15.3.4 Inverse document frequency

• ad-hoc retrieval $B$G$h$/MQ$$$i$l$k(B IDF $B$@$,(B, 15.2.2 $B$G$O(B heuristically $B$K@bL@$7$?(B, $B$3$3$G$O(B term distribution model $B$K4p$E$$$F(B IDF $B$r8!>Z$9$k(B
• $B$"$k(B document d $B$,(B $BEz$($H$7$F(B relevant$B$G$"$k(B odds O(d)
  
  $$\begin{eqnarray*}O(d) = \frac{P(R\vert d)}{P(\bar{R}\vert d)} \end{eqnarray*}$$
  
  log $B$r$H$C$F(B baye's rule $BE83+(B
  
  $$\begin{eqnarray*}\log(O(d)) &=& \log \frac{P(R\vert d)}{P(\bar{R}\vert d)} \\ ... ...d\vert R) - \log P(d\vert\bar{R}) + \log P(R) - \log P(\bar{R}) \end{eqnarray*}$$
  
  $BC18l=89g(B w_i, $B$KBP$7(B X_i $B$H$$$&(B binary $B$NG[Ns$rMQ0U(B
  (if w_i $B$,(B d $B$KB8:_$9$k(B then X_i = 1, if w_i $B$,(B d $B$KB8:_$7$J$$(B then X_i = 0)
  
  $$\begin{eqnarray*}\log(O(d)) = \sum_i[\log P(X_i\vert R) - \log(X_i\vert\bar{R})] + \log P(R) - \log P(\bar{R}) \end{eqnarray*}$$
  
  $\log P(R) - \log P(\bar{R})$ $B$ODj?t9`$J$N$GL5;k(B,$Bg(d)$B$H$9$k(B
  $B3FC18l(B w_i $B$,(B relevant $B$+$I$&$+$r<($9G[Ns$rMQ0U(B
  
  $$\begin{eqnarray*}p_i = P(X_i=1\vert R) &\rightarrow & w_i $B$,(B relevant $B$J3NN((B \\ ... ... P(X_i=1\vert\bar{R}) &\rightarrow & w_i $B$,(B non\ relevant$B$J3NN((B \end{eqnarray*}$$
  
  
  
  $$\begin{eqnarray*}g(d) &=& \sum_i[\log P(X_i\vert R) - \log(X_i\vert\bar{R})] \\ ... ... X_i \log \frac{1-q_i}{q_i} + \sum_i \log \frac{1-p_i}{1-q_i} \end{eqnarray*}$$
  
  $\sum_i \log \frac{1-p_i}{1-q_i}$ $B$ODj?t9`$J$N$GL5;k(B, $Bg'(d) $B$H$*$/(B
  
  $$\begin{eqnarray*}g'(d) = \sum_i X_i \log \frac{p_i}{1-p_i} + \sum_i X_i \log \frac{1-q_i}{q_i} \end{eqnarray*}$$
  
  
• IR $B$G$O(B p_i,q_i $B$r?dDj$7$J$1$l$P$J$i$J$$(B
  ad-hoc retrieval $B$G$O(B, $B:G=i$K2?$N>pJs$bM?$($i$l$J$$$N$G(B p_i,q_i $B$rC1=c$J
• p_i $B$O>.$5$/(B,$BDj?t(B
  
  
  $$\begin{eqnarray*}\sum_i X_i \log \frac{p_i}{1-p_i} \simeq c \sum_i X_i \end{eqnarray*}$$
  
  
• q_i, $B$[$H$s$I$NC18l$,(B non-relevent $\rightarrow$ $B$=$NC18l$N=P8=3NN($G6a;w(B $q_i = P(w_i) = \frac{df_i}{N}$
  
  $$\begin{eqnarray*}\frac{1-q_i}{q_i} = \frac{1-\frac{df_i}{N}}{\frac{df_i}{N}} = ... ...-q_i}{q_i} \simeq \sum_i X_i \log(2^{idf_i}) = \sum_i X_i idf_i \end{eqnarray*}$$
  
  

$$\begin{eqnarray*}g'(d) = c \sum_i X_i + \sum_i X_i idf_i \end{eqnarray*}$$

relevance-feedback ($BJdB-(B)

• $B$3$N3NN(?dDj$N1$B2sL\$N8!:w$GF@$i$l$?(B list $B$N$&$A(B, user $B$K(B relavant $B$J$b$N(B $BE,Ev$KA*$P$;$k(B or $B5!3#E*$K>e0L(B $B2?8D$+$r $\rightarrow$ relevant $B=89g(B V $B$H$9$k(B,
  
  
  $$\begin{eqnarray*}p_i &=& \frac{V_i}{V} \\ q_i &=& \frac{df_i-V_i}{N-V}\\ \end{eqnarray*}$$
  
  V_i $\rightarrow$ $BC18l(B w_i $B$r4^$`(B V $BCf$N(B document $B?t(B
  
• $B$3$l$rE,Ev$J2s?t7+$jJV$9(B ($B