title: How does Principle Component Initialization work for determining the weights of the map vectors in Self Organizing Maps?
body: <p>I studied on a fundamental SOM initialization and was looking to understand exactly how this process, PCI,  works for initializing weight vectors on the map.  My understanding is that for a two dimensional Map, this initialization method looks at the eigenvectors for the two largest eigenvalues of the data matrix and then uses the subspace spanned by these eigenvectors to initialize the map.  Does that mean that in order to get the initial map weights, does this method take random linear combinations of the largest two eigenvectors in order to generate the map weights?  Is there a patten? </p>
  
  <p>For example, for 40 input data vectors on the map, does the lininit initialization method take combinations a1*[e1] + a2*[e2] where [e1] and [e2] are the two largest eigenvectors and a1 and a2 are random integers ranging from -3 to 3?  Or is there a different mechanism?  I was looking to make sure I knew exactly how lininit takes the two largest eigenvectors of the input data matrix and uses them to construct the initial weight vectors for the map.</p>