I appreciate word2vec is used more to find the semantic similarities between words in a corpus, but here is my idea.
Train the word2vec model on a corpus
For each document in the corpus, find the Term Frequency (Tf) of each word (the same Tf in TfIDF)
Multiply the Tf of each word in a document by its corresponding word vector. Do this for each document
Sum the word vectors together element wise to get a single vector and return the $L2$ norm of this vector
Essentially, we are weighing and summing the word vectors for each word in a document.
Each document is now represented by an $N\times 1$ dimensional vector, where $N$ is the number of features chosen in word2vec (the dimensionality hyperparamter - and I have mine set quite low at 150).
Now that all documents create a sort of unit ball in the $N$ dimensional space, we can now find clusters of similar documents / the most similar documents given an input query document, using k-nearest neighbors or k-means.
My question is, is this method viable? I have tried doc2vec, TfIDF, LDA and used appropriate similarity metrics for each (with good results), but my documents are quite short (20-100 tokens) and word2vec has worked very well alone. So I want to know if I can apply the method above or is there anything blatantly wrong with what I am doing here? Any other tips + advice would also be much appreciated.