Automated keyphrase extraction is a fundamental textual information processing task concerned with the selection of representative phrases from a document that summarize its content. This work presents a novel unsupervised method for keyphrase extraction, whose main innovation is the use of local word embeddings (in particular GloVe vectors), i.e., embeddings trained from the single document under consideration... We argue that such local representation of words and keyphrases are able to accurately capture their semantics in the context of the document they are part of, and therefore can help in improving keyphrase extraction quality. Empirical results offer evidence that indeed local representations lead to better keyphrase extraction results compared to both embeddings trained on very large third corpora or larger corpora consisting of several documents of the same scientific field and to other state-of-the-art unsupervised keyphrase extraction methods. (read more)