title: Multi-way spectral clustering
body: <p>I am now looking into the multi-way spectral clustering problem. As introduced by <a href="http://www.kyb.mpg.de/fileadmin/user_upload/files/publications/attachments/Luxburg07_tutorial_4488%5b0%5d.pdf" rel="nofollow noreferrer">"A Tutorial on Spectral Clustering"</a>, the multi-way spectral clustering can be written as the following objective (see section 5.2)</p>
  
  <pre><code>min Tr(H'LH) s.t. H'H=I 
  </code></pre>
  
  <p>where L is the laplacian matrix and H is the new representation of data. However, the author simply say this is a standard form of trace minimization problem. I can't figure out the derivation for this problem (I can only do two way, i.e. H is a vector h). Anybody knows how to rigorously solve this problem?</p>