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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT 207 47 "Example From: Combating Web Spam with TrustRank"
 }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 47 "(For class presentation given
 by Rebecca Wills)" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 209 8 "Matrices" 
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0
 "> " 0 "" {MPLTEXT 1 0 20 "with(LinearAlgebra):" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 5 "n:=7:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 89 "H:=Matrix(n,n,0):H[1,2]:=1:H[2,3..4]:=1/2:H[3,2]:=1:H[4,5]:=1:H[
5,6..7]:=1/2:H[6,3]:=1:H;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
100 "U:=Matrix(n,n,0):U[2,1]:=1/2:U[2,3]:=1/2:U[3,2]:=1/2:U[3,6]:=1/2:
U[4,2]:=1:U[5,4]:=1:U[6..7,5]:=1:U;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "e:=Matrix(n,1,1):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{SECT 1 {PARA 3 "" 0 "" {TEXT 209 20 "Select Seed Function" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "s:=Transpose(e):" }}}{EXCHG {PARA 0
 "> " 0 "" {MPLTEXT 1 0 19 "alpha_seed:=85/100:" }}}{EXCHG {PARA 0 "> 
" 0 "" {MPLTEXT 1 0 11 "M_seed:=20:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "for i f
rom 1 to M_seed do\n" }{MPLTEXT 1 0 75 "  s:=alpha_seed*MatrixMatrixMu
ltiply(s,U)+(1-alpha_seed)/n * Transpose(e):\n" }{MPLTEXT 1 0 23 "  An
s[i]:=evalf[3](s):\n" }{MPLTEXT 1 0 7 "end do:" }}}{EXCHG {PARA 0 "> "
 0 "" {MPLTEXT 1 0 26 "for i from 1 to M_seed do\n" }{MPLTEXT 1 0 10 "
  Ans[i]:\n" }{MPLTEXT 1 0 7 "end do;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "evalf[3](s);" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 209 18 "TrustRank Function" 
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "v:=Matrix(1,n,0):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "s_sort:=sort([seq(s[1,i],i=1
..n)],`>`):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "oracle:=Matr
ix(1,n,[[1,1,1,1,0,0,0]]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
5 "L:=3:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "for i from 1 to
 n do\n" }{MPLTEXT 1 0 66 "   if (s[1,i] >= s_sort[L]) then v[1,i]:=or
acle[1,i] else end if;\n" }{MPLTEXT 1 0 7 "end do;" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 2 "v;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 22 "v:=v/Norm(v,infinity);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 100 
"Note: I'm not sure why they bother to start with a probability vector
 since they do not maintain it." }}{PARA 0 "" 0 "" {TEXT 200 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "alpha_trust:=85/100:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "M_trust:=20:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "t:=v:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "for i from 1 to M_trust do\n" }{MPLTEXT 1 0 62 "t:=al
pha_trust*MatrixMatrixMultiply(t,H)+(1-alpha_trust) * v:\n" }{MPLTEXT 
1 0 24 "  Ans2[i]:=evalf[3](t):\n" }{MPLTEXT 1 0 7 "end do:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "for i from 1 to M_trust do\n
" }{MPLTEXT 1 0 11 "  Ans2[i]:\n" }{MPLTEXT 1 0 7 "end do;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Ans2[M_trust];" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 29 "evalf[2](t/Norm(t,infinity));" }}}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 
209 14 "PageRank check" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "S:
=H:S[n,1..n]:=v[1,1..n]:S;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
14 "alpha:=85/100:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "G:=al
pha*S + (1-alpha)*MatrixMatrixMultiply(e,v);" }}}{EXCHG {PARA 0 "> " 0
 "" {MPLTEXT 1 0 36 "(e1,v1):=Eigenvectors(Transpose(G)):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "for i from 1 to n do\n" }{MPLTEXT 
1 0 40 "  if (e1[i]=1) then loc:=i else end if;\n" }{MPLTEXT 1 0 7 "en
d do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "evalf[2](Transpose
(e1));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "evalf[2](Transpos
e((v1[1..7,loc]/Norm(v1[1..7,loc],1))));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 5 "x:=v:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "fo
r i from 1 to M_trust do\n" }{MPLTEXT 1 0 30 "x:=MatrixMatrixMultiply(
x,G):\n" }{MPLTEXT 1 0 24 "  Ans3[i]:=evalf[3](x):\n" }{MPLTEXT 1 0 7 
"end do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalf[2](x);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "evalf[2](t/Norm(t,infinity
));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 209 63 "P
ageRank with the uniform vector for the Personalization vector" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "G2:=alpha*S + (1-alpha)*Matr
ixMatrixMultiply(e,1/n*Transpose(e));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 37 "(e2,v2):=Eigenvectors(Transpose(G2)):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "for i from 1 to n do\n" }{MPLTEXT 
1 0 41 "  if (e2[i]=1) then loc2:=i else end if;\n" }{MPLTEXT 1 0 7 "e
nd do:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
24 "evalf[2](Transpose(e2));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 59 "evalf[2](Transpose((v2[1..7,loc2]/Norm(v2[1..7,loc2],1))));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "PR:=convert(Transpose((v2[1.
.7,loc2]/Norm(v2[1..7,loc2],1))),Matrix);" }}}{EXCHG {PARA 0 "> " 0 ""
 {MPLTEXT 1 0 28 "MatrixMatrixMultiply(PR,G2);" }}}{EXCHG {PARA 0 "> "
 0 "" {MPLTEXT 1 0 13 "evalf[3](PR);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "rank_PR:=[7,1,2,3,4,5,5];" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 29 "evalf[2](t/Norm(t,infinity));" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 24 "rank_t:=[6,1,4,2,3,5,5];" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 206 "" 0 "" {TEXT 208 8 "Co
mment:" }{TEXT 200 104 " I think the authors could have chosen a bette
r example.  TrustRank ranks vertex 5 higher than vertex 3." }}}}{PARA 
0 "" 0 "" {TEXT 200 0 "" }}}
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