Thinking Cap Questions

["Subbarao Kambhampati" <rao@asu.edu>]

Occasionally, I will send you "thinking cap" questions. These are broad questions (some very simple, some somewhat deep) for which, if you have an answer or opinion, you should post it on the blog (as a comment to the question).

Here go the first batch:


1. I mentioned that any two vectors, not just the orthogonal ones, can be used as coordinate axes to define a space. We know that if we have a vector
P= (4,7), its "coordinate" in Y direction is 7 and X direction is 4.  If our coordinate axes are not X and Y axes but rather two arbitrary vectors u and v (assume u and v are unit vectors), then what are the coordinates of P in this space? What is the restriction on u and v such that  we can always give coordinates to any point in the space this way?

2. How does stemming affect precision and recall?

3. I pointed out two of the problems with the canned relevance judgments used in TREC. That they represent just one user, and they typically represent "binary" judgements. Recalling the form of the R( ) function we dicussed in the class, can you think of other ways these judgements are not really enough to evaluate a ranked list of results?