title: Clustering conceptually similar documents together?
body: <p>This is more of a conceptual question than an actual implementation and am hoping someone could clarify. My goal is the following: Given a set of documents, I want to cluster them such that documents belonging to the same cluster have the same "concept". </p>
  
  <p>From what I understand, <a href="http://en.wikipedia.org/wiki/Latent_semantic_analysis" rel="nofollow noreferrer">Latent Semantic Analysis</a> lets me find a low rank approximation of a term-document matrix i.e. given a matrix <strong>X</strong>, it will decompose <strong>X</strong> as a product of three matrices, out of which one would be a diagonal matrix <strong>Σ</strong>:</p>
  
  <p><img src="https://i.stack.imgur.com/Ejhy5.png" alt="SVD"></p>
  
  <p>Now, I would proceed by choosing a low rank approximation i.e. choose only the top-k values from <strong>Σ</strong>, and then calculate <strong>X'</strong>. Once I have this matrix, I have to apply some clustering algorithm and the end result would be set of clusters grouping documents with similar concepts. Is this the right way of applying clustering? I mean, calculating <strong>X'</strong> and then applying clustering on top of it or is there some other method that is followed?</p>
  
  <p>Also, in a somewhat <a href="https://stackoverflow.com/questions/5751114/nearest-neighbors-in-high-dimensional-data">related question</a> of mine, I was told that the meaning of a <em>neighbor</em> is lost as the number of dimensions increases. In that case, what is the justification for clustering these high dimensional data points from <strong>X'</strong>? I am guessing that the requirement to cluster similar documents is a real-world requirement in which case, how does one go about addressing this?</p>