Determination of System Dimensionality from Observing Near-Normal Distributions

Figure 4

Two-dimensional plot of data points in a 2-dimensional sphere (a) and ellipse model (b). The distribution is of uniform type when observing all dimensions but becomes skewed when observing fewer (one) dimensions. The histogram of sphere (c) and ellipse (d) data points shows greater data point count at the center, that is, where the value of dimension is 0, as compared to the extremities. Histogram bins maintain the same relative ratio for both sphere and ellipse.

(a)

(b)

(c)

(d)