Schwab, Lafourcade, Prince, pres. by
Ch. Boitet
Antonymy and
Conceptual Vectors
The angular
distance
is a true distance
is a true distance
DA(x, y) = acos(sim(x,y))
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
by
definitionDA(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)