The design idea of vertical search engine sort algorithm under supervision

This article is written a long time ago, just turned over the hard drive, and now put it out. This is just a formal idea, temporarily no time to implement, I have simply verified the formal process, the temporary has not found a problem, but do not guarantee that the process is not a problem. If you find a problem, please correct me, thank you!

In the field of vertical search, there is no standard for judging the result of ranking, so the role of supervisor is introduced, and the algorithm is designed so as to close the order result of the search engine.

1 experts were introduced as supervisors S. s select Keyword K. Input k, retrieve m strip result, then randomly select n result in M bar result, get sequence s_r={r₀, R₁,......, r_n-1}.

s according to experience, the n results are sorted. The sequence s={......,s_i,j,......}, wherein the pin I of S_i,j represents the position of S_i,j in the source sequence s_R , and J represents the sequence s_i,j the position in S_s . such as S_4,2 represents this task in the source sequence corresponding to R₄, in the new sequence s in the 3rd (the foot mark is 2, but because the element foot is starting from 0, so row 3rd position.) ）。

Defines the position of the function Φ_s(R_J) as R _J in the sequence s. Assuming the sequences ={s_5,0, S_2,1,......, s_74,312}, there is Φ_S(R₅) = 0; Φ_S(R₂) = 1; Φ_S (R) = 312;

So that x is a sort algorithm, x pairs sequence s_R sort Get sequence s_x. Φ_x (R_J) is the position of R_J in the sequence s_x .

The order (r_m, R_N) is a combined sequence of different elements in S_r . These sequences make up the collection:

C = {(R_m, R_n) | m≠n, R_m∈s_R, r_N∈s_r }.

make Ω_x(R_M, R_n) =-sign (Φ_x(R_m)-φ_x(r_N)).

which

Ω_x(R_M, R_N) >0 means that the sort algorithm X ranks R_M in front of R_N .

Make e_x,s,r A set of sequences in C that are inconsistent with the results of the X sort and the S order:

E_X,s,r= {(R_m, R_N) | (R_M, R_N) ∈c,ω_X(r_M, R_N) ≠ω_S(r_m, R N) )}.

The order λ_(RM,RN) is a cost function inconsistent with the results of the order x and the order of S, using the following cost function:

λ_(rm,rn)=|m-n|

Make the total cost Λ (_{E x,s,r})_{=σλ (RM,RN)}, (R_M, R_N) ∈e_x,s,r