I have been reading up on some clustering evaluation techniques in this Stanford NLP textbook
On page 359, it defines each of TP, TN, FP & FN. I am having trouble understanding why the definition of TP holds.
A true positive (TP) decision assigns two similar documents to the same cluster
Initially this made sense to me until I got to the example. (with associated Figure 16.4 on page 357)
Of these, the x pairs in cluster 1, the o pairs in cluster 2, the ⋄ pairs in cluster 3, and the x pair in cluster 3 are true positives.
So, keeping both of these quotes in mind, any cluster with 2 documents from the same True Category are TP. I realise that the TP definition has to change from how it is used with classification, but this seems too lenient of an assumption for a TP, particularly as N gets large. I.e. How can the x values be TP in two different clusters?
Any help would be appreciated,