In today's post we look at some of the details on graph based word similarity measures. While we looked at word similarity measure in the Saluja, Navratil 2012 paper, I'm going to focus on normalization of words. We mentioned the holing system in Bieman and Riedl. This holing system is only part of their system but they describe a way to capture distributional and contextual similarity.  The idea here is to represent observations as <t,c> pair where t is the term (at a certain offset) and c is the context feature. The position of t in c is denoted by the @ hole symbol. The authors give an example where dependency (nsub;gave2;I1) could be transferred to <gave2, (nsub; @; I1) > Notice how the holing operator is used to give the position of the term. and this in turn could be represented by <I1, (nsub; gave2;@)>. Note the change in the context with the terms and the use of the holing operator. In the second dependency representation, the @ symbol has been introduced to give the position of gave2 and in the third representation the @ symbol gives the position of I1. The last two dependency representations are in the <t,c> pairs.
This paper also uses a term-context feature bipartite graph just like the last paper we saw. In addition it calculates a significance score sig for each pair <t,c> using the counts of the terms, the counts of the context features and the counts of their co-occurrence. If the significance score is negative, the corresponding edge is not added. Also features that have more than a thousand words is removed because they are overly general. This way the distributional similarity is calculated but the contextual similarity is calculated instead from the second order graph.
This way the authors showed that with the sentence "I caught a nasty cold" the holing system produced <cold5, (amod,@, nasty4)>, and <cold5, (dobj;caught2; @)> and the scores were <heat, (dobj; caught; @)> with an LMI score of 42.0 and <weather, (amod; @; nasty)> with a score of 139.4. The word disease came highest in rank for the above sentence.

we will continue on this discussion.