triplets "object i is more similar to object j than to object k", we consider the problem of finding an embedding of these objects in a metric space. This problem is generally referred to as triplet embedding. Our main focus in this paper is the case where a subset of triplets are corrupted by noise, such that the order of objects in a triple is reversed. In a crowdsourcing application, for instance, this noise may arise due to varying skill levels or different opinions of the human evaluators. As we show, all existing triplet embedding methods fail to handle even low levels of noise. Inspired by recent advances in robust binary classification and ranking, we introduce a new technique, called t-Exponential Triplet Embedding (t-ETE), that produces high-quality embeddings even in the presence of significant amount of noise in the triplets. By an extensive set of experiments on both synthetic and real-world datasets, we show that our method outperforms all the other methods, giving rise to new insights on real-world data, which have been impossible to observe using the previous techniques.
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