Given two points on the hypersphere, we can draw the
plane containing these points and the origin.
DF
r
DP
r
Procrustes
Distances is r.
DP = 2 sin ( r/2)
DF = sin r.
• These are
all monotonic in r. So the same choice of rotation minimizes all three.
• DF is easy to compute, others are
easy to compute from DF.