Determination of System Dimensionality from Observing Near-Normal Distributions

Figure 5

Distribution curves for one vector component () in spherical (a) and elliptical (b) models. (a) Seven spherical models of different dimensionality, ranging from 1-ball to 7-ball, with radius . As the dimensionality of the model increases, the original uniform distribution of vectors is seen more like the normal distribution for its vector components. (b) Seven ellipsoidal models ranging from 1-ellipse to 7-ellipse. Here radii of the ellipse are = 25, = 50, = 12.5, = 75, = 8.33, = 100, = 6.25, = 125, = 5, = 150, and = 4.16.

(a)

(b)