Help to solve this Equation

[louise1120]

Hi,

Can anyone please help me solve this equation? I managed to understand the top bit, but can't dictate the bottom part. Let's say that I want to see how many times do users, specifically students which are from an online group write the word cool. I will have to use the following equation to calculate the prototypical score of a word w (example: cool) for the class ci (example: students):

According to the equation |w, Si| is the number of times the word w is “used” by all users (Si) for class ci. Now I am struggling with the bottom part of the equation. Is this the sum (total) of all words “used” by all users for class ci? Thank you in advance.

 

[lex]

It would appear that for [imath]|w,S_i|[/imath] we take each individual of the class [imath]c_i[/imath], record the number of times the individual uses the word w, and find the total of these values over all individuals in the class [imath]c_i[/imath].
So for [imath]\dfrac{|w,S_i|}{\sum \limits_{j=1}^{n} |w,S_j|}[/imath] the bottom line does the same, not just for the individuals of class [imath]c_i[/imath], but for individuals from all the classes [imath]c_j, j=1...n[/imath]
In other words [imath]proto(w,c_i)[/imath] is the fraction of the total number of uses of the word w (contributed by any individual in any of the classes), which are contributed by members of the class [imath]c_i[/imath].