I am reading the paper, Classification in Networked Data: A Toolkit and a Univariate Case Study. And I have a question about the terminology of this paper, on page 938:
Also, see the following equation, on page 947:
Here we have,
- $\chi$ (not quite the same font with the paper)
I can understand that 1 is the vector of all class labels since it is big and bold. That makes totally sense.
And 2 is an item of (1) on the index $i$, if I understand correctly. However what is the difference between 2 and 3?
4 also makes sense. However, why do we have $c_1, c_2, ...$ etc. instead of basically having $\chi_1$, $\chi_2$, etc.
Is the second equation even correct? Instead of $P(x_i = c~|~N_i)$ don't we need big $X$ like $P(X_i = c~|~N_i)$?
Summary: Can you explain the difference between these 4 X's like explaining to a 10-year-old? (examples are strongly encouraged)