Question: In the field of Data Mining, is there a specific sub-discipline called 'Similarity'? If yes, what does it deal with. Any examples, links, references will be helpful.

Also, being new to the field, I would like the community opinion on how closely related Data Mining and Artificial Intelligence are. Are they synonyms, is one the subset of the other?

Thanks in advance for sharing your knowledge.

Answer: 
Appropriate definitions of 'similarity' (which features you extract, what you do with them afterwards) are almost the definition of clustering, and clustering is a fairly wide sub-field of data mining.

If you make the standard cynical definition of AI as the set of problems we can't solve well (indeed, that we can't specify well enough to start solving), data mining shades into it once the space in which you're looking for correlations starts to be larger than your algorithms can handle.
Similarity is a concept that is used in several data mining tasks such as clustering, classification. Dependings on what kind of data you have, you may used different similarity measures such as cosine similarity for text documents, euclidian distance, etc