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I came across the word subjective interestingness measures in my book, where author says that:

Subjective interestingness measures are based on user belief in the data. These measures find patterns interesting if they are unexpected (contradicting user's belief) or offer strategic information on which user can act.

(Data Mining and Concepts and Techniques, by Jiawei Han and Micheline Kamber)

I very much confused how can "unexpected" data be an interesting pattern? Am I understanding the concept wrongly? Could you provide me with an illustration?

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Consider, a classic example of the following rule:

IF (patient is pregnant) THEN (patient is female).

This rule is very accurate and comprehensible, but it is not interesting, since it represents the obvious. Another Example from real world data set,

IF (used_seat_belt = ‘yes’) THEN (injury = ‘no’).......................................................(1)

IF ((used_seat_belt = ‘yes’) Λ (passenger = child)) THEN (injury = ‘yes’)...............(2)

Rule (1) is a general and an obvious rule. But rule (2) contradicts the knowledge represented by rule (1) and so the user's belief. This kind of knowledge is unexpected from users preset beliefs and it is always interesting to extract this interesting (or surprising) knowledge from data sets. “Unexpectedness” means knowledge which is unexpected from the beliefs of users i.e. A decision rule is considered to be interesting (or surprising) if it represents knowledge that was not only previously unknown to the users but also contradicts the original beliefs of the users.

I hope, these examples may help you to understand the concept more clearly.

Edit
Yes, firstly, discover the general rules and then discover exceptions to these general rules. For example,

A general rule : If bird then fly

However, there are few exceptional birds like emu and penguin that do not fly. It would definitely be valuable to discover such exceptions along with the rule, making the rule more accurate, comprehensible as well as interesting.

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    $\begingroup$ (+1) As my professor put it: The first step of data mining is to detect the relationships the client already knows, proving that your methods are working. The second step is to detect relationships the client did not know yet, demonstrating the real value of data mining. $\endgroup$
    – steffen
    Aug 14, 2012 at 8:01

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