Discussion Notes

Feb 09, 2001

Unification of IR Models

• VSM:

  

  Models only direct similarities, does not bring disconnected portions together, since no modeling of term-term correlations is made.
  
  
• GVSM: From the SVD, we know that the U matrix models term-term correspondences and the V matrix models document-document correspondences. GVSM is just a way of using term-term correspondences explicitly, either by using the original matrix A, or by another user-supplied lexicon.
  
  
• LSI: Models indirect similarities, only brings disconnected portions together in one special, negligible case (a guaranteed "A" in the course for the first person who brings this pathological case to my attention *and* proves this property of LSI formally).
  
  
• VSM and GVSM not typically cast as matrix decompositions; Fang and Littman appear to have made this connection. Typically, we vary the left and right matrices of a decomposition and cast the diagonal matrix (middle) as dependent on the constraints (see, for example the SDD paper). In this paper, the authors freeze the left and right matrices and show how (the middle part) is to be varied (i.e., the weightage assigned to each dimension).
  
  
• The rank is not reduced by their manuevering of ADE: their metric appears to be precision and not really reducing dimensionality.
  
  
• Connections to cross-language IR:

  

  Normally the document space is not "doubled", since each document has a one-one correspondence to a counterpart in the other language. The terms are now doubled in number, to account for matchings in two different languages. To see why ADE (and hence, props of LSI) are really necessary: consider an English, German, and French collection, given by:

  

  Traditionally, since GVSM only makes one-step connections, the French documents will not be retrieved for English, and vice versa. ADE is expected to bring the French and English documents together. Procrustes is the name given to a greek agent who manuevers things into "fitting." In this application, the mappings to German (from English) and from German (to French) are being procrustesed (at the German end of the stick).