title: Where do dimensions in Word2Vec come from?
body: <p>I am using word2vec model for training a neural network and building a neural embedding for finding the similar words on the vector space. But my question is about dimensions in the word and context embeddings (matrices), which we initialise them by random numbers(vectors) at the beginning of the training, like this <a href="https://iksinc.wordpress.com/2015/04/13/words-as-vectors/" rel="nofollow">https://iksinc.wordpress.com/2015/04/13/words-as-vectors/</a></p>
  
  <p>Lets say we want to display {book,paper,notebook,novel} words on a graph, first of all we should build a matrix with this dimensions 4x2 or 4x3 or 4x4 etc, I know the first dimension of the matrix its the size of our vocabulary |v|. But the second dimension of the matrix (number of vector's dimensions), for example this is a vector for word “book"  [0.3,0.01,0.04], what are these numbers? do they have any meaning? for example the 0.3 number related to the relation between word “book" and “paper” in the vocabulary, the 0.01 is the relation between book and notebook, etc.
  Just like TF-IDF, or Co-Occurence matrices that each dimension (column) Y has a meaning - its a word or document related to the word in row X.</p>