15.2.1 Vector similarity

• vector $B$NN`;wEY$r7W;;(B, cosine $B$rMQ$$$k$3$H$,B?$$(B
  
  $$\begin{eqnarray*}cos(\vec{q},\vec{d}) = \frac{\sum_{i=1}^n q_i d_i} {\sqrt{\sum_{i=i}^n q_i^2} \sqrt{\sum_{i=i}^n d_i^2}} \end{eqnarray*}$$
  
  
• vector $B$,(B normalize $B$5$l$F$$$l$P(B..
  • cosine $B$O(B dot-product ($BFb@Q(B)$B$@$1$G$9$`(B
  • document size $B$K$h$kIT8xJ?$r8:$i$9(B
• Euclidean distance
  vector $B$,(B normalize $B$5$l$F$l$P(B...
  
  $$\begin{eqnarray*}(\vert\vec{x}-\vec{y}\vert)^2 &=& \sum_{i=1}^n(x_i - y_i)^2 \\ ... ...& 1-2 \sum_{i=1}^n x_i y_i +1\\ &=& 2(1-\sum_{i=1}^n x_i y_i) \end{eqnarray*}$$
  
  $B$H$J$k$+$i(B, $B7k6I$N$H$3$m(B cosine $B$GHf$Y$F$k$N$H$$$C$7$g(B