As described here and here, $\chi^2$ feature selection can be used in order to filter a set of words that have a low dependency with a given class C.
In my case, I have a corpus of documents where each is assigned a sentiment (positive or negative). After pre-processing my text—stopwords, stemming and removing words that appear in less than 1% or in more than 50% of my documents—I define my positive class as any word contained in a document with positive sentiment and similarly for the negative one.
I then use the $\chi^2$ filtering approach with contingency tables. Below is an example of for word 'increase' and my positive class:
The problem I have is that my 2 classes are quite broad (hence the $\chi^2$ filtering!) and there's always a word from each class in any document. Which makes my $N_{01}$ and $N_{00}$ equal to 0 for all the words.
The denominator of my $\chi^2$ formula (below) is then systematically equal to 0 because of the 4th term.
$$ \chi^2(D, t, c) = \frac{N\left(N_{11}N_{00} - N_{10}N_{01}\right)^2} {(N_{11}+N_{01})(N_{11}+N_{10})(N_{10}+N_{00})(N_{01}+N_{00})}[4] $$
Is there something that I'm not doing well? If not, is there a trick or an alternative I could use to avoid this problem?
Many thanks!
