¥Distance
= acos(similarity)
¥ DA(x, y) = acos(x.y/|x||y|))
¥
¥DA(x, x)
= 0
¥DA(x, y)
= DA(y,
x)
¥DA(x, y)
+ DA(y, z) ³ DA(x,
z)
¥DA(0, 0) = 0 and DA(x, 0) = p/2 by definition
¥
¥DA(ax, by) = DA(x, y) with ab > 0
¥DA(ax, by) = p - DA(x, y)
with ab < 0
¥DA(x+x,
x+y) = DA(x,
x+y) £ DA(x, y)