While the embedding of words has revolutionized the field of Natural Language Processing, the embedding of concepts has received much less attention so far. A dense and meaningful representation of concepts, however, could prove useful for several tasks in computational linguistics, especially those involving cross-linguistic data or sparse data from low resource languages. First methods that have been proposed so far embed concepts from automatically constructed colexification networks. While these approaches depart from automatically inferred polysemies, attested across a larger number of languages, they are restricted to the word level, ignoring lexical relations that would only hold for parts of the words in a given language. Building on recently introduced methods for the inference of partial colexifications, we show how they can be used to improve concept embeddings in meaningful ways. The learned embeddings are evaluated against lexical similarity ratings, recorded instances of semantic shift, and word association data. We show that in all evaluation tasks, the inclusion of partial colexifications lead to improved concept representations and better results. Our results further show that the learned embeddings are able to capture and represent different semantic relationships between concepts.