Unformatted text preview: s of the objects, but this won’t matter here.)
We will select our ranking r as a minimizer of the total preference violation penalty, deﬁned as
m φ ( v (k ) ) , J=
k=1 where v (k) is the preference violation of (i(k) , j (k) ) with r, and φ is a nondecreasing convex penalty
function that satisﬁes φ(u) = 0 for u ≤ 0.
(a) Make a (simple, please) suggestion for φ for each of the following two situations:
(i) We don’t mind some small violations, but we really want to avoid large violations.
(ii) We want as many preferences as possible to be consistent with the ranking, but will accept
some (hopefully, few) larger preference violations.
(b) Find the rankings obtained using the penalty functions proposed in part (a), on the data
set found in rank_aggr_data.m. Plot a histogram of preference violations for each case and
brieﬂy comment on the diﬀerences between them. Give the number of positive preference
violations for each case. (Use sum(v>0.001) to determine this number.) 149 Remark. The objects could be candidates for a position, papers at a conference, movies, we...
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- Fall '13
- The Aeneid