I am looking for advice on where to find information about this topic. I
have looked in several textbooks, web pages etc but cannot see anything
quite like what I have in mind. If anyone could point me in the right
direction, I'd be delighted!
The problem I am tring to solve is essentially "horses for courses". (Not
real horses, I might say!) I have a number of horses each of which
performs differently on a number of different courses.
I want a measure of how good the horses are. If the courses were all
equally distinct, I could just compute the arithmetic mean of each horse's
performance on each course. But the courses are not equally distinct: some
are very distinct, and some are very similar, to the extent perhaps of
being identical. So I would like to compute a weighted mean of each
horse's performance, with a suitable weight for each course, the weight
being a measure of how different that course is from the others.
For example, if there were 5 courses, but they were in clusters of two
virtually identical and three virtually identical courses, then the two
would each get a weight of about 25% and the three would each get a weight
of about 17%.
The problem is: what are the weights? The courses are points in a vector
space so I can define a Euclidean distance measure for them. I have an
idea of how to calculate the weights starting from a distance matrix but
there are theoretical issues - is there always a solution? - and I don't
want to reinvent a wheel.
My question is: has this already been done, and if so, what is it called?
--
Norman Paterson http://www.dcs.st-and.ac.uk/~norman/
Shake, oh shake, the ketchup bottle:
First none'll come, then a lot'll! - Ogden Nash
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