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'Best Paper Award' in WSDM'13 …
'Best Paper Award' in WSDM'13
The paper talks about a generized way to interleave two ranking list of retrieval task.
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e.g. rank*(d, A) = position of d in A, or |A|+1 if doesn’t exist
So for any pair <i,j>, with (i<j), pickup a pair in L as:
p = Li, q = Lj. it is supposed to see:
rank*(p, A) <= rank*(q, A) && rank*(p, B) <= rank*(q, B): no misorder in A,B
rank*(p, A) > rank*(q, A) && rank*(p, B) > rank*(q, B): not possible, that means (d1,d2) & (d1,d2) creates (d2,d1)
rank*(p, A) > rank*(q, A) && rank*(p, B) <= rank*(q, B): misorder, also misorder in A, B
rank*(p, A) <= rank*(q, A) && rank*(p, B) > rank*(q, B): misorder, also misorder in A, B
Insensitivity comes because weight of position is not taken into consideration when doing evaluation
Property 7 is guaranteed by property 4
Seems that the author enforce L != A and L != B, so that we get fewer unknown factor?
misorder(A,L_2) = {(d4, d3)}, misorder(B,L_2)={(d1,d2)}, misorder(A,B)={(d1,d2)}
So... misorder(A,L_2) + misorder(B,L_2) > misroder(A,B)???
Be careful: misorder(B, L_2) = {(d1, d2), (d5, d3)}, misorder(A,B) = {(d1, d2), (d3, d5), (d3, d4)}