Title: Open-Set Representation Learning through Combinatorial Embedding. Abstract: Visual recognition tasks are often limited to dealing with a small subset of classes simply because the labels for the remaining classes are unavailable. We are interested in identifying novel concepts in a dataset through representation learning based on the examples in both labeled and unlabeled classes, and extending the horizon of recognition to both known and novel classes. To address this challenging task, we propose a combinatorial learning approach, which naturally clusters the examples in unseen classes using the compositional knowledge given by multiple supervised meta-classifiers on heterogeneous label spaces. We also introduce a metric learning strategy to estimate pairwise pseudo-labels for improving representations of unlabeled examples, which preserves semantic relations across known and novel classes effectively. The proposed algorithm discovers novel concepts via a joint optimization of enhancing the discrimitiveness of unseen classes as well as learning the representations of known classes generalizable to novel ones. Our extensive experiments demonstrate remarkable performance gains by the proposed approach in multiple image retrieval and novel class discovery benchmarks.