I am clustering comments.
After preprocessing and a vectorization of a text, I have inferred vectors from my doc2vec model and applied kmeans.
After that I want to convert cluster centroid vectors to words to kinda look at the semantic cores of the clusters. Is it possible?
Edit: I use python/gensim.
There are a bunch of potential approaches you could try, and see which might offer what you want.
First & foremost, some of the Gensim Doc2Vec modes co-train word-vectors into the same coordinate system as the doc-vectors – allowing direct comparisons betwee words & docs, sometimes even to the level of compositional 'vector-arithmetic' (like in the famous word2vec analogy-solving examples).
You can see this potential discussed in the paper "Document Embedding with Paragraph Vectors".
The default PV-DM mode (parameter dm=1) automatically co-trains words and docs in the same space. You can also add interleaved word-vector skip-gram training into the other PV-DBOW dm=0 mode by adding the optional parameter dbow_words=1.
While it is still the case that d2v_model.dv.most_similar(docvec_or_doctag) will only return doc-vector results, and d2v_model.wv.most_similar(wordvec_or_word_token) will only return word-vector results, you can absolutely provide a raw vector of a document to the set of word-vectors, or a word-vector to the set of doc-vectors, to get the nearest-neighbors of the other type.
So in one of these modes, with doc-vector, you can use...
d2v_model.wv.most_simlar(positive=[doc_vector])
...to get a list-of-words that are closest to that doc-vector. Whether they're sufficiently representative will vary based on lots of factors. (If they seem totally random, there may be other problems with your data-sufficiency or process, or you may be using the dm=0, dbow_words=0 mode that leaves words random & untrained.)
You could use this on the centroid of your clusters – but note, a centroid might hide lots of the variety of a larger grouping, which might include docs not all in a tight 'ball' around the centroid. So you could also use this on all docs in a cluster, to get the top-N closest words to each – and then summarize the cluster as the words most often appearing in those many top-N lists, or most uniquely appearing in those top-N lists (versus the top-N lists of other clusters). That might describe more of the full cluster.
Separately, there's a method from Gensim's Word2Vec, predict_output_word(), which vaguely simulates the word2vec training-predictions to give a ranked list of predictions of a word from its surrounding words. The same code could be generalized to predict document-words from a doc-vector – there's an open pending issue to do so, and it'd be a simple bit of coding, though no-one's tackled it yet. (It'd be a welcome, and pretty easy, 1ast contribution to the Gensim project.)
Also: after having established your clusters, you could even put the Doc2Vec model aside, and use more traditional direct counting/frequency methods to pick out the most-salient words in each cluster. For example, turn each cluser into a single synthetic pseudodocument. Rank the words inside by TF-IDF, compared to the other cluster pseudodocs. (Or, get the top TF-IDF terms for every one of the individual original documents; describe each cluster by the most-often-relevant words tallied across all cluster docs.)