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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.

It is:

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,

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It's all about pairs. Clusters themselves are not distinguishable.

So two objects x, y. If they are in the same cluster, they are a pair $(x,y)$. Otherwise they are not.

If this pair exists in both, TP. If it exists in neither, TN. But if one clustering says x and y are dimilar, and the other says they are dissimilar, then that is a disagreement.

it is actually the same as in classification. Except that not objects, bit pairs are used. There are two classes: Class A: object pair (x,y) is similar ("exists"). Class B: object pair (x,y) is dissimilar ("does not exist"). Now you compute the confusion matrix of predicting, whether two objects are similar (A), or not (B).

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  • $\begingroup$ So to be clear in terms of document clustering, a pair is two documents? If this is the case, then what I don't understand is why a pair of documents counts as TP. For example, if I have 2 categories that I know a-priori (a,b) and 6 documents. I cluster the documents using some algorithm, and it comes back with all 6 documents in one cluster. In this situation I would have 6 TP would I not? This is what seems incorrect to me, because intuitively I would have though half of these would be considered incorrect. Perhaps it is incorrect to be looking at TP independently in this instance. $\endgroup$ Commented Sep 24, 2015 at 21:29
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    $\begingroup$ Assuming that 3 are in category 1, 3 are in category 2, you have 3*2 "category pairs" each. Your clustering has 6*5=30 pairs. You have 100% recall (12TP), but 18 FP+FN, a pretty bad precision of 40%. $\endgroup$ Commented Sep 24, 2015 at 23:05
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    $\begingroup$ Never only look at TP. Indeed, putting everything into the same cluster means every pair exist, so 100% recall. That's why you do not use recall with clustering. Use ARI. $\endgroup$ Commented Sep 24, 2015 at 23:09

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