# Can I apply word2vec to find document similarity?

I appreciate word2vec is used more to find the semantic similarities between words in a corpus, but here is my idea.

1. Train the word2vec model on a corpus

2. For each document in the corpus, find the Term Frequency (Tf) of each word (the same Tf in TfIDF)

3. Multiply the Tf of each word in a document by its corresponding word vector. Do this for each document

4. 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.

I also made plots of truncated SVD/PCA of the encoded documents - it seems like aggregated embeddings just make everything close to everything. To illustrate this I tried to find closest words for document encodings in Word embeddings space - it seems like they just lie close to common words (see Closest $10$ words to mean-aggregated texts).